diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c
index 907172433..a8f4e9e12 100644
--- a/src/secp256k1/src/bench_internal.c
+++ b/src/secp256k1/src/bench_internal.c
@@ -1,369 +1,369 @@
 /**********************************************************************
  * Copyright (c) 2014-2015 Pieter Wuille                              *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 #include <stdio.h>
 
 #include "include/secp256k1.h"
 
 #include "util.h"
 #include "hash_impl.h"
 #include "num_impl.h"
 #include "field_impl.h"
 #include "group_impl.h"
 #include "scalar_impl.h"
 #include "ecmult_const_impl.h"
 #include "ecmult_impl.h"
 #include "bench.h"
 #include "secp256k1.c"
 
 typedef struct {
     secp256k1_scalar scalar_x, scalar_y;
     secp256k1_fe fe_x, fe_y;
     secp256k1_ge ge_x, ge_y;
     secp256k1_gej gej_x, gej_y;
     unsigned char data[64];
     int wnaf[256];
 } bench_inv;
 
 void bench_setup(void* arg) {
     bench_inv *data = (bench_inv*)arg;
 
     static const unsigned char init_x[32] = {
         0x02, 0x03, 0x05, 0x07, 0x0b, 0x0d, 0x11, 0x13,
         0x17, 0x1d, 0x1f, 0x25, 0x29, 0x2b, 0x2f, 0x35,
         0x3b, 0x3d, 0x43, 0x47, 0x49, 0x4f, 0x53, 0x59,
         0x61, 0x65, 0x67, 0x6b, 0x6d, 0x71, 0x7f, 0x83
     };
 
     static const unsigned char init_y[32] = {
         0x82, 0x83, 0x85, 0x87, 0x8b, 0x8d, 0x81, 0x83,
         0x97, 0xad, 0xaf, 0xb5, 0xb9, 0xbb, 0xbf, 0xc5,
         0xdb, 0xdd, 0xe3, 0xe7, 0xe9, 0xef, 0xf3, 0xf9,
         0x11, 0x15, 0x17, 0x1b, 0x1d, 0xb1, 0xbf, 0xd3
     };
 
     secp256k1_scalar_set_b32(&data->scalar_x, init_x, NULL);
     secp256k1_scalar_set_b32(&data->scalar_y, init_y, NULL);
     secp256k1_fe_set_b32(&data->fe_x, init_x);
     secp256k1_fe_set_b32(&data->fe_y, init_y);
     CHECK(secp256k1_ge_set_xo_var(&data->ge_x, &data->fe_x, 0));
     CHECK(secp256k1_ge_set_xo_var(&data->ge_y, &data->fe_y, 1));
     secp256k1_gej_set_ge(&data->gej_x, &data->ge_x);
     secp256k1_gej_set_ge(&data->gej_y, &data->ge_y);
     memcpy(data->data, init_x, 32);
     memcpy(data->data + 32, init_y, 32);
 }
 
 void bench_scalar_add(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 2000000; i++) {
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 
 void bench_scalar_negate(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 2000000; i++) {
         secp256k1_scalar_negate(&data->scalar_x, &data->scalar_x);
     }
 }
 
 void bench_scalar_sqr(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_scalar_sqr(&data->scalar_x, &data->scalar_x);
     }
 }
 
 void bench_scalar_mul(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_scalar_mul(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 
 #ifdef USE_ENDOMORPHISM
 void bench_scalar_split(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_scalar l, r;
         secp256k1_scalar_split_lambda(&l, &r, &data->scalar_x);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 #endif
 
 void bench_scalar_inverse(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 2000; i++) {
         secp256k1_scalar_inverse(&data->scalar_x, &data->scalar_x);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 
 void bench_scalar_inverse_var(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 2000; i++) {
         secp256k1_scalar_inverse_var(&data->scalar_x, &data->scalar_x);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 
 void bench_field_normalize(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 2000000; i++) {
         secp256k1_fe_normalize(&data->fe_x);
     }
 }
 
 void bench_field_normalize_weak(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 2000000; i++) {
         secp256k1_fe_normalize_weak(&data->fe_x);
     }
 }
 
 void bench_field_mul(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_fe_mul(&data->fe_x, &data->fe_x, &data->fe_y);
     }
 }
 
 void bench_field_sqr(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_fe_sqr(&data->fe_x, &data->fe_x);
     }
 }
 
 void bench_field_inverse(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_fe_inv(&data->fe_x, &data->fe_x);
         secp256k1_fe_add(&data->fe_x, &data->fe_y);
     }
 }
 
 void bench_field_inverse_var(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_fe_inv_var(&data->fe_x, &data->fe_x);
         secp256k1_fe_add(&data->fe_x, &data->fe_y);
     }
 }
 
 void bench_field_sqrt(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_fe t;
 
     for (i = 0; i < 20000; i++) {
         t = data->fe_x;
         secp256k1_fe_sqrt(&data->fe_x, &t);
         secp256k1_fe_add(&data->fe_x, &data->fe_y);
     }
 }
 
 void bench_group_double_var(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_gej_double_var(&data->gej_x, &data->gej_x, NULL);
     }
 }
 
 void bench_group_add_var(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y, NULL);
     }
 }
 
 void bench_group_add_affine(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_gej_add_ge(&data->gej_x, &data->gej_x, &data->ge_y);
     }
 }
 
 void bench_group_add_affine_var(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 200000; i++) {
         secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y, NULL);
     }
 }
 
 void bench_group_jacobi_var(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_gej_has_quad_y_var(&data->gej_x);
     }
 }
 
 void bench_ecmult_wnaf(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar_x, WINDOW_A);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 
 void bench_wnaf_const(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_wnaf_const(data->wnaf, data->scalar_x, WINDOW_A, 256);
+        secp256k1_wnaf_const(data->wnaf, &data->scalar_x, WINDOW_A, 256);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
 
 
 void bench_sha256(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_sha256 sha;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_sha256_initialize(&sha);
         secp256k1_sha256_write(&sha, data->data, 32);
         secp256k1_sha256_finalize(&sha, data->data);
     }
 }
 
 void bench_hmac_sha256(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_hmac_sha256 hmac;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_hmac_sha256_initialize(&hmac, data->data, 32);
         secp256k1_hmac_sha256_write(&hmac, data->data, 32);
         secp256k1_hmac_sha256_finalize(&hmac, data->data);
     }
 }
 
 void bench_rfc6979_hmac_sha256(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_rfc6979_hmac_sha256 rng;
 
     for (i = 0; i < 20000; i++) {
         secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64);
         secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
     }
 }
 
 void bench_context_verify(void* arg) {
     int i;
     (void)arg;
     for (i = 0; i < 20; i++) {
         secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY));
     }
 }
 
 void bench_context_sign(void* arg) {
     int i;
     (void)arg;
     for (i = 0; i < 200; i++) {
         secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN));
     }
 }
 
 #ifndef USE_NUM_NONE
 void bench_num_jacobi(void* arg) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_num nx, norder;
 
     secp256k1_scalar_get_num(&nx, &data->scalar_x);
     secp256k1_scalar_order_get_num(&norder);
     secp256k1_scalar_get_num(&norder, &data->scalar_y);
 
     for (i = 0; i < 200000; i++) {
         secp256k1_num_jacobi(&nx, &norder);
     }
 }
 #endif
 
 int main(int argc, char **argv) {
     bench_inv data;
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, 2000000);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, 2000000);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, 200000);
 #ifdef USE_ENDOMORPHISM
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, 20000);
 #endif
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, 2000);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, 2000);
 
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, 2000000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, 2000000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "jacobi")) run_benchmark("group_jacobi_var", bench_group_jacobi_var, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 20);
     if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 200);
 
 #ifndef USE_NUM_NONE
     if (have_flag(argc, argv, "num") || have_flag(argc, argv, "jacobi")) run_benchmark("num_jacobi", bench_num_jacobi, bench_setup, NULL, &data, 10, 200000);
 #endif
     return 0;
 }
diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h
index 8411752eb..b599316b8 100644
--- a/src/secp256k1/src/ecmult_const_impl.h
+++ b/src/secp256k1/src/ecmult_const_impl.h
@@ -1,257 +1,257 @@
 /**********************************************************************
  * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
 #ifndef SECP256K1_ECMULT_CONST_IMPL_H
 #define SECP256K1_ECMULT_CONST_IMPL_H
 
 #include "scalar.h"
 #include "group.h"
 #include "ecmult_const.h"
 #include "ecmult_impl.h"
 
 /* This is like `ECMULT_TABLE_GET_GE` but is constant time */
 #define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
     int m; \
     int abs_n = (n) * (((n) > 0) * 2 - 1); \
     int idx_n = abs_n / 2; \
     secp256k1_fe neg_y; \
     VERIFY_CHECK(((n) & 1) == 1); \
     VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
     VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
     VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
     VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
     for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
         /* This loop is used to avoid secret data in array indices. See
          * the comment in ecmult_gen_impl.h for rationale. */ \
         secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
         secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
     } \
     (r)->infinity = 0; \
     secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
     secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
 } while(0)
 
 
 /** Convert a number to WNAF notation.
  *  The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
  *  It has the following guarantees:
  *  - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
  *  - each wnaf[i] is nonzero
  *  - the number of words set is always WNAF_SIZE(w) + 1
  *
  *  Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
  *  Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
  *  CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
  *
  *  Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
  */
-static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) {
+static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) {
     int global_sign;
     int skew = 0;
     int word = 0;
 
     /* 1 2 3 */
     int u_last;
     int u;
 
     int flip;
     int bit;
-    secp256k1_scalar neg_s;
+    secp256k1_scalar s;
     int not_neg_one;
     /* Note that we cannot handle even numbers by negating them to be odd, as is
      * done in other implementations, since if our scalars were specified to have
      * width < 256 for performance reasons, their negations would have width 256
      * and we'd lose any performance benefit. Instead, we use a technique from
      * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
      * or 2 (for odd) to the number we are encoding, returning a skew value indicating
      * this, and having the caller compensate after doing the multiplication.
      *
      * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
      * particular, to ensure that the outputs from the endomorphism-split fit into
      * 128 bits). If we negate, the parity of our number flips, inverting which of
      * {1, 2} we want to add to the scalar when ensuring that it's odd. Further
      * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and
      * we need to special-case it in this logic. */
-    flip = secp256k1_scalar_is_high(&s);
+    flip = secp256k1_scalar_is_high(scalar);
     /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
-    bit = flip ^ !secp256k1_scalar_is_even(&s);
+    bit = flip ^ !secp256k1_scalar_is_even(scalar);
     /* We check for negative one, since adding 2 to it will cause an overflow */
-    secp256k1_scalar_negate(&neg_s, &s);
-    not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+    secp256k1_scalar_negate(&s, scalar);
+    not_neg_one = !secp256k1_scalar_is_one(&s);
+    s = *scalar;
     secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
     /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
      * that we added two to it and flipped it. In fact for -1 these operations are
      * identical. We only flipped, but since skewing is required (in the sense that
      * the skew must be 1 or 2, never zero) and flipping is not, we need to change
      * our flags to claim that we only skewed. */
     global_sign = secp256k1_scalar_cond_negate(&s, flip);
     global_sign *= not_neg_one * 2 - 1;
     skew = 1 << bit;
 
     /* 4 */
     u_last = secp256k1_scalar_shr_int(&s, w);
     while (word * w < size) {
         int sign;
         int even;
 
         /* 4.1 4.4 */
         u = secp256k1_scalar_shr_int(&s, w);
         /* 4.2 */
         even = ((u & 1) == 0);
         sign = 2 * (u_last > 0) - 1;
         u += sign * even;
         u_last -= sign * even * (1 << w);
 
         /* 4.3, adapted for global sign change */
         wnaf[word++] = u_last * global_sign;
 
         u_last = u;
     }
     wnaf[word] = u * global_sign;
 
     VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
     VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
     return skew;
 }
 
 static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {
     secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
     secp256k1_ge tmpa;
     secp256k1_fe Z;
 
     int skew_1;
 #ifdef USE_ENDOMORPHISM
     secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
     int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
     int skew_lam;
     secp256k1_scalar q_1, q_lam;
 #endif
     int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
 
     int i;
-    secp256k1_scalar sc = *scalar;
 
     /* build wnaf representation for q. */
     int rsize = size;
 #ifdef USE_ENDOMORPHISM
     if (size > 128) {
         rsize = 128;
         /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
-        secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
-        skew_1   = secp256k1_wnaf_const(wnaf_1,   q_1,   WINDOW_A - 1, 128);
-        skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1, 128);
+        secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar);
+        skew_1   = secp256k1_wnaf_const(wnaf_1,   &q_1,   WINDOW_A - 1, 128);
+        skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
     } else
 #endif
     {
-        skew_1   = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size);
+        skew_1   = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size);
 #ifdef USE_ENDOMORPHISM
         skew_lam = 0;
 #endif
     }
 
     /* Calculate odd multiples of a.
      * All multiples are brought to the same Z 'denominator', which is stored
      * in Z. Due to secp256k1' isomorphism we can do all operations pretending
      * that the Z coordinate was 1, use affine addition formulae, and correct
      * the Z coordinate of the result once at the end.
      */
     secp256k1_gej_set_ge(r, a);
     secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
     for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
         secp256k1_fe_normalize_weak(&pre_a[i].y);
     }
 #ifdef USE_ENDOMORPHISM
     if (size > 128) {
         for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
             secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
         }
     }
 #endif
 
     /* first loop iteration (separated out so we can directly set r, rather
      * than having it start at infinity, get doubled several times, then have
      * its new value added to it) */
     i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
     VERIFY_CHECK(i != 0);
     ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
     secp256k1_gej_set_ge(r, &tmpa);
 #ifdef USE_ENDOMORPHISM
     if (size > 128) {
         i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
         VERIFY_CHECK(i != 0);
         ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
         secp256k1_gej_add_ge(r, r, &tmpa);
     }
 #endif
     /* remaining loop iterations */
     for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
         int n;
         int j;
         for (j = 0; j < WINDOW_A - 1; ++j) {
             secp256k1_gej_double_nonzero(r, r, NULL);
         }
 
         n = wnaf_1[i];
         ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
         VERIFY_CHECK(n != 0);
         secp256k1_gej_add_ge(r, r, &tmpa);
 #ifdef USE_ENDOMORPHISM
         if (size > 128) {
             n = wnaf_lam[i];
             ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
             VERIFY_CHECK(n != 0);
             secp256k1_gej_add_ge(r, r, &tmpa);
         }
 #endif
     }
 
     secp256k1_fe_mul(&r->z, &r->z, &Z);
 
     {
         /* Correct for wNAF skew */
         secp256k1_ge correction = *a;
         secp256k1_ge_storage correction_1_stor;
 #ifdef USE_ENDOMORPHISM
         secp256k1_ge_storage correction_lam_stor;
 #endif
         secp256k1_ge_storage a2_stor;
         secp256k1_gej tmpj;
         secp256k1_gej_set_ge(&tmpj, &correction);
         secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
         secp256k1_ge_set_gej(&correction, &tmpj);
         secp256k1_ge_to_storage(&correction_1_stor, a);
 #ifdef USE_ENDOMORPHISM
         if (size > 128) {
             secp256k1_ge_to_storage(&correction_lam_stor, a);
         }
 #endif
         secp256k1_ge_to_storage(&a2_stor, &correction);
 
         /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
         secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
 #ifdef USE_ENDOMORPHISM
         if (size > 128) {
             secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
         }
 #endif
 
         /* Apply the correction */
         secp256k1_ge_from_storage(&correction, &correction_1_stor);
         secp256k1_ge_neg(&correction, &correction);
         secp256k1_gej_add_ge(r, r, &correction);
 
 #ifdef USE_ENDOMORPHISM
         if (size > 128) {
             secp256k1_ge_from_storage(&correction, &correction_lam_stor);
             secp256k1_ge_neg(&correction, &correction);
             secp256k1_ge_mul_lambda(&correction, &correction);
             secp256k1_gej_add_ge(r, r, &correction);
         }
 #endif
     }
 }
 
 #endif /* SECP256K1_ECMULT_CONST_IMPL_H */
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index 78f1531fe..9c866d86b 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -1,5166 +1,5166 @@
 /**********************************************************************
  * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
 #if defined HAVE_CONFIG_H
 #include "libsecp256k1-config.h"
 #endif
 
 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>
 
 #include <time.h>
 
 #include "secp256k1.c"
 #include "include/secp256k1.h"
 #include "testrand_impl.h"
 
 #ifdef ENABLE_OPENSSL_TESTS
 #include "openssl/bn.h"
 #include "openssl/ec.h"
 #include "openssl/ecdsa.h"
 #include "openssl/obj_mac.h"
 # if OPENSSL_VERSION_NUMBER < 0x10100000L
 void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;}
 # endif
 #endif
 
 #include "contrib/lax_der_parsing.c"
 #include "contrib/lax_der_privatekey_parsing.c"
 
 #if !defined(VG_CHECK)
 # if defined(VALGRIND)
 #  include <valgrind/memcheck.h>
 #  define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
 #  define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
 # else
 #  define VG_UNDEF(x,y)
 #  define VG_CHECK(x,y)
 # endif
 #endif
 
 static int count = 64;
 static secp256k1_context *ctx = NULL;
 
 static void counting_illegal_callback_fn(const char* str, void* data) {
     /* Dummy callback function that just counts. */
     int32_t *p;
     (void)str;
     p = data;
     (*p)++;
 }
 
 static void uncounting_illegal_callback_fn(const char* str, void* data) {
     /* Dummy callback function that just counts (backwards). */
     int32_t *p;
     (void)str;
     p = data;
     (*p)--;
 }
 
 void random_field_element_test(secp256k1_fe *fe) {
     do {
         unsigned char b32[32];
         secp256k1_rand256_test(b32);
         if (secp256k1_fe_set_b32(fe, b32)) {
             break;
         }
     } while(1);
 }
 
 void random_field_element_magnitude(secp256k1_fe *fe) {
     secp256k1_fe zero;
     int n = secp256k1_rand_int(9);
     secp256k1_fe_normalize(fe);
     if (n == 0) {
         return;
     }
     secp256k1_fe_clear(&zero);
     secp256k1_fe_negate(&zero, &zero, 0);
     secp256k1_fe_mul_int(&zero, n - 1);
     secp256k1_fe_add(fe, &zero);
     VERIFY_CHECK(fe->magnitude == n);
 }
 
 void random_group_element_test(secp256k1_ge *ge) {
     secp256k1_fe fe;
     do {
         random_field_element_test(&fe);
         if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
             secp256k1_fe_normalize(&ge->y);
             break;
         }
     } while(1);
 }
 
 void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
     secp256k1_fe z2, z3;
     do {
         random_field_element_test(&gej->z);
         if (!secp256k1_fe_is_zero(&gej->z)) {
             break;
         }
     } while(1);
     secp256k1_fe_sqr(&z2, &gej->z);
     secp256k1_fe_mul(&z3, &z2, &gej->z);
     secp256k1_fe_mul(&gej->x, &ge->x, &z2);
     secp256k1_fe_mul(&gej->y, &ge->y, &z3);
     gej->infinity = ge->infinity;
 }
 
 void random_scalar_order_test(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
         int overflow = 0;
         secp256k1_rand256_test(b32);
         secp256k1_scalar_set_b32(num, b32, &overflow);
         if (overflow || secp256k1_scalar_is_zero(num)) {
             continue;
         }
         break;
     } while(1);
 }
 
 void random_scalar_order(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
         int overflow = 0;
         secp256k1_rand256(b32);
         secp256k1_scalar_set_b32(num, b32, &overflow);
         if (overflow || secp256k1_scalar_is_zero(num)) {
             continue;
         }
         break;
     } while(1);
 }
 
 void run_context_tests(void) {
     secp256k1_pubkey pubkey;
     secp256k1_pubkey zero_pubkey;
     secp256k1_ecdsa_signature sig;
     unsigned char ctmp[32];
     int32_t ecount;
     int32_t ecount2;
     secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
     secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
     secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
 
     secp256k1_gej pubj;
     secp256k1_ge pub;
     secp256k1_scalar msg, key, nonce;
     secp256k1_scalar sigr, sigs;
 
     memset(&zero_pubkey, 0, sizeof(zero_pubkey));
 
     ecount = 0;
     ecount2 = 10;
     secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
     secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
     secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL);
     CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
 
     /*** clone and destroy all of them to make sure cloning was complete ***/
     {
         secp256k1_context *ctx_tmp;
 
         ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_destroy(ctx_tmp);
         ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_destroy(ctx_tmp);
         ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_destroy(ctx_tmp);
         ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_destroy(ctx_tmp);
     }
 
     /* Verify that the error callback makes it across the clone. */
     CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
     /* And that it resets back to default. */
     secp256k1_context_set_error_callback(sign, NULL, NULL);
     CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
 
     /*** attempt to use them ***/
     random_scalar_order_test(&msg);
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
 
     /* Verify context-type checking illegal-argument errors. */
     memset(ctmp, 1, 32);
     CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
     CHECK(ecount == 1);
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
     CHECK(ecount == 2);
     VG_UNDEF(&sig, sizeof(sig));
     CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
     VG_CHECK(&sig, sizeof(sig));
     CHECK(ecount2 == 10);
     CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
     CHECK(ecount2 == 11);
     CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
     CHECK(ecount == 2);
     CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
     CHECK(ecount2 == 12);
     CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
     CHECK(ecount == 2);
     CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
     CHECK(ecount2 == 13);
     CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1);
     CHECK(ecount == 2);
     CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1);
     CHECK(ecount == 2);
     CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0);
     CHECK(ecount2 == 14);
     CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0);
     CHECK(ecount == 3);
     CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
     CHECK(ecount == 3);
     CHECK(secp256k1_context_randomize(vrfy, ctmp) == 1);
     CHECK(ecount == 3);
     CHECK(secp256k1_context_randomize(vrfy, NULL) == 1);
     CHECK(ecount == 3);
     CHECK(secp256k1_context_randomize(sign, ctmp) == 1);
     CHECK(ecount2 == 14);
     CHECK(secp256k1_context_randomize(sign, NULL) == 1);
     CHECK(ecount2 == 14);
     secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
     secp256k1_context_set_illegal_callback(sign, NULL, NULL);
 
     /* This shouldn't leak memory, due to already-set tests. */
     secp256k1_ecmult_gen_context_build(&sign->ecmult_gen_ctx, NULL);
     secp256k1_ecmult_context_build(&vrfy->ecmult_ctx, NULL);
 
     /* obtain a working nonce */
     do {
         random_scalar_order_test(&nonce);
     } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
 
     /* try signing */
     CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
     CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
 
     /* try verifying */
     CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
     CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
 
     /* cleanup */
     secp256k1_context_destroy(none);
     secp256k1_context_destroy(sign);
     secp256k1_context_destroy(vrfy);
     secp256k1_context_destroy(both);
     /* Defined as no-op. */
     secp256k1_context_destroy(NULL);
 }
 
 void run_scratch_tests(void) {
     int32_t ecount = 0;
     secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
     secp256k1_scratch_space *scratch;
 
     /* Test public API */
     secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
 
     scratch = secp256k1_scratch_space_create(none, 1000);
     CHECK(scratch != NULL);
     CHECK(ecount == 0);
 
     /* Test internal API */
     CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
     CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 1000);
 
     /* Allocating 500 bytes with no frame fails */
     CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
     CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
 
     /* ...but pushing a new stack frame does affect the max allocation */
     CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 1);
     CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 500); /* 500 - ALIGNMENT */
     CHECK(secp256k1_scratch_alloc(scratch, 500) != NULL);
     CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
 
     CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 0);
 
     /* ...and this effect is undone by popping the frame */
     secp256k1_scratch_deallocate_frame(scratch);
     CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
     CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
 
     /* cleanup */
     secp256k1_scratch_space_destroy(scratch);
     secp256k1_context_destroy(none);
 }
 
 /***** HASH TESTS *****/
 
 void run_sha256_tests(void) {
     static const char *inputs[8] = {
         "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
         "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
         "For this sample, this 63-byte string will be used as input data",
         "This is exactly 64 bytes long, not counting the terminating byte"
     };
     static const unsigned char outputs[8][32] = {
         {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
         {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
         {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
         {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d},
         {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
         {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
         {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
         {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
     };
     int i;
     for (i = 0; i < 8; i++) {
         unsigned char out[32];
         secp256k1_sha256 hasher;
         secp256k1_sha256_initialize(&hasher);
         secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
         secp256k1_sha256_finalize(&hasher, out);
         CHECK(memcmp(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
             int split = secp256k1_rand_int(strlen(inputs[i]));
             secp256k1_sha256_initialize(&hasher);
             secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
             secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
             secp256k1_sha256_finalize(&hasher, out);
             CHECK(memcmp(out, outputs[i], 32) == 0);
         }
     }
 }
 
 void run_hmac_sha256_tests(void) {
     static const char *keys[6] = {
         "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
         "\x4a\x65\x66\x65",
         "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
         "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19",
         "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
         "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
     };
     static const char *inputs[6] = {
         "\x48\x69\x20\x54\x68\x65\x72\x65",
         "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f",
         "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd",
         "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd",
         "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74",
         "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e"
     };
     static const unsigned char outputs[6][32] = {
         {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7},
         {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43},
         {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe},
         {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b},
         {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54},
         {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
     };
     int i;
     for (i = 0; i < 6; i++) {
         secp256k1_hmac_sha256 hasher;
         unsigned char out[32];
         secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
         secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
         secp256k1_hmac_sha256_finalize(&hasher, out);
         CHECK(memcmp(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
             int split = secp256k1_rand_int(strlen(inputs[i]));
             secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
             secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
             secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
             secp256k1_hmac_sha256_finalize(&hasher, out);
             CHECK(memcmp(out, outputs[i], 32) == 0);
         }
     }
 }
 
 void run_rfc6979_hmac_sha256_tests(void) {
     static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
     static const unsigned char out1[3][32] = {
         {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
         {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
         {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
     };
 
     static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
     static const unsigned char out2[3][32] = {
         {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
         {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
         {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
     };
 
     secp256k1_rfc6979_hmac_sha256 rng;
     unsigned char out[32];
     int i;
 
     secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
         CHECK(memcmp(out, out1[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
     secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
         CHECK(memcmp(out, out1[i], 32) != 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
     secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
         CHECK(memcmp(out, out2[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 }
 
 /***** RANDOM TESTS *****/
 
 void test_rand_bits(int rand32, int bits) {
     /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
      * get a false negative chance below once in a billion */
     static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
     /* We try multiplying the results with various odd numbers, which shouldn't
      * influence the uniform distribution modulo a power of 2. */
     static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
     /* We only select up to 6 bits from the output to analyse */
     unsigned int usebits = bits > 6 ? 6 : bits;
     unsigned int maxshift = bits - usebits;
     /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
        number, track all observed outcomes, one per bit in a uint64_t. */
     uint64_t x[6][27] = {{0}};
     unsigned int i, shift, m;
     /* Multiply the output of all rand calls with the odd number m, which
        should not change the uniformity of its distribution. */
     for (i = 0; i < rounds[usebits]; i++) {
         uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
         CHECK((((uint64_t)r) >> bits) == 0);
         for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
             uint32_t rm = r * mults[m];
             for (shift = 0; shift <= maxshift; shift++) {
                 x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
             }
         }
     }
     for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
         for (shift = 0; shift <= maxshift; shift++) {
             /* Test that the lower usebits bits of x[shift] are 1 */
             CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
         }
     }
 }
 
 /* Subrange must be a whole divisor of range, and at most 64 */
 void test_rand_int(uint32_t range, uint32_t subrange) {
     /* (1-1/subrange)^rounds < 1/10^9 */
     int rounds = (subrange * 2073) / 100;
     int i;
     uint64_t x = 0;
     CHECK((range % subrange) == 0);
     for (i = 0; i < rounds; i++) {
         uint32_t r = secp256k1_rand_int(range);
         CHECK(r < range);
         r = r % subrange;
         x |= (((uint64_t)1) << r);
     }
     /* Test that the lower subrange bits of x are 1. */
     CHECK(((~x) << (64 - subrange)) == 0);
 }
 
 void run_rand_bits(void) {
     size_t b;
     test_rand_bits(1, 32);
     for (b = 1; b <= 32; b++) {
         test_rand_bits(0, b);
     }
 }
 
 void run_rand_int(void) {
     static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
     static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
     unsigned int m, s;
     for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
         for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
             test_rand_int(ms[m] * ss[s], ss[s]);
         }
     }
 }
 
 /***** NUM TESTS *****/
 
 #ifndef USE_NUM_NONE
 void random_num_negate(secp256k1_num *num) {
     if (secp256k1_rand_bits(1)) {
         secp256k1_num_negate(num);
     }
 }
 
 void random_num_order_test(secp256k1_num *num) {
     secp256k1_scalar sc;
     random_scalar_order_test(&sc);
     secp256k1_scalar_get_num(num, &sc);
 }
 
 void random_num_order(secp256k1_num *num) {
     secp256k1_scalar sc;
     random_scalar_order(&sc);
     secp256k1_scalar_get_num(num, &sc);
 }
 
 void test_num_negate(void) {
     secp256k1_num n1;
     secp256k1_num n2;
     random_num_order_test(&n1); /* n1 = R */
     random_num_negate(&n1);
     secp256k1_num_copy(&n2, &n1); /* n2 = R */
     secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */
     CHECK(secp256k1_num_is_zero(&n1));
     secp256k1_num_copy(&n1, &n2); /* n1 = R */
     secp256k1_num_negate(&n1); /* n1 = -R */
     CHECK(!secp256k1_num_is_zero(&n1));
     secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */
     CHECK(secp256k1_num_is_zero(&n1));
     secp256k1_num_copy(&n1, &n2); /* n1 = R */
     secp256k1_num_negate(&n1); /* n1 = -R */
     CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
     secp256k1_num_negate(&n1); /* n1 = R */
     CHECK(secp256k1_num_eq(&n1, &n2));
 }
 
 void test_num_add_sub(void) {
     int i;
     secp256k1_scalar s;
     secp256k1_num n1;
     secp256k1_num n2;
     secp256k1_num n1p2, n2p1, n1m2, n2m1;
     random_num_order_test(&n1); /* n1 = R1 */
     if (secp256k1_rand_bits(1)) {
         random_num_negate(&n1);
     }
     random_num_order_test(&n2); /* n2 = R2 */
     if (secp256k1_rand_bits(1)) {
         random_num_negate(&n2);
     }
     secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
     secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */
     secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */
     secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */
     CHECK(secp256k1_num_eq(&n1p2, &n2p1));
     CHECK(!secp256k1_num_eq(&n1p2, &n1m2));
     secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */
     CHECK(secp256k1_num_eq(&n2m1, &n1m2));
     CHECK(!secp256k1_num_eq(&n2m1, &n1));
     secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */
     CHECK(secp256k1_num_eq(&n2m1, &n1));
     CHECK(!secp256k1_num_eq(&n2p1, &n1));
     secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
     CHECK(secp256k1_num_eq(&n2p1, &n1));
 
     /* check is_one */
     secp256k1_scalar_set_int(&s, 1);
     secp256k1_scalar_get_num(&n1, &s);
     CHECK(secp256k1_num_is_one(&n1));
     /* check that 2^n + 1 is never 1 */
     secp256k1_scalar_get_num(&n2, &s);
     for (i = 0; i < 250; ++i) {
         secp256k1_num_add(&n1, &n1, &n1);    /* n1 *= 2 */
         secp256k1_num_add(&n1p2, &n1, &n2);  /* n1p2 = n1 + 1 */
         CHECK(!secp256k1_num_is_one(&n1p2));
     }
 }
 
 void test_num_mod(void) {
     int i;
     secp256k1_scalar s;
     secp256k1_num order, n;
 
     /* check that 0 mod anything is 0 */
     random_scalar_order_test(&s);
     secp256k1_scalar_get_num(&order, &s);
     secp256k1_scalar_set_int(&s, 0);
     secp256k1_scalar_get_num(&n, &s);
     secp256k1_num_mod(&n, &order);
     CHECK(secp256k1_num_is_zero(&n));
 
     /* check that anything mod 1 is 0 */
     secp256k1_scalar_set_int(&s, 1);
     secp256k1_scalar_get_num(&order, &s);
     secp256k1_scalar_get_num(&n, &s);
     secp256k1_num_mod(&n, &order);
     CHECK(secp256k1_num_is_zero(&n));
 
     /* check that increasing the number past 2^256 does not break this */
     random_scalar_order_test(&s);
     secp256k1_scalar_get_num(&n, &s);
     /* multiply by 2^8, which'll test this case with high probability */
     for (i = 0; i < 8; ++i) {
         secp256k1_num_add(&n, &n, &n);
     }
     secp256k1_num_mod(&n, &order);
     CHECK(secp256k1_num_is_zero(&n));
 }
 
 void test_num_jacobi(void) {
     secp256k1_scalar sqr;
     secp256k1_scalar small;
     secp256k1_scalar five;  /* five is not a quadratic residue */
     secp256k1_num order, n;
     int i;
     /* squares mod 5 are 1, 4 */
     const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
 
     /* check some small values with 5 as the order */
     secp256k1_scalar_set_int(&five, 5);
     secp256k1_scalar_get_num(&order, &five);
     for (i = 0; i < 10; ++i) {
         secp256k1_scalar_set_int(&small, i);
         secp256k1_scalar_get_num(&n, &small);
         CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
     }
 
     /** test large values with 5 as group order */
     secp256k1_scalar_get_num(&order, &five);
     /* we first need a scalar which is not a multiple of 5 */
     do {
         secp256k1_num fiven;
         random_scalar_order_test(&sqr);
         secp256k1_scalar_get_num(&fiven, &five);
         secp256k1_scalar_get_num(&n, &sqr);
         secp256k1_num_mod(&n, &fiven);
     } while (secp256k1_num_is_zero(&n));
     /* next force it to be a residue. 2 is a nonresidue mod 5 so we can
      * just multiply by two, i.e. add the number to itself */
     if (secp256k1_num_jacobi(&n, &order) == -1) {
         secp256k1_num_add(&n, &n, &n);
     }
 
     /* test residue */
     CHECK(secp256k1_num_jacobi(&n, &order) == 1);
     /* test nonresidue */
     secp256k1_num_add(&n, &n, &n);
     CHECK(secp256k1_num_jacobi(&n, &order) == -1);
 
     /** test with secp group order as order */
     secp256k1_scalar_order_get_num(&order);
     random_scalar_order_test(&sqr);
     secp256k1_scalar_sqr(&sqr, &sqr);
     /* test residue */
     secp256k1_scalar_get_num(&n, &sqr);
     CHECK(secp256k1_num_jacobi(&n, &order) == 1);
     /* test nonresidue */
     secp256k1_scalar_mul(&sqr, &sqr, &five);
     secp256k1_scalar_get_num(&n, &sqr);
     CHECK(secp256k1_num_jacobi(&n, &order) == -1);
     /* test multiple of the order*/
     CHECK(secp256k1_num_jacobi(&order, &order) == 0);
 
     /* check one less than the order */
     secp256k1_scalar_set_int(&small, 1);
     secp256k1_scalar_get_num(&n, &small);
     secp256k1_num_sub(&n, &order, &n);
     CHECK(secp256k1_num_jacobi(&n, &order) == 1);  /* sage confirms this is 1 */
 }
 
 void run_num_smalltests(void) {
     int i;
     for (i = 0; i < 100*count; i++) {
         test_num_negate();
         test_num_add_sub();
         test_num_mod();
         test_num_jacobi();
     }
 }
 #endif
 
 /***** SCALAR TESTS *****/
 
 void scalar_test(void) {
     secp256k1_scalar s;
     secp256k1_scalar s1;
     secp256k1_scalar s2;
 #ifndef USE_NUM_NONE
     secp256k1_num snum, s1num, s2num;
     secp256k1_num order, half_order;
 #endif
     unsigned char c[32];
 
     /* Set 's' to a random scalar, with value 'snum'. */
     random_scalar_order_test(&s);
 
     /* Set 's1' to a random scalar, with value 's1num'. */
     random_scalar_order_test(&s1);
 
     /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
     random_scalar_order_test(&s2);
     secp256k1_scalar_get_b32(c, &s2);
 
 #ifndef USE_NUM_NONE
     secp256k1_scalar_get_num(&snum, &s);
     secp256k1_scalar_get_num(&s1num, &s1);
     secp256k1_scalar_get_num(&s2num, &s2);
 
     secp256k1_scalar_order_get_num(&order);
     half_order = order;
     secp256k1_num_shift(&half_order, 1);
 #endif
 
     {
         int i;
         /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
         secp256k1_scalar n;
         secp256k1_scalar_set_int(&n, 0);
         for (i = 0; i < 256; i += 4) {
             secp256k1_scalar t;
             int j;
             secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
             for (j = 0; j < 4; j++) {
                 secp256k1_scalar_add(&n, &n, &n);
             }
             secp256k1_scalar_add(&n, &n, &t);
         }
         CHECK(secp256k1_scalar_eq(&n, &s));
     }
 
     {
         /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
         secp256k1_scalar n;
         int i = 0;
         secp256k1_scalar_set_int(&n, 0);
         while (i < 256) {
             secp256k1_scalar t;
             int j;
             int now = secp256k1_rand_int(15) + 1;
             if (now + i > 256) {
                 now = 256 - i;
             }
             secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
             for (j = 0; j < now; j++) {
                 secp256k1_scalar_add(&n, &n, &n);
             }
             secp256k1_scalar_add(&n, &n, &t);
             i += now;
         }
         CHECK(secp256k1_scalar_eq(&n, &s));
     }
 
 #ifndef USE_NUM_NONE
     {
         /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
         secp256k1_num rnum;
         secp256k1_num r2num;
         secp256k1_scalar r;
         secp256k1_num_add(&rnum, &snum, &s2num);
         secp256k1_num_mod(&rnum, &order);
         secp256k1_scalar_add(&r, &s, &s2);
         secp256k1_scalar_get_num(&r2num, &r);
         CHECK(secp256k1_num_eq(&rnum, &r2num));
     }
 
     {
         /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */
         secp256k1_scalar r;
         secp256k1_num r2num;
         secp256k1_num rnum;
         secp256k1_num_mul(&rnum, &snum, &s2num);
         secp256k1_num_mod(&rnum, &order);
         secp256k1_scalar_mul(&r, &s, &s2);
         secp256k1_scalar_get_num(&r2num, &r);
         CHECK(secp256k1_num_eq(&rnum, &r2num));
         /* The result can only be zero if at least one of the factors was zero. */
         CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
         /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
         CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
         CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
     }
 
     {
         secp256k1_scalar neg;
         secp256k1_num negnum;
         secp256k1_num negnum2;
         /* Check that comparison with zero matches comparison with zero on the number. */
         CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
         /* Check that comparison with the half order is equal to testing for high scalar. */
         CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
         secp256k1_scalar_negate(&neg, &s);
         secp256k1_num_sub(&negnum, &order, &snum);
         secp256k1_num_mod(&negnum, &order);
         /* Check that comparison with the half order is equal to testing for high scalar after negation. */
         CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
         /* Negating should change the high property, unless the value was already zero. */
         CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
         secp256k1_scalar_get_num(&negnum2, &neg);
         /* Negating a scalar should be equal to (order - n) mod order on the number. */
         CHECK(secp256k1_num_eq(&negnum, &negnum2));
         secp256k1_scalar_add(&neg, &neg, &s);
         /* Adding a number to its negation should result in zero. */
         CHECK(secp256k1_scalar_is_zero(&neg));
         secp256k1_scalar_negate(&neg, &neg);
         /* Negating zero should still result in zero. */
         CHECK(secp256k1_scalar_is_zero(&neg));
     }
 
     {
         /* Test secp256k1_scalar_mul_shift_var. */
         secp256k1_scalar r;
         secp256k1_num one;
         secp256k1_num rnum;
         secp256k1_num rnum2;
         unsigned char cone[1] = {0x01};
         unsigned int shift = 256 + secp256k1_rand_int(257);
         secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
         secp256k1_num_mul(&rnum, &s1num, &s2num);
         secp256k1_num_shift(&rnum, shift - 1);
         secp256k1_num_set_bin(&one, cone, 1);
         secp256k1_num_add(&rnum, &rnum, &one);
         secp256k1_num_shift(&rnum, 1);
         secp256k1_scalar_get_num(&rnum2, &r);
         CHECK(secp256k1_num_eq(&rnum, &rnum2));
     }
 
     {
         /* test secp256k1_scalar_shr_int */
         secp256k1_scalar r;
         int i;
         random_scalar_order_test(&r);
         for (i = 0; i < 100; ++i) {
             int low;
             int shift = 1 + secp256k1_rand_int(15);
             int expected = r.d[0] % (1 << shift);
             low = secp256k1_scalar_shr_int(&r, shift);
             CHECK(expected == low);
         }
     }
 #endif
 
     {
         /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
         if (!secp256k1_scalar_is_zero(&s)) {
             secp256k1_scalar inv;
 #ifndef USE_NUM_NONE
             secp256k1_num invnum;
             secp256k1_num invnum2;
 #endif
             secp256k1_scalar_inverse(&inv, &s);
 #ifndef USE_NUM_NONE
             secp256k1_num_mod_inverse(&invnum, &snum, &order);
             secp256k1_scalar_get_num(&invnum2, &inv);
             CHECK(secp256k1_num_eq(&invnum, &invnum2));
 #endif
             secp256k1_scalar_mul(&inv, &inv, &s);
             /* Multiplying a scalar with its inverse must result in one. */
             CHECK(secp256k1_scalar_is_one(&inv));
             secp256k1_scalar_inverse(&inv, &inv);
             /* Inverting one must result in one. */
             CHECK(secp256k1_scalar_is_one(&inv));
 #ifndef USE_NUM_NONE
             secp256k1_scalar_get_num(&invnum, &inv);
             CHECK(secp256k1_num_is_one(&invnum));
 #endif
         }
     }
 
     {
         /* Test commutativity of add. */
         secp256k1_scalar r1, r2;
         secp256k1_scalar_add(&r1, &s1, &s2);
         secp256k1_scalar_add(&r2, &s2, &s1);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
         secp256k1_scalar r1, r2;
         secp256k1_scalar b;
         int i;
         /* Test add_bit. */
         int bit = secp256k1_rand_bits(8);
         secp256k1_scalar_set_int(&b, 1);
         CHECK(secp256k1_scalar_is_one(&b));
         for (i = 0; i < bit; i++) {
             secp256k1_scalar_add(&b, &b, &b);
         }
         r1 = s1;
         r2 = s1;
         if (!secp256k1_scalar_add(&r1, &r1, &b)) {
             /* No overflow happened. */
             secp256k1_scalar_cadd_bit(&r2, bit, 1);
             CHECK(secp256k1_scalar_eq(&r1, &r2));
             /* cadd is a noop when flag is zero */
             secp256k1_scalar_cadd_bit(&r2, bit, 0);
             CHECK(secp256k1_scalar_eq(&r1, &r2));
         }
     }
 
     {
         /* Test commutativity of mul. */
         secp256k1_scalar r1, r2;
         secp256k1_scalar_mul(&r1, &s1, &s2);
         secp256k1_scalar_mul(&r2, &s2, &s1);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
         /* Test associativity of add. */
         secp256k1_scalar r1, r2;
         secp256k1_scalar_add(&r1, &s1, &s2);
         secp256k1_scalar_add(&r1, &r1, &s);
         secp256k1_scalar_add(&r2, &s2, &s);
         secp256k1_scalar_add(&r2, &s1, &r2);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
         /* Test associativity of mul. */
         secp256k1_scalar r1, r2;
         secp256k1_scalar_mul(&r1, &s1, &s2);
         secp256k1_scalar_mul(&r1, &r1, &s);
         secp256k1_scalar_mul(&r2, &s2, &s);
         secp256k1_scalar_mul(&r2, &s1, &r2);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
         /* Test distributitivity of mul over add. */
         secp256k1_scalar r1, r2, t;
         secp256k1_scalar_add(&r1, &s1, &s2);
         secp256k1_scalar_mul(&r1, &r1, &s);
         secp256k1_scalar_mul(&r2, &s1, &s);
         secp256k1_scalar_mul(&t, &s2, &s);
         secp256k1_scalar_add(&r2, &r2, &t);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
         /* Test square. */
         secp256k1_scalar r1, r2;
         secp256k1_scalar_sqr(&r1, &s1);
         secp256k1_scalar_mul(&r2, &s1, &s1);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
         /* Test multiplicative identity. */
         secp256k1_scalar r1, v1;
         secp256k1_scalar_set_int(&v1,1);
         secp256k1_scalar_mul(&r1, &s1, &v1);
         CHECK(secp256k1_scalar_eq(&r1, &s1));
     }
 
     {
         /* Test additive identity. */
         secp256k1_scalar r1, v0;
         secp256k1_scalar_set_int(&v0,0);
         secp256k1_scalar_add(&r1, &s1, &v0);
         CHECK(secp256k1_scalar_eq(&r1, &s1));
     }
 
     {
         /* Test zero product property. */
         secp256k1_scalar r1, v0;
         secp256k1_scalar_set_int(&v0,0);
         secp256k1_scalar_mul(&r1, &s1, &v0);
         CHECK(secp256k1_scalar_eq(&r1, &v0));
     }
 
 }
 
 void run_scalar_tests(void) {
     int i;
     for (i = 0; i < 128 * count; i++) {
         scalar_test();
     }
 
     {
         /* (-1)+1 should be zero. */
         secp256k1_scalar s, o;
         secp256k1_scalar_set_int(&s, 1);
         CHECK(secp256k1_scalar_is_one(&s));
         secp256k1_scalar_negate(&o, &s);
         secp256k1_scalar_add(&o, &o, &s);
         CHECK(secp256k1_scalar_is_zero(&o));
         secp256k1_scalar_negate(&o, &o);
         CHECK(secp256k1_scalar_is_zero(&o));
     }
 
 #ifndef USE_NUM_NONE
     {
         /* A scalar with value of the curve order should be 0. */
         secp256k1_num order;
         secp256k1_scalar zero;
         unsigned char bin[32];
         int overflow = 0;
         secp256k1_scalar_order_get_num(&order);
         secp256k1_num_get_bin(bin, 32, &order);
         secp256k1_scalar_set_b32(&zero, bin, &overflow);
         CHECK(overflow == 1);
         CHECK(secp256k1_scalar_is_zero(&zero));
     }
 #endif
 
     {
         /* Does check_overflow check catch all ones? */
         static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST(
             0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
             0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
         );
         CHECK(secp256k1_scalar_check_overflow(&overflowed));
     }
 
     {
         /* Static test vectors.
          * These were reduced from ~10^12 random vectors based on comparison-decision
          *  and edge-case coverage on 32-bit and 64-bit implementations.
          * The responses were generated with Sage 5.9.
          */
         secp256k1_scalar x;
         secp256k1_scalar y;
         secp256k1_scalar z;
         secp256k1_scalar zz;
         secp256k1_scalar one;
         secp256k1_scalar r1;
         secp256k1_scalar r2;
 #if defined(USE_SCALAR_INV_NUM)
         secp256k1_scalar zzv;
 #endif
         int overflow;
         unsigned char chal[33][2][32] = {
             {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
               0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
               0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
             {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
               0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
              {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
               0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
             {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
               0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
               0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
              {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
             {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
               0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
               0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
               0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
             {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
               0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
               0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
               0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
               0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
             {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
               0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
               0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
              {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
               0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
               0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
               0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
               0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
               0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
               0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
              {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
             {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
               0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
               0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
             {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
             {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
              {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
               0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
               0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
               0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
              {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
             {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
               0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
               0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
               0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
               0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
               0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
             {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
              {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
             {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
               0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
              {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
             {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
               0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
               0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
              {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
               0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
              {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
               0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
               0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
             {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
               0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
               0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
               0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
               0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
             {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
              {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
               0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
               0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
               0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
             {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
               0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
               0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
               0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
               0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
              {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
             {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
               0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
               0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
               0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
             {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
              {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
               0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
               0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
             {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
               0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
              {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
               0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
               0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
               0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
               0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
               0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
              {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
               0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
               0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
             {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
               0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
               0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
               0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
              {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
               0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
             {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
               0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
               0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
              {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
               0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
               0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
               0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
         };
         unsigned char res[33][2][32] = {
             {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
               0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
               0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
               0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
              {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
               0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
               0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
               0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
             {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
               0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
               0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
               0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
              {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
               0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
               0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
               0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
             {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
               0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
               0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
               0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
              {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
               0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
               0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
               0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
             {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
               0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
               0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
               0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
              {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
               0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
               0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
               0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
             {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
               0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
               0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
               0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
              {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
               0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
               0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
               0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
             {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
               0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
               0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
               0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
              {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
               0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
               0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
               0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
             {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
               0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
               0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
               0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
              {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
               0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
               0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
               0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
             {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
               0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
               0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
               0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
              {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
               0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
               0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
               0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
             {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
               0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
               0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
               0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
              {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
               0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
               0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
               0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
             {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
               0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
               0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
               0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
              {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
               0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
               0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
               0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
             {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
               0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
               0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
               0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
              {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
               0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
               0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
               0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
             {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
               0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
               0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
               0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
              {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
               0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
               0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
               0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
             {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
               0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
               0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
               0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
              {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
               0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
               0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
               0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
             {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
               0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
               0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
               0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
              {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
               0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
               0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
               0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
             {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
               0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
               0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
               0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
              {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
               0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
               0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
               0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
             {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
               0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
               0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
               0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
              {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
               0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
               0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
               0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
             {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
               0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
               0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
               0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
              {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
               0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
               0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
               0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
             {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
               0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
               0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
               0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
              {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
               0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
               0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
               0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
             {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
               0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
               0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
               0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
              {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
               0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
               0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
               0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
             {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
               0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
               0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
               0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
              {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
               0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
               0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
               0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
             {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
               0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
               0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
               0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
              {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
               0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
               0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
               0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
             {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
               0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
               0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
               0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
              {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
               0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
               0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
               0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
             {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
               0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
               0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
              {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
               0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
               0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
               0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
             {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
               0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
               0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
              {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
             {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
               0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
               0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
               0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
              {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
               0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
               0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
               0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
             {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
               0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
               0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
               0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
              {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
               0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
               0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
               0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
             {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
               0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
               0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
               0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
              {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
               0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
               0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
               0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
             {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
               0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
               0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
               0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
              {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
               0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
               0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
               0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
             {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
               0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
               0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
               0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
              {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
               0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
               0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
               0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
             {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
               0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
               0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
               0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
              {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
               0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
               0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
               0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
             {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
               0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
               0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
               0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
              {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
               0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
               0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
               0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
         };
         secp256k1_scalar_set_int(&one, 1);
         for (i = 0; i < 33; i++) {
             secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
             CHECK(!overflow);
             secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
             CHECK(!overflow);
             secp256k1_scalar_set_b32(&r1, res[i][0], &overflow);
             CHECK(!overflow);
             secp256k1_scalar_set_b32(&r2, res[i][1], &overflow);
             CHECK(!overflow);
             secp256k1_scalar_mul(&z, &x, &y);
             CHECK(!secp256k1_scalar_check_overflow(&z));
             CHECK(secp256k1_scalar_eq(&r1, &z));
             if (!secp256k1_scalar_is_zero(&y)) {
                 secp256k1_scalar_inverse(&zz, &y);
                 CHECK(!secp256k1_scalar_check_overflow(&zz));
 #if defined(USE_SCALAR_INV_NUM)
                 secp256k1_scalar_inverse_var(&zzv, &y);
                 CHECK(secp256k1_scalar_eq(&zzv, &zz));
 #endif
                 secp256k1_scalar_mul(&z, &z, &zz);
                 CHECK(!secp256k1_scalar_check_overflow(&z));
                 CHECK(secp256k1_scalar_eq(&x, &z));
                 secp256k1_scalar_mul(&zz, &zz, &y);
                 CHECK(!secp256k1_scalar_check_overflow(&zz));
                 CHECK(secp256k1_scalar_eq(&one, &zz));
             }
             secp256k1_scalar_mul(&z, &x, &x);
             CHECK(!secp256k1_scalar_check_overflow(&z));
             secp256k1_scalar_sqr(&zz, &x);
             CHECK(!secp256k1_scalar_check_overflow(&zz));
             CHECK(secp256k1_scalar_eq(&zz, &z));
             CHECK(secp256k1_scalar_eq(&r2, &zz));
         }
     }
 }
 
 /***** FIELD TESTS *****/
 
 void random_fe(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
         secp256k1_rand256(bin);
         if (secp256k1_fe_set_b32(x, bin)) {
             return;
         }
     } while(1);
 }
 
 void random_fe_test(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
         secp256k1_rand256_test(bin);
         if (secp256k1_fe_set_b32(x, bin)) {
             return;
         }
     } while(1);
 }
 
 void random_fe_non_zero(secp256k1_fe *nz) {
     int tries = 10;
     while (--tries >= 0) {
         random_fe(nz);
         secp256k1_fe_normalize(nz);
         if (!secp256k1_fe_is_zero(nz)) {
             break;
         }
     }
     /* Infinitesimal probability of spurious failure here */
     CHECK(tries >= 0);
 }
 
 void random_fe_non_square(secp256k1_fe *ns) {
     secp256k1_fe r;
     random_fe_non_zero(ns);
     if (secp256k1_fe_sqrt(&r, ns)) {
         secp256k1_fe_negate(ns, ns, 1);
     }
 }
 
 int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
     secp256k1_fe an = *a;
     secp256k1_fe bn = *b;
     secp256k1_fe_normalize_weak(&an);
     secp256k1_fe_normalize_var(&bn);
     return secp256k1_fe_equal_var(&an, &bn);
 }
 
 int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) {
     secp256k1_fe x;
     secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
     secp256k1_fe_mul(&x, a, ai);
     return check_fe_equal(&x, &one);
 }
 
 void run_field_convert(void) {
     static const unsigned char b32[32] = {
         0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
         0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
         0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29,
         0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40
     };
     static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST(
         0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
         0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
     );
     static const secp256k1_fe fe = SECP256K1_FE_CONST(
         0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
         0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
     );
     secp256k1_fe fe2;
     unsigned char b322[32];
     secp256k1_fe_storage fes2;
     /* Check conversions to fe. */
     CHECK(secp256k1_fe_set_b32(&fe2, b32));
     CHECK(secp256k1_fe_equal_var(&fe, &fe2));
     secp256k1_fe_from_storage(&fe2, &fes);
     CHECK(secp256k1_fe_equal_var(&fe, &fe2));
     /* Check conversion from fe. */
     secp256k1_fe_get_b32(b322, &fe);
     CHECK(memcmp(b322, b32, 32) == 0);
     secp256k1_fe_to_storage(&fes2, &fe);
     CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
 }
 
 int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
     secp256k1_fe t = *b;
 #ifdef VERIFY
     t.magnitude = a->magnitude;
     t.normalized = a->normalized;
 #endif
     return memcmp(a, &t, sizeof(secp256k1_fe));
 }
 
 void run_field_misc(void) {
     secp256k1_fe x;
     secp256k1_fe y;
     secp256k1_fe z;
     secp256k1_fe q;
     secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
     int i, j;
     for (i = 0; i < 5*count; i++) {
         secp256k1_fe_storage xs, ys, zs;
         random_fe(&x);
         random_fe_non_zero(&y);
         /* Test the fe equality and comparison operations. */
         CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
         CHECK(secp256k1_fe_equal_var(&x, &x));
         z = x;
         secp256k1_fe_add(&z,&y);
         /* Test fe conditional move; z is not normalized here. */
         q = x;
         secp256k1_fe_cmov(&x, &z, 0);
         VERIFY_CHECK(!x.normalized && x.magnitude == z.magnitude);
         secp256k1_fe_cmov(&x, &x, 1);
         CHECK(fe_memcmp(&x, &z) != 0);
         CHECK(fe_memcmp(&x, &q) == 0);
         secp256k1_fe_cmov(&q, &z, 1);
         VERIFY_CHECK(!q.normalized && q.magnitude == z.magnitude);
         CHECK(fe_memcmp(&q, &z) == 0);
         secp256k1_fe_normalize_var(&x);
         secp256k1_fe_normalize_var(&z);
         CHECK(!secp256k1_fe_equal_var(&x, &z));
         secp256k1_fe_normalize_var(&q);
         secp256k1_fe_cmov(&q, &z, (i&1));
         VERIFY_CHECK(q.normalized && q.magnitude == 1);
         for (j = 0; j < 6; j++) {
             secp256k1_fe_negate(&z, &z, j+1);
             secp256k1_fe_normalize_var(&q);
             secp256k1_fe_cmov(&q, &z, (j&1));
             VERIFY_CHECK(!q.normalized && q.magnitude == (j+2));
         }
         secp256k1_fe_normalize_var(&z);
         /* Test storage conversion and conditional moves. */
         secp256k1_fe_to_storage(&xs, &x);
         secp256k1_fe_to_storage(&ys, &y);
         secp256k1_fe_to_storage(&zs, &z);
         secp256k1_fe_storage_cmov(&zs, &xs, 0);
         secp256k1_fe_storage_cmov(&zs, &zs, 1);
         CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0);
         secp256k1_fe_storage_cmov(&ys, &xs, 1);
         CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0);
         secp256k1_fe_from_storage(&x, &xs);
         secp256k1_fe_from_storage(&y, &ys);
         secp256k1_fe_from_storage(&z, &zs);
         /* Test that mul_int, mul, and add agree. */
         secp256k1_fe_add(&y, &x);
         secp256k1_fe_add(&y, &x);
         z = x;
         secp256k1_fe_mul_int(&z, 3);
         CHECK(check_fe_equal(&y, &z));
         secp256k1_fe_add(&y, &x);
         secp256k1_fe_add(&z, &x);
         CHECK(check_fe_equal(&z, &y));
         z = x;
         secp256k1_fe_mul_int(&z, 5);
         secp256k1_fe_mul(&q, &x, &fe5);
         CHECK(check_fe_equal(&z, &q));
         secp256k1_fe_negate(&x, &x, 1);
         secp256k1_fe_add(&z, &x);
         secp256k1_fe_add(&q, &x);
         CHECK(check_fe_equal(&y, &z));
         CHECK(check_fe_equal(&q, &y));
     }
 }
 
 void run_field_inv(void) {
     secp256k1_fe x, xi, xii;
     int i;
     for (i = 0; i < 10*count; i++) {
         random_fe_non_zero(&x);
         secp256k1_fe_inv(&xi, &x);
         CHECK(check_fe_inverse(&x, &xi));
         secp256k1_fe_inv(&xii, &xi);
         CHECK(check_fe_equal(&x, &xii));
     }
 }
 
 void run_field_inv_var(void) {
     secp256k1_fe x, xi, xii;
     int i;
     for (i = 0; i < 10*count; i++) {
         random_fe_non_zero(&x);
         secp256k1_fe_inv_var(&xi, &x);
         CHECK(check_fe_inverse(&x, &xi));
         secp256k1_fe_inv_var(&xii, &xi);
         CHECK(check_fe_equal(&x, &xii));
     }
 }
 
 void run_field_inv_all_var(void) {
     secp256k1_fe x[16], xi[16], xii[16];
     int i;
     /* Check it's safe to call for 0 elements */
     secp256k1_fe_inv_all_var(xi, x, 0);
     for (i = 0; i < count; i++) {
         size_t j;
         size_t len = secp256k1_rand_int(15) + 1;
         for (j = 0; j < len; j++) {
             random_fe_non_zero(&x[j]);
         }
         secp256k1_fe_inv_all_var(xi, x, len);
         for (j = 0; j < len; j++) {
             CHECK(check_fe_inverse(&x[j], &xi[j]));
         }
         secp256k1_fe_inv_all_var(xii, xi, len);
         for (j = 0; j < len; j++) {
             CHECK(check_fe_equal(&x[j], &xii[j]));
         }
     }
 }
 
 void run_sqr(void) {
     secp256k1_fe x, s;
 
     {
         int i;
         secp256k1_fe_set_int(&x, 1);
         secp256k1_fe_negate(&x, &x, 1);
 
         for (i = 1; i <= 512; ++i) {
             secp256k1_fe_mul_int(&x, 2);
             secp256k1_fe_normalize(&x);
             secp256k1_fe_sqr(&s, &x);
         }
     }
 }
 
 void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
     secp256k1_fe r1, r2;
     int v = secp256k1_fe_sqrt(&r1, a);
     CHECK((v == 0) == (k == NULL));
 
     if (k != NULL) {
         /* Check that the returned root is +/- the given known answer */
         secp256k1_fe_negate(&r2, &r1, 1);
         secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k);
         secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2);
         CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2));
     }
 }
 
 void run_sqrt(void) {
     secp256k1_fe ns, x, s, t;
     int i;
 
     /* Check sqrt(0) is 0 */
     secp256k1_fe_set_int(&x, 0);
     secp256k1_fe_sqr(&s, &x);
     test_sqrt(&s, &x);
 
     /* Check sqrt of small squares (and their negatives) */
     for (i = 1; i <= 100; i++) {
         secp256k1_fe_set_int(&x, i);
         secp256k1_fe_sqr(&s, &x);
         test_sqrt(&s, &x);
         secp256k1_fe_negate(&t, &s, 1);
         test_sqrt(&t, NULL);
     }
 
     /* Consistency checks for large random values */
     for (i = 0; i < 10; i++) {
         int j;
         random_fe_non_square(&ns);
         for (j = 0; j < count; j++) {
             random_fe(&x);
             secp256k1_fe_sqr(&s, &x);
             test_sqrt(&s, &x);
             secp256k1_fe_negate(&t, &s, 1);
             test_sqrt(&t, NULL);
             secp256k1_fe_mul(&t, &s, &ns);
             test_sqrt(&t, NULL);
         }
     }
 }
 
 /***** GROUP TESTS *****/
 
 void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
     CHECK(a->infinity == b->infinity);
     if (a->infinity) {
         return;
     }
     CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
     CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
 }
 
 /* This compares jacobian points including their Z, not just their geometric meaning. */
 int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
     secp256k1_gej a2;
     secp256k1_gej b2;
     int ret = 1;
     ret &= a->infinity == b->infinity;
     if (ret && !a->infinity) {
         a2 = *a;
         b2 = *b;
         secp256k1_fe_normalize(&a2.x);
         secp256k1_fe_normalize(&a2.y);
         secp256k1_fe_normalize(&a2.z);
         secp256k1_fe_normalize(&b2.x);
         secp256k1_fe_normalize(&b2.y);
         secp256k1_fe_normalize(&b2.z);
         ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0;
         ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0;
         ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0;
     }
     return ret;
 }
 
 void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
     secp256k1_fe z2s;
     secp256k1_fe u1, u2, s1, s2;
     CHECK(a->infinity == b->infinity);
     if (a->infinity) {
         return;
     }
     /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
     secp256k1_fe_sqr(&z2s, &b->z);
     secp256k1_fe_mul(&u1, &a->x, &z2s);
     u2 = b->x; secp256k1_fe_normalize_weak(&u2);
     secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
     s2 = b->y; secp256k1_fe_normalize_weak(&s2);
     CHECK(secp256k1_fe_equal_var(&u1, &u2));
     CHECK(secp256k1_fe_equal_var(&s1, &s2));
 }
 
 void test_ge(void) {
     int i, i1;
 #ifdef USE_ENDOMORPHISM
     int runs = 6;
 #else
     int runs = 4;
 #endif
     /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
      * The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
      * All magnitudes are randomized.
      * All 17*17 combinations of points are added to each other, using all applicable methods.
      *
      * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
      */
     secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs));
     secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs));
     secp256k1_fe *zinv = (secp256k1_fe *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
     secp256k1_fe zf;
     secp256k1_fe zfi2, zfi3;
 
     secp256k1_gej_set_infinity(&gej[0]);
     secp256k1_ge_clear(&ge[0]);
     secp256k1_ge_set_gej_var(&ge[0], &gej[0]);
     for (i = 0; i < runs; i++) {
         int j;
         secp256k1_ge g;
         random_group_element_test(&g);
 #ifdef USE_ENDOMORPHISM
         if (i >= runs - 2) {
             secp256k1_ge_mul_lambda(&g, &ge[1]);
         }
         if (i >= runs - 1) {
             secp256k1_ge_mul_lambda(&g, &g);
         }
 #endif
         ge[1 + 4 * i] = g;
         ge[2 + 4 * i] = g;
         secp256k1_ge_neg(&ge[3 + 4 * i], &g);
         secp256k1_ge_neg(&ge[4 + 4 * i], &g);
         secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]);
         random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]);
         secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
         random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
         for (j = 0; j < 4; j++) {
             random_field_element_magnitude(&ge[1 + j + 4 * i].x);
             random_field_element_magnitude(&ge[1 + j + 4 * i].y);
             random_field_element_magnitude(&gej[1 + j + 4 * i].x);
             random_field_element_magnitude(&gej[1 + j + 4 * i].y);
             random_field_element_magnitude(&gej[1 + j + 4 * i].z);
         }
     }
 
     /* Compute z inverses. */
     {
         secp256k1_fe *zs = checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
         for (i = 0; i < 4 * runs + 1; i++) {
             if (i == 0) {
                 /* The point at infinity does not have a meaningful z inverse. Any should do. */
                 do {
                     random_field_element_test(&zs[i]);
                 } while(secp256k1_fe_is_zero(&zs[i]));
             } else {
                 zs[i] = gej[i].z;
             }
         }
         secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
         free(zs);
     }
 
     /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
     do {
         random_field_element_test(&zf);
     } while(secp256k1_fe_is_zero(&zf));
     random_field_element_magnitude(&zf);
     secp256k1_fe_inv_var(&zfi3, &zf);
     secp256k1_fe_sqr(&zfi2, &zfi3);
     secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
 
     for (i1 = 0; i1 < 1 + 4 * runs; i1++) {
         int i2;
         for (i2 = 0; i2 < 1 + 4 * runs; i2++) {
             /* Compute reference result using gej + gej (var). */
             secp256k1_gej refj, resj;
             secp256k1_ge ref;
             secp256k1_fe zr;
             secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
             /* Check Z ratio. */
             if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
                 secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
                 CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
             }
             secp256k1_ge_set_gej_var(&ref, &refj);
 
             /* Test gej + ge with Z ratio result (var). */
             secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
             ge_equals_gej(&ref, &resj);
             if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
                 secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
                 CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
             }
 
             /* Test gej + ge (var, with additional Z factor). */
             {
                 secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
                 secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
                 secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
                 random_field_element_magnitude(&ge2_zfi.x);
                 random_field_element_magnitude(&ge2_zfi.y);
                 secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
                 ge_equals_gej(&ref, &resj);
             }
 
             /* Test gej + ge (const). */
             if (i2 != 0) {
                 /* secp256k1_gej_add_ge does not support its second argument being infinity. */
                 secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]);
                 ge_equals_gej(&ref, &resj);
             }
 
             /* Test doubling (var). */
             if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) {
                 secp256k1_fe zr2;
                 /* Normal doubling with Z ratio result. */
                 secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
                 ge_equals_gej(&ref, &resj);
                 /* Check Z ratio. */
                 secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
                 CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
                 /* Normal doubling. */
                 secp256k1_gej_double_var(&resj, &gej[i2], NULL);
                 ge_equals_gej(&ref, &resj);
             }
 
             /* Test adding opposites. */
             if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) {
                 CHECK(secp256k1_ge_is_infinity(&ref));
             }
 
             /* Test adding infinity. */
             if (i1 == 0) {
                 CHECK(secp256k1_ge_is_infinity(&ge[i1]));
                 CHECK(secp256k1_gej_is_infinity(&gej[i1]));
                 ge_equals_gej(&ref, &gej[i2]);
             }
             if (i2 == 0) {
                 CHECK(secp256k1_ge_is_infinity(&ge[i2]));
                 CHECK(secp256k1_gej_is_infinity(&gej[i2]));
                 ge_equals_gej(&ref, &gej[i1]);
             }
         }
     }
 
     /* Test adding all points together in random order equals infinity. */
     {
         secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
         secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_gej));
         for (i = 0; i < 4 * runs + 1; i++) {
             gej_shuffled[i] = gej[i];
         }
         for (i = 0; i < 4 * runs + 1; i++) {
             int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
             if (swap != i) {
                 secp256k1_gej t = gej_shuffled[i];
                 gej_shuffled[i] = gej_shuffled[swap];
                 gej_shuffled[swap] = t;
             }
         }
         for (i = 0; i < 4 * runs + 1; i++) {
             secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
         }
         CHECK(secp256k1_gej_is_infinity(&sum));
         free(gej_shuffled);
     }
 
     /* Test batch gej -> ge conversion with and without known z ratios. */
     {
         secp256k1_fe *zr = (secp256k1_fe *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_fe));
         secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
         for (i = 0; i < 4 * runs + 1; i++) {
             /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
             if (i < 4 * runs) {
                 secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
             }
         }
         secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1);
         for (i = 0; i < 4 * runs + 1; i++) {
             secp256k1_fe s;
             random_fe_non_zero(&s);
             secp256k1_gej_rescale(&gej[i], &s);
             ge_equals_gej(&ge_set_all[i], &gej[i]);
         }
         free(ge_set_all);
         free(zr);
     }
 
     /* Test batch gej -> ge conversion with many infinities. */
     for (i = 0; i < 4 * runs + 1; i++) {
         random_group_element_test(&ge[i]);
         /* randomly set half the points to infinitiy */
         if(secp256k1_fe_is_odd(&ge[i].x)) {
             secp256k1_ge_set_infinity(&ge[i]);
         }
         secp256k1_gej_set_ge(&gej[i], &ge[i]);
     }
     /* batch invert */
     secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1);
     /* check result */
     for (i = 0; i < 4 * runs + 1; i++) {
         ge_equals_gej(&ge[i], &gej[i]);
     }
 
     free(ge);
     free(gej);
     free(zinv);
 }
 
 void test_add_neg_y_diff_x(void) {
     /* The point of this test is to check that we can add two points
      * whose y-coordinates are negatives of each other but whose x
      * coordinates differ. If the x-coordinates were the same, these
      * points would be negatives of each other and their sum is
      * infinity. This is cool because it "covers up" any degeneracy
      * in the addition algorithm that would cause the xy coordinates
      * of the sum to be wrong (since infinity has no xy coordinates).
      * HOWEVER, if the x-coordinates are different, infinity is the
      * wrong answer, and such degeneracies are exposed. This is the
      * root of https://github.com/bitcoin-core/secp256k1/issues/257
      * which this test is a regression test for.
      *
      * These points were generated in sage as
      * # secp256k1 params
      * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
      * C = EllipticCurve ([F (0), F (7)])
      * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
      * N = FiniteField(G.order())
      *
      * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
      * x = polygen(N)
      * lam  = (1 - x^3).roots()[1][0]
      *
      * # random "bad pair"
      * P = C.random_element()
      * Q = -int(lam) * P
      * print "    P: %x %x" % P.xy()
      * print "    Q: %x %x" % Q.xy()
      * print "P + Q: %x %x" % (P + Q).xy()
      */
     secp256k1_gej aj = SECP256K1_GEJ_CONST(
         0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
         0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
         0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
         0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
     );
     secp256k1_gej bj = SECP256K1_GEJ_CONST(
         0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
         0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
         0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
         0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
     );
     secp256k1_gej sumj = SECP256K1_GEJ_CONST(
         0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
         0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
         0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
         0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
     );
     secp256k1_ge b;
     secp256k1_gej resj;
     secp256k1_ge res;
     secp256k1_ge_set_gej(&b, &bj);
 
     secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
     secp256k1_ge_set_gej(&res, &resj);
     ge_equals_gej(&res, &sumj);
 
     secp256k1_gej_add_ge(&resj, &aj, &b);
     secp256k1_ge_set_gej(&res, &resj);
     ge_equals_gej(&res, &sumj);
 
     secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
     secp256k1_ge_set_gej(&res, &resj);
     ge_equals_gej(&res, &sumj);
 }
 
 void run_ge(void) {
     int i;
     for (i = 0; i < count * 32; i++) {
         test_ge();
     }
     test_add_neg_y_diff_x();
 }
 
 void test_ec_combine(void) {
     secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
     secp256k1_pubkey data[6];
     const secp256k1_pubkey* d[6];
     secp256k1_pubkey sd;
     secp256k1_pubkey sd2;
     secp256k1_gej Qj;
     secp256k1_ge Q;
     int i;
     for (i = 1; i <= 6; i++) {
         secp256k1_scalar s;
         random_scalar_order_test(&s);
         secp256k1_scalar_add(&sum, &sum, &s);
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
         secp256k1_ge_set_gej(&Q, &Qj);
         secp256k1_pubkey_save(&data[i - 1], &Q);
         d[i - 1] = &data[i - 1];
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
         secp256k1_ge_set_gej(&Q, &Qj);
         secp256k1_pubkey_save(&sd, &Q);
         CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
         CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
     }
 }
 
 void run_ec_combine(void) {
     int i;
     for (i = 0; i < count * 8; i++) {
          test_ec_combine();
     }
 }
 
 void test_group_decompress(const secp256k1_fe* x) {
     /* The input itself, normalized. */
     secp256k1_fe fex = *x;
     secp256k1_fe fez;
     /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
     secp256k1_ge ge_quad, ge_even, ge_odd;
     secp256k1_gej gej_quad;
     /* Return values of the above calls. */
     int res_quad, res_even, res_odd;
 
     secp256k1_fe_normalize_var(&fex);
 
     res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex);
     res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
     res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);
 
     CHECK(res_quad == res_even);
     CHECK(res_quad == res_odd);
 
     if (res_quad) {
         secp256k1_fe_normalize_var(&ge_quad.x);
         secp256k1_fe_normalize_var(&ge_odd.x);
         secp256k1_fe_normalize_var(&ge_even.x);
         secp256k1_fe_normalize_var(&ge_quad.y);
         secp256k1_fe_normalize_var(&ge_odd.y);
         secp256k1_fe_normalize_var(&ge_even.y);
 
         /* No infinity allowed. */
         CHECK(!ge_quad.infinity);
         CHECK(!ge_even.infinity);
         CHECK(!ge_odd.infinity);
 
         /* Check that the x coordinates check out. */
         CHECK(secp256k1_fe_equal_var(&ge_quad.x, x));
         CHECK(secp256k1_fe_equal_var(&ge_even.x, x));
         CHECK(secp256k1_fe_equal_var(&ge_odd.x, x));
 
         /* Check that the Y coordinate result in ge_quad is a square. */
         CHECK(secp256k1_fe_is_quad_var(&ge_quad.y));
 
         /* Check odd/even Y in ge_odd, ge_even. */
         CHECK(secp256k1_fe_is_odd(&ge_odd.y));
         CHECK(!secp256k1_fe_is_odd(&ge_even.y));
 
         /* Check secp256k1_gej_has_quad_y_var. */
         secp256k1_gej_set_ge(&gej_quad, &ge_quad);
         CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
         do {
             random_fe_test(&fez);
         } while (secp256k1_fe_is_zero(&fez));
         secp256k1_gej_rescale(&gej_quad, &fez);
         CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
         secp256k1_gej_neg(&gej_quad, &gej_quad);
         CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
         do {
             random_fe_test(&fez);
         } while (secp256k1_fe_is_zero(&fez));
         secp256k1_gej_rescale(&gej_quad, &fez);
         CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
         secp256k1_gej_neg(&gej_quad, &gej_quad);
         CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
     }
 }
 
 void run_group_decompress(void) {
     int i;
     for (i = 0; i < count * 4; i++) {
         secp256k1_fe fe;
         random_fe_test(&fe);
         test_group_decompress(&fe);
     }
 }
 
 /***** ECMULT TESTS *****/
 
 void run_ecmult_chain(void) {
     /* random starting point A (on the curve) */
     secp256k1_gej a = SECP256K1_GEJ_CONST(
         0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3,
         0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004,
         0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f,
         0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f
     );
     /* two random initial factors xn and gn */
     secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
         0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
         0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
     );
     secp256k1_scalar gn = SECP256K1_SCALAR_CONST(
         0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9,
         0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de
     );
     /* two small multipliers to be applied to xn and gn in every iteration: */
     static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
     static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
     /* accumulators with the resulting coefficients to A and G */
     secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
     secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
     /* actual points */
     secp256k1_gej x;
     secp256k1_gej x2;
     int i;
 
     /* the point being computed */
     x = a;
     for (i = 0; i < 200*count; i++) {
         /* in each iteration, compute X = xn*X + gn*G; */
         secp256k1_ecmult(&ctx->ecmult_ctx, &x, &x, &xn, &gn);
         /* also compute ae and ge: the actual accumulated factors for A and G */
         /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */
         secp256k1_scalar_mul(&ae, &ae, &xn);
         secp256k1_scalar_mul(&ge, &ge, &xn);
         secp256k1_scalar_add(&ge, &ge, &gn);
         /* modify xn and gn */
         secp256k1_scalar_mul(&xn, &xn, &xf);
         secp256k1_scalar_mul(&gn, &gn, &gf);
 
         /* verify */
         if (i == 19999) {
             /* expected result after 19999 iterations */
             secp256k1_gej rp = SECP256K1_GEJ_CONST(
                 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
                 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
                 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
                 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
             );
 
             secp256k1_gej_neg(&rp, &rp);
             secp256k1_gej_add_var(&rp, &rp, &x, NULL);
             CHECK(secp256k1_gej_is_infinity(&rp));
         }
     }
     /* redo the computation, but directly with the resulting ae and ge coefficients: */
     secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
     secp256k1_gej_neg(&x2, &x2);
     secp256k1_gej_add_var(&x2, &x2, &x, NULL);
     CHECK(secp256k1_gej_is_infinity(&x2));
 }
 
 void test_point_times_order(const secp256k1_gej *point) {
     /* X * (point + G) + (order-X) * (pointer + G) = 0 */
     secp256k1_scalar x;
     secp256k1_scalar nx;
     secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
     secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
     secp256k1_gej res1, res2;
     secp256k1_ge res3;
     unsigned char pub[65];
     size_t psize = 65;
     random_scalar_order_test(&x);
     secp256k1_scalar_negate(&nx, &x);
     secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
     secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
     secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
     CHECK(secp256k1_gej_is_infinity(&res1));
     CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
     secp256k1_ge_set_gej(&res3, &res1);
     CHECK(secp256k1_ge_is_infinity(&res3));
     CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
     CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
     psize = 65;
     CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
     /* check zero/one edge cases */
     secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
     secp256k1_ge_set_gej(&res3, &res1);
     CHECK(secp256k1_ge_is_infinity(&res3));
     secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
     secp256k1_ge_set_gej(&res3, &res1);
     ge_equals_gej(&res3, point);
     secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
     secp256k1_ge_set_gej(&res3, &res1);
     ge_equals_ge(&res3, &secp256k1_ge_const_g);
 }
 
 void run_point_times_order(void) {
     int i;
     secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
     static const secp256k1_fe xr = SECP256K1_FE_CONST(
         0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
         0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
     );
     for (i = 0; i < 500; i++) {
         secp256k1_ge p;
         if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
             secp256k1_gej j;
             CHECK(secp256k1_ge_is_valid_var(&p));
             secp256k1_gej_set_ge(&j, &p);
             CHECK(secp256k1_gej_is_valid_var(&j));
             test_point_times_order(&j);
         }
         secp256k1_fe_sqr(&x, &x);
     }
     secp256k1_fe_normalize_var(&x);
     CHECK(secp256k1_fe_equal_var(&x, &xr));
 }
 
 void ecmult_const_random_mult(void) {
     /* random starting point A (on the curve) */
     secp256k1_ge a = SECP256K1_GE_CONST(
         0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
         0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
         0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
         0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
     );
     /* random initial factor xn */
     secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
         0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
         0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
     );
     /* expected xn * A (from sage) */
     secp256k1_ge expected_b = SECP256K1_GE_CONST(
         0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
         0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
         0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
         0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
     );
     secp256k1_gej b;
     secp256k1_ecmult_const(&b, &a, &xn, 256);
 
     CHECK(secp256k1_ge_is_valid_var(&a));
     ge_equals_gej(&expected_b, &b);
 }
 
 void ecmult_const_commutativity(void) {
     secp256k1_scalar a;
     secp256k1_scalar b;
     secp256k1_gej res1;
     secp256k1_gej res2;
     secp256k1_ge mid1;
     secp256k1_ge mid2;
     random_scalar_order_test(&a);
     random_scalar_order_test(&b);
 
     secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256);
     secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256);
     secp256k1_ge_set_gej(&mid1, &res1);
     secp256k1_ge_set_gej(&mid2, &res2);
     secp256k1_ecmult_const(&res1, &mid1, &b, 256);
     secp256k1_ecmult_const(&res2, &mid2, &a, 256);
     secp256k1_ge_set_gej(&mid1, &res1);
     secp256k1_ge_set_gej(&mid2, &res2);
     ge_equals_ge(&mid1, &mid2);
 }
 
 void ecmult_const_mult_zero_one(void) {
     secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
     secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
     secp256k1_scalar negone;
     secp256k1_gej res1;
     secp256k1_ge res2;
     secp256k1_ge point;
     secp256k1_scalar_negate(&negone, &one);
 
     random_group_element_test(&point);
     secp256k1_ecmult_const(&res1, &point, &zero, 3);
     secp256k1_ge_set_gej(&res2, &res1);
     CHECK(secp256k1_ge_is_infinity(&res2));
     secp256k1_ecmult_const(&res1, &point, &one, 2);
     secp256k1_ge_set_gej(&res2, &res1);
     ge_equals_ge(&res2, &point);
     secp256k1_ecmult_const(&res1, &point, &negone, 256);
     secp256k1_gej_neg(&res1, &res1);
     secp256k1_ge_set_gej(&res2, &res1);
     ge_equals_ge(&res2, &point);
 }
 
 void ecmult_const_chain_multiply(void) {
     /* Check known result (randomly generated test problem from sage) */
     const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
         0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
         0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
     );
     const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
         0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
         0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
         0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
         0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
     );
     secp256k1_gej point;
     secp256k1_ge res;
     int i;
 
     secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
     for (i = 0; i < 100; ++i) {
         secp256k1_ge tmp;
         secp256k1_ge_set_gej(&tmp, &point);
         secp256k1_ecmult_const(&point, &tmp, &scalar, 256);
     }
     secp256k1_ge_set_gej(&res, &point);
     ge_equals_gej(&res, &expected_point);
 }
 
 void run_ecmult_const_tests(void) {
     ecmult_const_mult_zero_one();
     ecmult_const_random_mult();
     ecmult_const_commutativity();
     ecmult_const_chain_multiply();
 }
 
 typedef struct {
     secp256k1_scalar *sc;
     secp256k1_ge *pt;
 } ecmult_multi_data;
 
 static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
     ecmult_multi_data *data = (ecmult_multi_data*) cbdata;
     *sc = data->sc[idx];
     *pt = data->pt[idx];
     return 1;
 }
 
 static int ecmult_multi_false_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
     (void)sc;
     (void)pt;
     (void)idx;
     (void)cbdata;
     return 0;
 }
 
 void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) {
     int ncount;
     secp256k1_scalar szero;
     secp256k1_scalar sc[32];
     secp256k1_ge pt[32];
     secp256k1_gej r;
     secp256k1_gej r2;
     ecmult_multi_data data;
     secp256k1_scratch *scratch_empty;
 
     data.sc = sc;
     data.pt = pt;
     secp256k1_scalar_set_int(&szero, 0);
 
     /* No points to multiply */
     CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
 
     /* Check 1- and 2-point multiplies against ecmult */
     for (ncount = 0; ncount < count; ncount++) {
         secp256k1_ge ptg;
         secp256k1_gej ptgj;
         random_scalar_order(&sc[0]);
         random_scalar_order(&sc[1]);
 
         random_group_element_test(&ptg);
         secp256k1_gej_set_ge(&ptgj, &ptg);
         pt[0] = ptg;
         pt[1] = secp256k1_ge_const_g;
 
         /* only G scalar */
         secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &szero, &sc[0]);
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0));
         secp256k1_gej_neg(&r2, &r2);
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
 
         /* 1-point */
         secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &szero);
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 1));
         secp256k1_gej_neg(&r2, &r2);
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
 
         /* Try to multiply 1 point, but scratch space is empty */
         scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0);
         CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
         secp256k1_scratch_destroy(scratch_empty);
 
         /* Try to multiply 1 point, but callback returns false */
         CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1));
 
         /* 2-point */
         secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 2));
         secp256k1_gej_neg(&r2, &r2);
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
 
         /* 2-point with G scalar */
         secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1));
         secp256k1_gej_neg(&r2, &r2);
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
     }
 
     /* Check infinite outputs of various forms */
     for (ncount = 0; ncount < count; ncount++) {
         secp256k1_ge ptg;
         size_t i, j;
         size_t sizes[] = { 2, 10, 32 };
 
         for (j = 0; j < 3; j++) {
             for (i = 0; i < 32; i++) {
                 random_scalar_order(&sc[i]);
                 secp256k1_ge_set_infinity(&pt[i]);
             }
             CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
         }
 
         for (j = 0; j < 3; j++) {
             for (i = 0; i < 32; i++) {
                 random_group_element_test(&ptg);
                 pt[i] = ptg;
                 secp256k1_scalar_set_int(&sc[i], 0);
             }
             CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
         }
 
         for (j = 0; j < 3; j++) {
             random_group_element_test(&ptg);
             for (i = 0; i < 16; i++) {
                 random_scalar_order(&sc[2*i]);
                 secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]);
                 pt[2 * i] = ptg;
                 pt[2 * i + 1] = ptg;
             }
 
             CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
 
             random_scalar_order(&sc[0]);
             for (i = 0; i < 16; i++) {
                 random_group_element_test(&ptg);
 
                 sc[2*i] = sc[0];
                 sc[2*i+1] = sc[0];
                 pt[2 * i] = ptg;
                 secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]);
             }
 
             CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
             CHECK(secp256k1_gej_is_infinity(&r));
         }
 
         random_group_element_test(&ptg);
         secp256k1_scalar_set_int(&sc[0], 0);
         pt[0] = ptg;
         for (i = 1; i < 32; i++) {
             pt[i] = ptg;
 
             random_scalar_order(&sc[i]);
             secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]);
             secp256k1_scalar_negate(&sc[i], &sc[i]);
         }
 
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 32));
         CHECK(secp256k1_gej_is_infinity(&r));
     }
 
     /* Check random points, constant scalar */
     for (ncount = 0; ncount < count; ncount++) {
         size_t i;
         secp256k1_gej_set_infinity(&r);
 
         random_scalar_order(&sc[0]);
         for (i = 0; i < 20; i++) {
             secp256k1_ge ptg;
             sc[i] = sc[0];
             random_group_element_test(&ptg);
             pt[i] = ptg;
             secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL);
         }
 
         secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r, &sc[0], &szero);
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
         secp256k1_gej_neg(&r2, &r2);
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
     }
 
     /* Check random scalars, constant point */
     for (ncount = 0; ncount < count; ncount++) {
         size_t i;
         secp256k1_ge ptg;
         secp256k1_gej p0j;
         secp256k1_scalar rs;
         secp256k1_scalar_set_int(&rs, 0);
 
         random_group_element_test(&ptg);
         for (i = 0; i < 20; i++) {
             random_scalar_order(&sc[i]);
             pt[i] = ptg;
             secp256k1_scalar_add(&rs, &rs, &sc[i]);
         }
 
         secp256k1_gej_set_ge(&p0j, &pt[0]);
         secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &p0j, &rs, &szero);
         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
         secp256k1_gej_neg(&r2, &r2);
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
     }
 
     /* Sanity check that zero scalars don't cause problems */
     for (ncount = 0; ncount < 20; ncount++) {
          random_scalar_order(&sc[ncount]);
          random_group_element_test(&pt[ncount]);
     }
     secp256k1_scalar_clear(&sc[0]);
     CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
     secp256k1_scalar_clear(&sc[1]);
     secp256k1_scalar_clear(&sc[2]);
     secp256k1_scalar_clear(&sc[3]);
     secp256k1_scalar_clear(&sc[4]);
     CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 6));
     CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 5));
     CHECK(secp256k1_gej_is_infinity(&r));
 
     /* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */
     {
         const size_t TOP = 8;
         size_t s0i, s1i;
         size_t t0i, t1i;
         secp256k1_ge ptg;
         secp256k1_gej ptgj;
 
         random_group_element_test(&ptg);
         secp256k1_gej_set_ge(&ptgj, &ptg);
 
         for(t0i = 0; t0i < TOP; t0i++) {
             for(t1i = 0; t1i < TOP; t1i++) {
                 secp256k1_gej t0p, t1p;
                 secp256k1_scalar t0, t1;
 
                 secp256k1_scalar_set_int(&t0, (t0i + 1) / 2);
                 secp256k1_scalar_cond_negate(&t0, t0i & 1);
                 secp256k1_scalar_set_int(&t1, (t1i + 1) / 2);
                 secp256k1_scalar_cond_negate(&t1, t1i & 1);
 
                 secp256k1_ecmult(&ctx->ecmult_ctx, &t0p, &ptgj, &t0, &szero);
                 secp256k1_ecmult(&ctx->ecmult_ctx, &t1p, &ptgj, &t1, &szero);
 
                 for(s0i = 0; s0i < TOP; s0i++) {
                     for(s1i = 0; s1i < TOP; s1i++) {
                         secp256k1_scalar tmp1, tmp2;
                         secp256k1_gej expected, actual;
 
                         secp256k1_ge_set_gej(&pt[0], &t0p);
                         secp256k1_ge_set_gej(&pt[1], &t1p);
 
                         secp256k1_scalar_set_int(&sc[0], (s0i + 1) / 2);
                         secp256k1_scalar_cond_negate(&sc[0], s0i & 1);
                         secp256k1_scalar_set_int(&sc[1], (s1i + 1) / 2);
                         secp256k1_scalar_cond_negate(&sc[1], s1i & 1);
 
                         secp256k1_scalar_mul(&tmp1, &t0, &sc[0]);
                         secp256k1_scalar_mul(&tmp2, &t1, &sc[1]);
                         secp256k1_scalar_add(&tmp1, &tmp1, &tmp2);
 
                         secp256k1_ecmult(&ctx->ecmult_ctx, &expected, &ptgj, &tmp1, &szero);
                         CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &actual, &szero, ecmult_multi_callback, &data, 2));
                         secp256k1_gej_neg(&expected, &expected);
                         secp256k1_gej_add_var(&actual, &actual, &expected, NULL);
                         CHECK(secp256k1_gej_is_infinity(&actual));
                     }
                 }
             }
         }
     }
 }
 
 void test_secp256k1_pippenger_bucket_window_inv(void) {
     int i;
 
     CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0);
     for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) {
 #ifdef USE_ENDOMORPHISM
         /* Bucket_window of 8 is not used with endo */
         if (i == 8) {
             continue;
         }
 #endif
         CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i);
         if (i != PIPPENGER_MAX_BUCKET_WINDOW) {
             CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i);
         }
     }
 }
 
 /**
  * Probabilistically test the function returning the maximum number of possible points
  * for a given scratch space.
  */
 void test_ecmult_multi_pippenger_max_points(void) {
     size_t scratch_size = secp256k1_rand_int(256);
     size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12);
     secp256k1_scratch *scratch;
     size_t n_points_supported;
     int bucket_window = 0;
 
     for(; scratch_size < max_size; scratch_size+=256) {
         scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size);
         CHECK(scratch != NULL);
         n_points_supported = secp256k1_pippenger_max_points(scratch);
         if (n_points_supported == 0) {
             secp256k1_scratch_destroy(scratch);
             continue;
         }
         bucket_window = secp256k1_pippenger_bucket_window(n_points_supported);
         CHECK(secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points_supported, bucket_window), PIPPENGER_SCRATCH_OBJECTS));
         secp256k1_scratch_deallocate_frame(scratch);
         secp256k1_scratch_destroy(scratch);
     }
     CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW);
 }
 
 void test_ecmult_multi_batch_size_helper(void) {
     size_t n_batches, n_batch_points, max_n_batch_points, n;
 
     max_n_batch_points = 0;
     n = 1;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0);
 
     max_n_batch_points = 1;
     n = 0;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
     CHECK(n_batches == 0);
     CHECK(n_batch_points == 0);
 
     max_n_batch_points = 2;
     n = 5;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
     CHECK(n_batches == 3);
     CHECK(n_batch_points == 2);
 
     max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH;
     n = ECMULT_MAX_POINTS_PER_BATCH;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
     CHECK(n_batches == 1);
     CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH);
 
     max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH + 1;
     n = ECMULT_MAX_POINTS_PER_BATCH + 1;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
     CHECK(n_batches == 2);
     CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH/2 + 1);
 
     max_n_batch_points = 1;
     n = SIZE_MAX;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
     CHECK(n_batches == SIZE_MAX);
     CHECK(n_batch_points == 1);
 
     max_n_batch_points = 2;
     n = SIZE_MAX;
     CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
     CHECK(n_batches == SIZE_MAX/2 + 1);
     CHECK(n_batch_points == 2);
 }
 
 /**
  * Run secp256k1_ecmult_multi_var with num points and a scratch space restricted to
  * 1 <= i <= num points.
  */
 void test_ecmult_multi_batching(void) {
     static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD;
     secp256k1_scalar scG;
     secp256k1_scalar szero;
     secp256k1_scalar *sc = (secp256k1_scalar *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_scalar) * n_points);
     secp256k1_ge *pt = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * n_points);
     secp256k1_gej r;
     secp256k1_gej r2;
     ecmult_multi_data data;
     int i;
     secp256k1_scratch *scratch;
 
     secp256k1_gej_set_infinity(&r2);
     secp256k1_scalar_set_int(&szero, 0);
 
     /* Get random scalars and group elements and compute result */
     random_scalar_order(&scG);
     secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r2, &szero, &scG);
     for(i = 0; i < n_points; i++) {
         secp256k1_ge ptg;
         secp256k1_gej ptgj;
         random_group_element_test(&ptg);
         secp256k1_gej_set_ge(&ptgj, &ptg);
         pt[i] = ptg;
         random_scalar_order(&sc[i]);
         secp256k1_ecmult(&ctx->ecmult_ctx, &ptgj, &ptgj, &sc[i], NULL);
         secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL);
     }
     data.sc = sc;
     data.pt = pt;
 
     /* Test with empty scratch space */
     scratch = secp256k1_scratch_create(&ctx->error_callback, 0);
     CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
     secp256k1_scratch_destroy(scratch);
 
     /* Test with space for 1 point in pippenger. That's not enough because
      * ecmult_multi selects strauss which requires more memory. */
     scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
     CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
     secp256k1_scratch_destroy(scratch);
 
     secp256k1_gej_neg(&r2, &r2);
     for(i = 1; i <= n_points; i++) {
         if (i > ECMULT_PIPPENGER_THRESHOLD) {
             int bucket_window = secp256k1_pippenger_bucket_window(i);
             size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window);
             scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
         } else {
             size_t scratch_size = secp256k1_strauss_scratch_size(i);
             scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
         }
         CHECK(secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         CHECK(secp256k1_gej_is_infinity(&r));
         secp256k1_scratch_destroy(scratch);
     }
     free(sc);
     free(pt);
 }
 
 void run_ecmult_multi_tests(void) {
     secp256k1_scratch *scratch;
 
     test_secp256k1_pippenger_bucket_window_inv();
     test_ecmult_multi_pippenger_max_points();
     scratch = secp256k1_scratch_create(&ctx->error_callback, 819200);
     test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
     test_ecmult_multi(NULL, secp256k1_ecmult_multi_var);
     test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single);
     test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
     secp256k1_scratch_destroy(scratch);
 
     /* Run test_ecmult_multi with space for exactly one point */
     scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
     test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
     secp256k1_scratch_destroy(scratch);
 
     test_ecmult_multi_batch_size_helper();
     test_ecmult_multi_batching();
 }
 
 void test_wnaf(const secp256k1_scalar *number, int w) {
     secp256k1_scalar x, two, t;
     int wnaf[256];
     int zeroes = -1;
     int i;
     int bits;
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&two, 2);
     bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
     CHECK(bits <= 256);
     for (i = bits-1; i >= 0; i--) {
         int v = wnaf[i];
         secp256k1_scalar_mul(&x, &x, &two);
         if (v) {
             CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */
             zeroes=0;
             CHECK((v & 1) == 1); /* check non-zero elements are odd */
             CHECK(v <= (1 << (w-1)) - 1); /* check range below */
             CHECK(v >= -(1 << (w-1)) - 1); /* check range above */
         } else {
             CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */
             zeroes++;
         }
         if (v >= 0) {
             secp256k1_scalar_set_int(&t, v);
         } else {
             secp256k1_scalar_set_int(&t, -v);
             secp256k1_scalar_negate(&t, &t);
         }
         secp256k1_scalar_add(&x, &x, &t);
     }
     CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
 }
 
 void test_constant_wnaf_negate(const secp256k1_scalar *number) {
     secp256k1_scalar neg1 = *number;
     secp256k1_scalar neg2 = *number;
     int sign1 = 1;
     int sign2 = 1;
 
     if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
         secp256k1_scalar_negate(&neg1, &neg1);
         sign1 = -1;
     }
     sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
     CHECK(sign1 == sign2);
     CHECK(secp256k1_scalar_eq(&neg1, &neg2));
 }
 
 void test_constant_wnaf(const secp256k1_scalar *number, int w) {
     secp256k1_scalar x, shift;
     int wnaf[256] = {0};
     int i;
     int skew;
     int bits = 256;
     secp256k1_scalar num = *number;
 
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&shift, 1 << w);
     /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
 #ifdef USE_ENDOMORPHISM
     for (i = 0; i < 16; ++i) {
         secp256k1_scalar_shr_int(&num, 8);
     }
     bits = 128;
 #endif
-    skew = secp256k1_wnaf_const(wnaf, num, w, bits);
+    skew = secp256k1_wnaf_const(wnaf, &num, w, bits);
 
     for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) {
         secp256k1_scalar t;
         int v = wnaf[i];
         CHECK(v != 0); /* check nonzero */
         CHECK(v & 1);  /* check parity */
         CHECK(v > -(1 << w)); /* check range above */
         CHECK(v < (1 << w));  /* check range below */
 
         secp256k1_scalar_mul(&x, &x, &shift);
         if (v >= 0) {
             secp256k1_scalar_set_int(&t, v);
         } else {
             secp256k1_scalar_set_int(&t, -v);
             secp256k1_scalar_negate(&t, &t);
         }
         secp256k1_scalar_add(&x, &x, &t);
     }
     /* Skew num because when encoding numbers as odd we use an offset */
     secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
     CHECK(secp256k1_scalar_eq(&x, &num));
 }
 
 void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
     secp256k1_scalar x, shift;
     int wnaf[256] = {0};
     int i;
     int skew;
     secp256k1_scalar num = *number;
 
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&shift, 1 << w);
     /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
 #ifdef USE_ENDOMORPHISM
     for (i = 0; i < 16; ++i) {
         secp256k1_scalar_shr_int(&num, 8);
     }
 #endif
     skew = secp256k1_wnaf_fixed(wnaf, &num, w);
 
     for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
         secp256k1_scalar t;
         int v = wnaf[i];
         CHECK(v == 0 || v & 1);  /* check parity */
         CHECK(v > -(1 << w)); /* check range above */
         CHECK(v < (1 << w));  /* check range below */
 
         secp256k1_scalar_mul(&x, &x, &shift);
         if (v >= 0) {
             secp256k1_scalar_set_int(&t, v);
         } else {
             secp256k1_scalar_set_int(&t, -v);
             secp256k1_scalar_negate(&t, &t);
         }
         secp256k1_scalar_add(&x, &x, &t);
     }
     /* If skew is 1 then add 1 to num */
     secp256k1_scalar_cadd_bit(&num, 0, skew == 1);
     CHECK(secp256k1_scalar_eq(&x, &num));
 }
 
 /* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the
  * rest is 0.*/
 void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) {
     int i;
     for (i = WNAF_SIZE(w)-1; i >= 8; --i) {
         CHECK(wnaf[i] == 0);
     }
     for (i = 7; i >= 0; --i) {
         CHECK(wnaf[i] == wnaf_expected[i]);
     }
 }
 
 void test_fixed_wnaf_small(void) {
     int w = 4;
     int wnaf[256] = {0};
     int i;
     int skew;
     secp256k1_scalar num;
 
     secp256k1_scalar_set_int(&num, 0);
     skew = secp256k1_wnaf_fixed(wnaf, &num, w);
     for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
         int v = wnaf[i];
         CHECK(v == 0);
     }
     CHECK(skew == 0);
 
     secp256k1_scalar_set_int(&num, 1);
     skew = secp256k1_wnaf_fixed(wnaf, &num, w);
     for (i = WNAF_SIZE(w)-1; i >= 1; --i) {
         int v = wnaf[i];
         CHECK(v == 0);
     }
     CHECK(wnaf[0] == 1);
     CHECK(skew == 0);
 
     {
         int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf };
         secp256k1_scalar_set_int(&num, 0xffffffff);
         skew = secp256k1_wnaf_fixed(wnaf, &num, w);
         test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
         CHECK(skew == 0);
     }
     {
         int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf };
         secp256k1_scalar_set_int(&num, 0xeeeeeeee);
         skew = secp256k1_wnaf_fixed(wnaf, &num, w);
         test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
         CHECK(skew == 1);
     }
     {
         int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 };
         secp256k1_scalar_set_int(&num, 0x01010101);
         skew = secp256k1_wnaf_fixed(wnaf, &num, w);
         test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
         CHECK(skew == 0);
     }
     {
         int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 };
         secp256k1_scalar_set_int(&num, 0x01ef1ef1);
         skew = secp256k1_wnaf_fixed(wnaf, &num, w);
         test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
         CHECK(skew == 0);
     }
 }
 
 void run_wnaf(void) {
     int i;
     secp256k1_scalar n = {{0}};
 
     /* Sanity check: 1 and 2 are the smallest odd and even numbers and should
      *               have easier-to-diagnose failure modes  */
     n.d[0] = 1;
     test_constant_wnaf(&n, 4);
     n.d[0] = 2;
     test_constant_wnaf(&n, 4);
     /* Test 0 */
     test_fixed_wnaf_small();
     /* Random tests */
     for (i = 0; i < count; i++) {
         random_scalar_order(&n);
         test_wnaf(&n, 4+(i%10));
         test_constant_wnaf_negate(&n);
         test_constant_wnaf(&n, 4 + (i % 10));
         test_fixed_wnaf(&n, 4 + (i % 10));
     }
     secp256k1_scalar_set_int(&n, 0);
     CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1);
     CHECK(secp256k1_scalar_is_zero(&n));
     CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1);
     CHECK(secp256k1_scalar_is_zero(&n));
 }
 
 void test_ecmult_constants(void) {
     /* Test ecmult_gen() for [0..36) and [order-36..0). */
     secp256k1_scalar x;
     secp256k1_gej r;
     secp256k1_ge ng;
     int i;
     int j;
     secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
     for (i = 0; i < 36; i++ ) {
         secp256k1_scalar_set_int(&x, i);
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
         for (j = 0; j < i; j++) {
             if (j == i - 1) {
                 ge_equals_gej(&secp256k1_ge_const_g, &r);
             }
             secp256k1_gej_add_ge(&r, &r, &ng);
         }
         CHECK(secp256k1_gej_is_infinity(&r));
     }
     for (i = 1; i <= 36; i++ ) {
         secp256k1_scalar_set_int(&x, i);
         secp256k1_scalar_negate(&x, &x);
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
         for (j = 0; j < i; j++) {
             if (j == i - 1) {
                 ge_equals_gej(&ng, &r);
             }
             secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
         }
         CHECK(secp256k1_gej_is_infinity(&r));
     }
 }
 
 void run_ecmult_constants(void) {
     test_ecmult_constants();
 }
 
 void test_ecmult_gen_blind(void) {
     /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */
     secp256k1_scalar key;
     secp256k1_scalar b;
     unsigned char seed32[32];
     secp256k1_gej pgej;
     secp256k1_gej pgej2;
     secp256k1_gej i;
     secp256k1_ge pge;
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
     secp256k1_rand256(seed32);
     b = ctx->ecmult_gen_ctx.blind;
     i = ctx->ecmult_gen_ctx.initial;
     secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
     CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key);
     CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
     CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial));
     secp256k1_ge_set_gej(&pge, &pgej);
     ge_equals_gej(&pge, &pgej2);
 }
 
 void test_ecmult_gen_blind_reset(void) {
     /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
     secp256k1_scalar b;
     secp256k1_gej initial;
     secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
     b = ctx->ecmult_gen_ctx.blind;
     initial = ctx->ecmult_gen_ctx.initial;
     secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
     CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
     CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial));
 }
 
 void run_ecmult_gen_blind(void) {
     int i;
     test_ecmult_gen_blind_reset();
     for (i = 0; i < 10; i++) {
         test_ecmult_gen_blind();
     }
 }
 
 #ifdef USE_ENDOMORPHISM
 /***** ENDOMORPHISH TESTS *****/
 void test_scalar_split(void) {
     secp256k1_scalar full;
     secp256k1_scalar s1, slam;
     const unsigned char zero[32] = {0};
     unsigned char tmp[32];
 
     random_scalar_order_test(&full);
     secp256k1_scalar_split_lambda(&s1, &slam, &full);
 
     /* check that both are <= 128 bits in size */
     if (secp256k1_scalar_is_high(&s1)) {
         secp256k1_scalar_negate(&s1, &s1);
     }
     if (secp256k1_scalar_is_high(&slam)) {
         secp256k1_scalar_negate(&slam, &slam);
     }
 
     secp256k1_scalar_get_b32(tmp, &s1);
     CHECK(memcmp(zero, tmp, 16) == 0);
     secp256k1_scalar_get_b32(tmp, &slam);
     CHECK(memcmp(zero, tmp, 16) == 0);
 }
 
 void run_endomorphism_tests(void) {
     test_scalar_split();
 }
 #endif
 
 void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
     unsigned char pubkeyc[65];
     secp256k1_pubkey pubkey;
     secp256k1_ge ge;
     size_t pubkeyclen;
     int32_t ecount;
     ecount = 0;
     secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
     for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
         /* Smaller sizes are tested exhaustively elsewhere. */
         int32_t i;
         memcpy(&pubkeyc[1], input, 64);
         VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
         for (i = 0; i < 256; i++) {
             /* Try all type bytes. */
             int xpass;
             int ypass;
             int ysign;
             pubkeyc[0] = i;
             /* What sign does this point have? */
             ysign = (input[63] & 1) + 2;
             /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
             xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
             /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
             ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
                 ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
             if (xpass || ypass) {
                 /* These cases must parse. */
                 unsigned char pubkeyo[65];
                 size_t outl;
                 memset(&pubkey, 0, sizeof(pubkey));
                 VG_UNDEF(&pubkey, sizeof(pubkey));
                 ecount = 0;
                 CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
                 VG_CHECK(&pubkey, sizeof(pubkey));
                 outl = 65;
                 VG_UNDEF(pubkeyo, 65);
                 CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
                 VG_CHECK(pubkeyo, outl);
                 CHECK(outl == 33);
                 CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
                 CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
                 if (ypass) {
                     /* This test isn't always done because we decode with alternative signs, so the y won't match. */
                     CHECK(pubkeyo[0] == ysign);
                     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
                     memset(&pubkey, 0, sizeof(pubkey));
                     VG_UNDEF(&pubkey, sizeof(pubkey));
                     secp256k1_pubkey_save(&pubkey, &ge);
                     VG_CHECK(&pubkey, sizeof(pubkey));
                     outl = 65;
                     VG_UNDEF(pubkeyo, 65);
                     CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
                     VG_CHECK(pubkeyo, outl);
                     CHECK(outl == 65);
                     CHECK(pubkeyo[0] == 4);
                     CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
                 }
                 CHECK(ecount == 0);
             } else {
                 /* These cases must fail to parse. */
                 memset(&pubkey, 0xfe, sizeof(pubkey));
                 ecount = 0;
                 VG_UNDEF(&pubkey, sizeof(pubkey));
                 CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
                 VG_CHECK(&pubkey, sizeof(pubkey));
                 CHECK(ecount == 0);
                 CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
                 CHECK(ecount == 1);
             }
         }
     }
     secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
 }
 
 void run_ec_pubkey_parse_test(void) {
 #define SECP256K1_EC_PARSE_TEST_NVALID (12)
     const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
         {
             /* Point with leading and trailing zeros in x and y serialization. */
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
             0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
         },
         {
             /* Point with x equal to a 3rd root of unity.*/
             0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
             0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
             0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
             0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
         },
         {
             /* Point with largest x. (1/2) */
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
             0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
             0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
         },
         {
             /* Point with largest x. (2/2) */
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
             0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
             0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
         },
         {
             /* Point with smallest x. (1/2) */
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
             0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
             0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
         },
         {
             /* Point with smallest x. (2/2) */
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
             0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
             0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
         },
         {
             /* Point with largest y. (1/3) */
             0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
             0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
         },
         {
             /* Point with largest y. (2/3) */
             0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
             0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
         },
         {
             /* Point with largest y. (3/3) */
             0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
             0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
         },
         {
             /* Point with smallest y. (1/3) */
             0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
             0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
         },
         {
             /* Point with smallest y. (2/3) */
             0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
             0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
         },
         {
             /* Point with smallest y. (3/3) */
             0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
             0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
         }
     };
 #define SECP256K1_EC_PARSE_TEST_NXVALID (4)
     const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
         {
             /* Valid if y overflow ignored (y = 1 mod p). (1/3) */
             0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
             0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
         },
         {
             /* Valid if y overflow ignored (y = 1 mod p). (2/3) */
             0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
             0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
         },
         {
             /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
             0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
             0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
         },
         {
             /* x on curve, y is from y^2 = x^3 + 8. */
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03
         }
     };
 #define SECP256K1_EC_PARSE_TEST_NINVALID (7)
     const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
         {
             /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
             0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
             0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
         },
         {
             /* Valid if x overflow ignored (x = 1 mod p). */
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
             0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
             0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
         },
         {
             /* Valid if x overflow ignored (x = 1 mod p). */
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
             0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
             0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
         },
         {
             /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
             0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
             0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
         },
         {
             /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
             0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
             0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
         },
         {
             /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
             0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
         },
         {
             /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
             0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
         }
     };
     const unsigned char pubkeyc[66] = {
         /* Serialization of G. */
         0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
         0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
         0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08,
         0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4,
         0xB8, 0x00
     };
     unsigned char sout[65];
     unsigned char shortkey[2];
     secp256k1_ge ge;
     secp256k1_pubkey pubkey;
     size_t len;
     int32_t i;
     int32_t ecount;
     int32_t ecount2;
     ecount = 0;
     /* Nothing should be reading this far into pubkeyc. */
     VG_UNDEF(&pubkeyc[65], 1);
     secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
     /* Zero length claimed, fail, zeroize, no illegal arg error. */
     memset(&pubkey, 0xfe, sizeof(pubkey));
     ecount = 0;
     VG_UNDEF(shortkey, 2);
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 0);
     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
     CHECK(ecount == 1);
     /* Length one claimed, fail, zeroize, no illegal arg error. */
     for (i = 0; i < 256 ; i++) {
         memset(&pubkey, 0xfe, sizeof(pubkey));
         ecount = 0;
         shortkey[0] = i;
         VG_UNDEF(&shortkey[1], 1);
         VG_UNDEF(&pubkey, sizeof(pubkey));
         CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
         VG_CHECK(&pubkey, sizeof(pubkey));
         CHECK(ecount == 0);
         CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
         CHECK(ecount == 1);
     }
     /* Length two claimed, fail, zeroize, no illegal arg error. */
     for (i = 0; i < 65536 ; i++) {
         memset(&pubkey, 0xfe, sizeof(pubkey));
         ecount = 0;
         shortkey[0] = i & 255;
         shortkey[1] = i >> 8;
         VG_UNDEF(&pubkey, sizeof(pubkey));
         CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
         VG_CHECK(&pubkey, sizeof(pubkey));
         CHECK(ecount == 0);
         CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
         CHECK(ecount == 1);
     }
     memset(&pubkey, 0xfe, sizeof(pubkey));
     ecount = 0;
     VG_UNDEF(&pubkey, sizeof(pubkey));
     /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 0);
     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
     CHECK(ecount == 1);
     /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
     CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0);
     CHECK(ecount == 2);
     /* NULL input string. Illegal arg and zeroize output. */
     memset(&pubkey, 0xfe, sizeof(pubkey));
     ecount = 0;
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 1);
     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
     CHECK(ecount == 2);
     /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
     memset(&pubkey, 0xfe, sizeof(pubkey));
     ecount = 0;
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 0);
     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
     CHECK(ecount == 1);
     /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
     memset(&pubkey, 0xfe, sizeof(pubkey));
     ecount = 0;
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 0);
     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
     CHECK(ecount == 1);
     /* Valid parse. */
     memset(&pubkey, 0, sizeof(pubkey));
     ecount = 0;
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
     CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_no_precomp, &pubkey, pubkeyc, 65) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(ecount == 0);
     VG_UNDEF(&ge, sizeof(ge));
     CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
     VG_CHECK(&ge.x, sizeof(ge.x));
     VG_CHECK(&ge.y, sizeof(ge.y));
     VG_CHECK(&ge.infinity, sizeof(ge.infinity));
     ge_equals_ge(&secp256k1_ge_const_g, &ge);
     CHECK(ecount == 0);
     /* secp256k1_ec_pubkey_serialize illegal args. */
     ecount = 0;
     len = 65;
     CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
     CHECK(ecount == 1);
     CHECK(len == 0);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
     CHECK(ecount == 2);
     len = 65;
     VG_UNDEF(sout, 65);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0);
     VG_CHECK(sout, 65);
     CHECK(ecount == 3);
     CHECK(len == 0);
     len = 65;
     CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0);
     CHECK(ecount == 4);
     CHECK(len == 0);
     len = 65;
     VG_UNDEF(sout, 65);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
     VG_CHECK(sout, 65);
     CHECK(ecount == 4);
     CHECK(len == 65);
     /* Multiple illegal args. Should still set arg error only once. */
     ecount = 0;
     ecount2 = 11;
     CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
     CHECK(ecount == 1);
     /* Does the illegal arg callback actually change the behavior? */
     secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2);
     CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
     CHECK(ecount == 1);
     CHECK(ecount2 == 10);
     secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
     /* Try a bunch of prefabbed points with all possible encodings. */
     for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) {
         ec_pubkey_parse_pointtest(valid[i], 1, 1);
     }
     for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) {
         ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0);
     }
     for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) {
         ec_pubkey_parse_pointtest(invalid[i], 0, 0);
     }
 }
 
 void run_eckey_edge_case_test(void) {
     const unsigned char orderc[32] = {
         0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
         0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
         0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
         0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
     };
     const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00};
     unsigned char ctmp[33];
     unsigned char ctmp2[33];
     secp256k1_pubkey pubkey;
     secp256k1_pubkey pubkey2;
     secp256k1_pubkey pubkey_one;
     secp256k1_pubkey pubkey_negone;
     const secp256k1_pubkey *pubkeys[3];
     size_t len;
     int32_t ecount;
     /* Group order is too large, reject. */
     CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0);
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* Maximum value is too large, reject. */
     memset(ctmp, 255, 32);
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
     memset(&pubkey, 1, sizeof(pubkey));
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* Zero is too small, reject. */
     memset(ctmp, 0, 32);
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
     memset(&pubkey, 1, sizeof(pubkey));
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* One must be accepted. */
     ctmp[31] = 0x01;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
     memset(&pubkey, 0, sizeof(pubkey));
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     pubkey_one = pubkey;
     /* Group order + 1 is too large, reject. */
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x42;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
     memset(&pubkey, 1, sizeof(pubkey));
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* -1 must be accepted. */
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
     memset(&pubkey, 0, sizeof(pubkey));
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     pubkey_negone = pubkey;
     /* Tweak of zero leaves the value unchanged. */
     memset(ctmp2, 0, 32);
     CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, ctmp2) == 1);
     CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
     memcpy(&pubkey2, &pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
     CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     /* Multiply tweak of zero zeroizes the output. */
     CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, ctmp2) == 0);
     CHECK(memcmp(zeros, ctmp, 32) == 0);
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
     CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     /* Overflowing key tweak zeroizes. */
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, orderc) == 0);
     CHECK(memcmp(zeros, ctmp, 32) == 0);
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, orderc) == 0);
     CHECK(memcmp(zeros, ctmp, 32) == 0);
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
     CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
     CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     /* Private key tweaks results in a key of zero. */
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 0);
     CHECK(memcmp(zeros, ctmp2, 32) == 0);
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
     CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     /* Tweak computation wraps and results in a key of 1. */
     ctmp2[31] = 2;
     CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 1);
     CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
     ctmp2[31] = 2;
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
     CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     /* Tweak mul * 2 = 1+1. */
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
     ctmp2[31] = 2;
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
     CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     /* Test argument errors. */
     ecount = 0;
     secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
     CHECK(ecount == 0);
     /* Zeroize pubkey on parse error. */
     memset(&pubkey, 0, 32);
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
     CHECK(ecount == 1);
     CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     memset(&pubkey2, 0, 32);
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
     CHECK(ecount == 2);
     CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
     /* Plain argument errors. */
     ecount = 0;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
     CHECK(ecount == 0);
     CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0);
     CHECK(ecount == 1);
     ecount = 0;
     memset(ctmp2, 0, 32);
     ctmp2[31] = 4;
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0);
     CHECK(ecount == 2);
     ecount = 0;
     memset(ctmp2, 0, 32);
     ctmp2[31] = 4;
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0);
     CHECK(ecount == 2);
     ecount = 0;
     memset(ctmp2, 0, 32);
     CHECK(secp256k1_ec_privkey_tweak_add(ctx, NULL, ctmp2) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, NULL) == 0);
     CHECK(ecount == 2);
     ecount = 0;
     memset(ctmp2, 0, 32);
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_privkey_tweak_mul(ctx, NULL, ctmp2) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, NULL) == 0);
     CHECK(ecount == 2);
     ecount = 0;
     CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0);
     CHECK(ecount == 1);
     memset(&pubkey, 1, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
     CHECK(ecount == 2);
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* secp256k1_ec_pubkey_combine tests. */
     ecount = 0;
     pubkeys[0] = &pubkey_one;
     VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *));
     VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *));
     VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *));
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 2);
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 3);
     pubkeys[0] = &pubkey_negone;
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     CHECK(ecount == 3);
     len = 33;
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
     CHECK(memcmp(ctmp, ctmp2, 33) == 0);
     /* Result is infinity. */
     pubkeys[0] = &pubkey_one;
     pubkeys[1] = &pubkey_negone;
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 3);
     /* Passes through infinity but comes out one. */
     pubkeys[2] = &pubkey_one;
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     CHECK(ecount == 3);
     len = 33;
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
     CHECK(memcmp(ctmp, ctmp2, 33) == 0);
     /* Adds to two. */
     pubkeys[1] = &pubkey_one;
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     CHECK(ecount == 3);
     secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
 }
 
 void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
     secp256k1_scalar nonce;
     do {
         random_scalar_order_test(&nonce);
     } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
 }
 
 void test_ecdsa_sign_verify(void) {
     secp256k1_gej pubj;
     secp256k1_ge pub;
     secp256k1_scalar one;
     secp256k1_scalar msg, key;
     secp256k1_scalar sigr, sigs;
     int recid;
     int getrec;
     random_scalar_order_test(&msg);
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
     getrec = secp256k1_rand_bits(1);
     random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
     if (getrec) {
         CHECK(recid >= 0 && recid < 4);
     }
     CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
     secp256k1_scalar_set_int(&one, 1);
     secp256k1_scalar_add(&msg, &msg, &one);
     CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
 }
 
 void run_ecdsa_sign_verify(void) {
     int i;
     for (i = 0; i < 10*count; i++) {
         test_ecdsa_sign_verify();
     }
 }
 
 /** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
 static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
     (void)msg32;
     (void)key32;
     (void)algo16;
     memcpy(nonce32, data, 32);
     return (counter == 0);
 }
 
 static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
    /* Dummy nonce generator that has a fatal error on the first counter value. */
    if (counter == 0) {
        return 0;
    }
    return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
 }
 
 static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
    /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
    if (counter < 3) {
        memset(nonce32, counter==0 ? 0 : 255, 32);
        if (counter == 2) {
            nonce32[31]--;
        }
        return 1;
    }
    if (counter < 5) {
        static const unsigned char order[] = {
            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
            0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
            0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
        };
        memcpy(nonce32, order, 32);
        if (counter == 4) {
            nonce32[31]++;
        }
        return 1;
    }
    /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */
    /* If someone does fine a case where it retries for secp256k1, we'd like to know. */
    if (counter > 5) {
        return 0;
    }
    return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5);
 }
 
 int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
     static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
     return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
 }
 
 void test_ecdsa_end_to_end(void) {
     unsigned char extra[32] = {0x00};
     unsigned char privkey[32];
     unsigned char message[32];
     unsigned char privkey2[32];
     secp256k1_ecdsa_signature signature[6];
     secp256k1_scalar r, s;
     unsigned char sig[74];
     size_t siglen = 74;
     unsigned char pubkeyc[65];
     size_t pubkeyclen = 65;
     secp256k1_pubkey pubkey;
     secp256k1_pubkey pubkey_tmp;
     unsigned char seckey[300];
     size_t seckeylen = 300;
 
     /* Generate a random key and message. */
     {
         secp256k1_scalar msg, key;
         random_scalar_order_test(&msg);
         random_scalar_order_test(&key);
         secp256k1_scalar_get_b32(privkey, &key);
         secp256k1_scalar_get_b32(message, &msg);
     }
 
     /* Construct and verify corresponding public key. */
     CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
 
     /* Verify exporting and importing public key. */
     CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
     memset(&pubkey, 0, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
 
     /* Verify negation changes the key and changes it back */
     memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
     CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
     CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
     CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
 
     /* Verify private key import and export. */
     CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
     CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
     CHECK(memcmp(privkey, privkey2, 32) == 0);
 
     /* Optionally tweak the keys using addition. */
     if (secp256k1_rand_int(3) == 0) {
         int ret1;
         int ret2;
         unsigned char rnd[32];
         secp256k1_pubkey pubkey2;
         secp256k1_rand256_test(rnd);
         ret1 = secp256k1_ec_privkey_tweak_add(ctx, privkey, rnd);
         ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
         CHECK(ret1 == ret2);
         if (ret1 == 0) {
             return;
         }
         CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
         CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     }
 
     /* Optionally tweak the keys using multiplication. */
     if (secp256k1_rand_int(3) == 0) {
         int ret1;
         int ret2;
         unsigned char rnd[32];
         secp256k1_pubkey pubkey2;
         secp256k1_rand256_test(rnd);
         ret1 = secp256k1_ec_privkey_tweak_mul(ctx, privkey, rnd);
         ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
         CHECK(ret1 == ret2);
         if (ret1 == 0) {
             return;
         }
         CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
         CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     }
 
     /* Sign. */
     CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
     CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1);
     CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1);
     extra[31] = 1;
     CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1);
     extra[31] = 0;
     extra[0] = 1;
     CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
     CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
     CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
     CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
     CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
     CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
     CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
     CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
     /* Verify. */
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1);
     /* Test lower-S form, malleate, verify and fail, test again, malleate again */
     CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0]));
     secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]);
     secp256k1_scalar_negate(&s, &s);
     secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0);
     CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
     CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
     CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
     CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
     secp256k1_scalar_negate(&s, &s);
     secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
     CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
     CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
 
     /* Serialize/parse DER and verify again */
     CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
     memset(&signature[0], 0, sizeof(signature[0]));
     CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
     /* Serialize/destroy/parse DER and verify again. */
     siglen = 74;
     CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
     sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
     CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
           secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
 }
 
 void test_random_pubkeys(void) {
     secp256k1_ge elem;
     secp256k1_ge elem2;
     unsigned char in[65];
     /* Generate some randomly sized pubkeys. */
     size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
     if (secp256k1_rand_bits(2) == 0) {
         len = secp256k1_rand_bits(6);
     }
     if (len == 65) {
       in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
     } else {
       in[0] = secp256k1_rand_bits(1) ? 2 : 3;
     }
     if (secp256k1_rand_bits(3) == 0) {
         in[0] = secp256k1_rand_bits(8);
     }
     if (len > 1) {
         secp256k1_rand256(&in[1]);
     }
     if (len > 33) {
         secp256k1_rand256(&in[33]);
     }
     if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
         unsigned char out[65];
         unsigned char firstb;
         int res;
         size_t size = len;
         firstb = in[0];
         /* If the pubkey can be parsed, it should round-trip... */
         CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
         CHECK(size == len);
         CHECK(memcmp(&in[1], &out[1], len-1) == 0);
         /* ... except for the type of hybrid inputs. */
         if ((in[0] != 6) && (in[0] != 7)) {
             CHECK(in[0] == out[0]);
         }
         size = 65;
         CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0));
         CHECK(size == 65);
         CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
         ge_equals_ge(&elem,&elem2);
         /* Check that the X9.62 hybrid type is checked. */
         in[0] = secp256k1_rand_bits(1) ? 6 : 7;
         res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
         if (firstb == 2 || firstb == 3) {
             if (in[0] == firstb + 4) {
               CHECK(res);
             } else {
               CHECK(!res);
             }
         }
         if (res) {
             ge_equals_ge(&elem,&elem2);
             CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
             CHECK(memcmp(&in[1], &out[1], 64) == 0);
         }
     }
 }
 
 void run_random_pubkeys(void) {
     int i;
     for (i = 0; i < 10*count; i++) {
         test_random_pubkeys();
     }
 }
 
 void run_ecdsa_end_to_end(void) {
     int i;
     for (i = 0; i < 64*count; i++) {
         test_ecdsa_end_to_end();
     }
 }
 
 int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
     static const unsigned char zeroes[32] = {0};
 #ifdef ENABLE_OPENSSL_TESTS
     static const unsigned char max_scalar[32] = {
         0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
         0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
         0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
         0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
     };
 #endif
 
     int ret = 0;
 
     secp256k1_ecdsa_signature sig_der;
     unsigned char roundtrip_der[2048];
     unsigned char compact_der[64];
     size_t len_der = 2048;
     int parsed_der = 0, valid_der = 0, roundtrips_der = 0;
 
     secp256k1_ecdsa_signature sig_der_lax;
     unsigned char roundtrip_der_lax[2048];
     unsigned char compact_der_lax[64];
     size_t len_der_lax = 2048;
     int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
 
 #ifdef ENABLE_OPENSSL_TESTS
     ECDSA_SIG *sig_openssl;
     const BIGNUM *r = NULL, *s = NULL;
     const unsigned char *sigptr;
     unsigned char roundtrip_openssl[2048];
     int len_openssl = 2048;
     int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
 #endif
 
     parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
     if (parsed_der) {
         ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
         valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
     }
     if (valid_der) {
         ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
         roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
     }
 
     parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
     if (parsed_der_lax) {
         ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
         valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
     }
     if (valid_der_lax) {
         ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
         roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0;
     }
 
     if (certainly_der) {
         ret |= (!parsed_der) << 2;
     }
     if (certainly_not_der) {
         ret |= (parsed_der) << 17;
     }
     if (valid_der) {
         ret |= (!roundtrips_der) << 3;
     }
 
     if (valid_der) {
         ret |= (!roundtrips_der_lax) << 12;
         ret |= (len_der != len_der_lax) << 13;
         ret |= ((len_der != len_der_lax) || (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14;
     }
     ret |= (roundtrips_der != roundtrips_der_lax) << 15;
     if (parsed_der) {
         ret |= (!parsed_der_lax) << 16;
     }
 
 #ifdef ENABLE_OPENSSL_TESTS
     sig_openssl = ECDSA_SIG_new();
     sigptr = sig;
     parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
     if (parsed_openssl) {
         ECDSA_SIG_get0(sig_openssl, &r, &s);
         valid_openssl = !BN_is_negative(r) && !BN_is_negative(s) && BN_num_bits(r) > 0 && BN_num_bits(r) <= 256 && BN_num_bits(s) > 0 && BN_num_bits(s) <= 256;
         if (valid_openssl) {
             unsigned char tmp[32] = {0};
             BN_bn2bin(r, tmp + 32 - BN_num_bytes(r));
             valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
         }
         if (valid_openssl) {
             unsigned char tmp[32] = {0};
             BN_bn2bin(s, tmp + 32 - BN_num_bytes(s));
             valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
         }
     }
     len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
     if (len_openssl <= 2048) {
         unsigned char *ptr = roundtrip_openssl;
         CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
         roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
     } else {
         len_openssl = 0;
     }
     ECDSA_SIG_free(sig_openssl);
 
     ret |= (parsed_der && !parsed_openssl) << 4;
     ret |= (valid_der && !valid_openssl) << 5;
     ret |= (roundtrips_openssl && !parsed_der) << 6;
     ret |= (roundtrips_der != roundtrips_openssl) << 7;
     if (roundtrips_openssl) {
         ret |= (len_der != (size_t)len_openssl) << 8;
         ret |= ((len_der != (size_t)len_openssl) || (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0)) << 9;
     }
 #endif
     return ret;
 }
 
 static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
     size_t i;
     for (i = 0; i < ptrlen; i++) {
         int shift = ptrlen - 1 - i;
         if (shift >= 4) {
             ptr[i] = 0;
         } else {
             ptr[i] = (val >> shift) & 0xFF;
         }
     }
 }
 
 static void damage_array(unsigned char *sig, size_t *len) {
     int pos;
     int action = secp256k1_rand_bits(3);
     if (action < 1 && *len > 3) {
         /* Delete a byte. */
         pos = secp256k1_rand_int(*len);
         memmove(sig + pos, sig + pos + 1, *len - pos - 1);
         (*len)--;
         return;
     } else if (action < 2 && *len < 2048) {
         /* Insert a byte. */
         pos = secp256k1_rand_int(1 + *len);
         memmove(sig + pos + 1, sig + pos, *len - pos);
         sig[pos] = secp256k1_rand_bits(8);
         (*len)++;
         return;
     } else if (action < 4) {
         /* Modify a byte. */
         sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
         return;
     } else { /* action < 8 */
         /* Modify a bit. */
         sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
         return;
     }
 }
 
 static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
     int der;
     int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
     size_t tlen, elen, glen;
     int indet;
     int n;
 
     *len = 0;
     der = secp256k1_rand_bits(2) == 0;
     *certainly_der = der;
     *certainly_not_der = 0;
     indet = der ? 0 : secp256k1_rand_int(10) == 0;
 
     for (n = 0; n < 2; n++) {
         /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
         nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
         /* The length of the number in bytes (the first byte of which will always be nonzero) */
         nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
         CHECK(nlen[n] <= 232);
         /* The top bit of the number. */
         nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
         /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
         nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
         /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
         nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
         if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
             *certainly_not_der = 1;
         }
         CHECK(nlen[n] + nzlen[n] <= 300);
         /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
         nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
         if (!der) {
             /* nlenlen[n] max 127 bytes */
             int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
             nlenlen[n] += add;
             if (add != 0) {
                 *certainly_not_der = 1;
             }
         }
         CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
     }
 
     /* The total length of the data to go, so far */
     tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
     CHECK(tlen <= 856);
 
     /* The length of the garbage inside the tuple. */
     elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
     if (elen != 0) {
         *certainly_not_der = 1;
     }
     tlen += elen;
     CHECK(tlen <= 980);
 
     /* The length of the garbage after the end of the tuple. */
     glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
     if (glen != 0) {
         *certainly_not_der = 1;
     }
     CHECK(tlen + glen <= 990);
 
     /* Write the tuple header. */
     sig[(*len)++] = 0x30;
     if (indet) {
         /* Indeterminate length */
         sig[(*len)++] = 0x80;
         *certainly_not_der = 1;
     } else {
         int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
         if (!der) {
             int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
             tlenlen += add;
             if (add != 0) {
                 *certainly_not_der = 1;
             }
         }
         if (tlenlen == 0) {
             /* Short length notation */
             sig[(*len)++] = tlen;
         } else {
             /* Long length notation */
             sig[(*len)++] = 128 + tlenlen;
             assign_big_endian(sig + *len, tlenlen, tlen);
             *len += tlenlen;
         }
         tlen += tlenlen;
     }
     tlen += 2;
     CHECK(tlen + glen <= 1119);
 
     for (n = 0; n < 2; n++) {
         /* Write the integer header. */
         sig[(*len)++] = 0x02;
         if (nlenlen[n] == 0) {
             /* Short length notation */
             sig[(*len)++] = nlen[n] + nzlen[n];
         } else {
             /* Long length notation. */
             sig[(*len)++] = 128 + nlenlen[n];
             assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
             *len += nlenlen[n];
         }
         /* Write zero padding */
         while (nzlen[n] > 0) {
             sig[(*len)++] = 0x00;
             nzlen[n]--;
         }
         if (nlen[n] == 32 && !nlow[n]) {
             /* Special extra 16 0xFF bytes in "high" 32-byte numbers */
             int i;
             for (i = 0; i < 16; i++) {
                 sig[(*len)++] = 0xFF;
             }
             nlen[n] -= 16;
         }
         /* Write first byte of number */
         if (nlen[n] > 0) {
             sig[(*len)++] = nhbyte[n];
             nlen[n]--;
         }
         /* Generate remaining random bytes of number */
         secp256k1_rand_bytes_test(sig + *len, nlen[n]);
         *len += nlen[n];
         nlen[n] = 0;
     }
 
     /* Generate random garbage inside tuple. */
     secp256k1_rand_bytes_test(sig + *len, elen);
     *len += elen;
 
     /* Generate end-of-contents bytes. */
     if (indet) {
         sig[(*len)++] = 0;
         sig[(*len)++] = 0;
         tlen += 2;
     }
     CHECK(tlen + glen <= 1121);
 
     /* Generate random garbage outside tuple. */
     secp256k1_rand_bytes_test(sig + *len, glen);
     *len += glen;
     tlen += glen;
     CHECK(tlen <= 1121);
     CHECK(tlen == *len);
 }
 
 void run_ecdsa_der_parse(void) {
     int i,j;
     for (i = 0; i < 200 * count; i++) {
         unsigned char buffer[2048];
         size_t buflen = 0;
         int certainly_der = 0;
         int certainly_not_der = 0;
         random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der);
         CHECK(buflen <= 2048);
         for (j = 0; j < 16; j++) {
             int ret = 0;
             if (j > 0) {
                 damage_array(buffer, &buflen);
                 /* We don't know anything anymore about the DERness of the result */
                 certainly_der = 0;
                 certainly_not_der = 0;
             }
             ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der);
             if (ret != 0) {
                 size_t k;
                 fprintf(stderr, "Failure %x on ", ret);
                 for (k = 0; k < buflen; k++) {
                     fprintf(stderr, "%02x ", buffer[k]);
                 }
                 fprintf(stderr, "\n");
             }
             CHECK(ret == 0);
         }
     }
 }
 
 /* Tests several edge cases. */
 void test_ecdsa_edge_cases(void) {
     int t;
     secp256k1_ecdsa_signature sig;
 
     /* Test the case where ECDSA recomputes a point that is infinity. */
     {
         secp256k1_gej keyj;
         secp256k1_ge key;
         secp256k1_scalar msg;
         secp256k1_scalar sr, ss;
         secp256k1_scalar_set_int(&ss, 1);
         secp256k1_scalar_negate(&ss, &ss);
         secp256k1_scalar_inverse(&ss, &ss);
         secp256k1_scalar_set_int(&sr, 1);
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
         secp256k1_ge_set_gej(&key, &keyj);
         msg = ss;
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
     }
 
     /* Verify signature with r of zero fails. */
     {
         const unsigned char pubkey_mods_zero[33] = {
             0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
             0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
             0x41
         };
         secp256k1_ge key;
         secp256k1_scalar msg;
         secp256k1_scalar sr, ss;
         secp256k1_scalar_set_int(&ss, 1);
         secp256k1_scalar_set_int(&msg, 0);
         secp256k1_scalar_set_int(&sr, 0);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
     }
 
     /* Verify signature with s of zero fails. */
     {
         const unsigned char pubkey[33] = {
             0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x01
         };
         secp256k1_ge key;
         secp256k1_scalar msg;
         secp256k1_scalar sr, ss;
         secp256k1_scalar_set_int(&ss, 0);
         secp256k1_scalar_set_int(&msg, 0);
         secp256k1_scalar_set_int(&sr, 1);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
     }
 
     /* Verify signature with message 0 passes. */
     {
         const unsigned char pubkey[33] = {
             0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x02
         };
         const unsigned char pubkey2[33] = {
             0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
             0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
             0x43
         };
         secp256k1_ge key;
         secp256k1_ge key2;
         secp256k1_scalar msg;
         secp256k1_scalar sr, ss;
         secp256k1_scalar_set_int(&ss, 2);
         secp256k1_scalar_set_int(&msg, 0);
         secp256k1_scalar_set_int(&sr, 2);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
         CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_negate(&ss, &ss);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_set_int(&ss, 1);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
     }
 
     /* Verify signature with message 1 passes. */
     {
         const unsigned char pubkey[33] = {
             0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
             0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
             0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
             0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
             0x25
         };
         const unsigned char pubkey2[33] = {
             0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
             0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
             0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
             0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
             0x62
         };
         const unsigned char csr[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
             0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
             0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
         };
         secp256k1_ge key;
         secp256k1_ge key2;
         secp256k1_scalar msg;
         secp256k1_scalar sr, ss;
         secp256k1_scalar_set_int(&ss, 1);
         secp256k1_scalar_set_int(&msg, 1);
         secp256k1_scalar_set_b32(&sr, csr, NULL);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
         CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_negate(&ss, &ss);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
         secp256k1_scalar_set_int(&ss, 2);
         secp256k1_scalar_inverse_var(&ss, &ss);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
     }
 
     /* Verify signature with message -1 passes. */
     {
         const unsigned char pubkey[33] = {
             0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
             0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
             0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
             0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
             0xf1
         };
         const unsigned char csr[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
             0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
             0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
         };
         secp256k1_ge key;
         secp256k1_scalar msg;
         secp256k1_scalar sr, ss;
         secp256k1_scalar_set_int(&ss, 1);
         secp256k1_scalar_set_int(&msg, 1);
         secp256k1_scalar_negate(&msg, &msg);
         secp256k1_scalar_set_b32(&sr, csr, NULL);
         CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
         secp256k1_scalar_negate(&ss, &ss);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
         secp256k1_scalar_set_int(&ss, 3);
         secp256k1_scalar_inverse_var(&ss, &ss);
         CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
     }
 
     /* Signature where s would be zero. */
     {
         secp256k1_pubkey pubkey;
         size_t siglen;
         int32_t ecount;
         unsigned char signature[72];
         static const unsigned char nonce[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
         };
         static const unsigned char nonce2[32] = {
             0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
             0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
             0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
             0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
         };
         const unsigned char key[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
         };
         unsigned char msg[32] = {
             0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
             0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
             0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
             0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
         };
         ecount = 0;
         secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0);
         msg[31] = 0xaa;
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1);
         CHECK(ecount == 0);
         CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0);
         CHECK(ecount == 1);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0);
         CHECK(ecount == 2);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0);
         CHECK(ecount == 3);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
         CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1);
         CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0);
         CHECK(ecount == 4);
         CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0);
         CHECK(ecount == 5);
         CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0);
         CHECK(ecount == 6);
         CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1);
         CHECK(ecount == 6);
         CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
         CHECK(ecount == 7);
         /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
         CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0);
         CHECK(ecount == 8);
         siglen = 72;
         CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0);
         CHECK(ecount == 9);
         CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0);
         CHECK(ecount == 10);
         CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0);
         CHECK(ecount == 11);
         CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1);
         CHECK(ecount == 11);
         CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0);
         CHECK(ecount == 12);
         CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0);
         CHECK(ecount == 13);
         CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1);
         CHECK(ecount == 13);
         siglen = 10;
         /* Too little room for a signature does not fail via ARGCHECK. */
         CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0);
         CHECK(ecount == 13);
         ecount = 0;
         CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0);
         CHECK(ecount == 1);
         CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0);
         CHECK(ecount == 2);
         CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0);
         CHECK(ecount == 3);
         CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1);
         CHECK(ecount == 3);
         CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0);
         CHECK(ecount == 4);
         CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0);
         CHECK(ecount == 5);
         CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1);
         CHECK(ecount == 5);
         memset(signature, 255, 64);
         CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0);
         CHECK(ecount == 5);
         secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
     }
 
     /* Nonce function corner cases. */
     for (t = 0; t < 2; t++) {
         static const unsigned char zero[32] = {0x00};
         int i;
         unsigned char key[32];
         unsigned char msg[32];
         secp256k1_ecdsa_signature sig2;
         secp256k1_scalar sr[512], ss;
         const unsigned char *extra;
         extra = t == 0 ? NULL : zero;
         memset(msg, 0, 32);
         msg[31] = 1;
         /* High key results in signature failure. */
         memset(key, 0xFF, 32);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
         CHECK(is_empty_signature(&sig));
         /* Zero key results in signature failure. */
         memset(key, 0, 32);
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
         CHECK(is_empty_signature(&sig));
         /* Nonce function failure results in signature failure. */
         key[31] = 1;
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0);
         CHECK(is_empty_signature(&sig));
         /* The retry loop successfully makes its way to the first good value. */
         CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1);
         CHECK(!is_empty_signature(&sig));
         CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
         CHECK(!is_empty_signature(&sig2));
         CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
         /* The default nonce function is deterministic. */
         CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
         CHECK(!is_empty_signature(&sig2));
         CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
         /* The default nonce function changes output with different messages. */
         for(i = 0; i < 256; i++) {
             int j;
             msg[0] = i;
             CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
             CHECK(!is_empty_signature(&sig2));
             secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
             for (j = 0; j < i; j++) {
                 CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
             }
         }
         msg[0] = 0;
         msg[31] = 2;
         /* The default nonce function changes output with different keys. */
         for(i = 256; i < 512; i++) {
             int j;
             key[0] = i - 256;
             CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
             CHECK(!is_empty_signature(&sig2));
             secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
             for (j = 0; j < i; j++) {
                 CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
             }
         }
         key[0] = 0;
     }
 
     {
         /* Check that optional nonce arguments do not have equivalent effect. */
         const unsigned char zeros[32] = {0};
         unsigned char nonce[32];
         unsigned char nonce2[32];
         unsigned char nonce3[32];
         unsigned char nonce4[32];
         VG_UNDEF(nonce,32);
         VG_UNDEF(nonce2,32);
         VG_UNDEF(nonce3,32);
         VG_UNDEF(nonce4,32);
         CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1);
         VG_CHECK(nonce,32);
         CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1);
         VG_CHECK(nonce2,32);
         CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1);
         VG_CHECK(nonce3,32);
         CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
         VG_CHECK(nonce4,32);
         CHECK(memcmp(nonce, nonce2, 32) != 0);
         CHECK(memcmp(nonce, nonce3, 32) != 0);
         CHECK(memcmp(nonce, nonce4, 32) != 0);
         CHECK(memcmp(nonce2, nonce3, 32) != 0);
         CHECK(memcmp(nonce2, nonce4, 32) != 0);
         CHECK(memcmp(nonce3, nonce4, 32) != 0);
     }
 
 
     /* Privkey export where pubkey is the point at infinity. */
     {
         unsigned char privkey[300];
         unsigned char seckey[32] = {
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
             0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
             0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
             0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41,
         };
         size_t outlen = 300;
         CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0));
         outlen = 300;
         CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1));
     }
 }
 
 void run_ecdsa_edge_cases(void) {
     test_ecdsa_edge_cases();
 }
 
 #ifdef ENABLE_OPENSSL_TESTS
 EC_KEY *get_openssl_key(const unsigned char *key32) {
     unsigned char privkey[300];
     size_t privkeylen;
     const unsigned char* pbegin = privkey;
     int compr = secp256k1_rand_bits(1);
     EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
     CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
     CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
     CHECK(EC_KEY_check_key(ec_key));
     return ec_key;
 }
 
 void test_ecdsa_openssl(void) {
     secp256k1_gej qj;
     secp256k1_ge q;
     secp256k1_scalar sigr, sigs;
     secp256k1_scalar one;
     secp256k1_scalar msg2;
     secp256k1_scalar key, msg;
     EC_KEY *ec_key;
     unsigned int sigsize = 80;
     size_t secp_sigsize = 80;
     unsigned char message[32];
     unsigned char signature[80];
     unsigned char key32[32];
     secp256k1_rand256_test(message);
     secp256k1_scalar_set_b32(&msg, message, NULL);
     random_scalar_order_test(&key);
     secp256k1_scalar_get_b32(key32, &key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
     secp256k1_ge_set_gej(&q, &qj);
     ec_key = get_openssl_key(key32);
     CHECK(ec_key != NULL);
     CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
     CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
     CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
     secp256k1_scalar_set_int(&one, 1);
     secp256k1_scalar_add(&msg2, &msg, &one);
     CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
 
     random_sign(&sigr, &sigs, &key, &msg, NULL);
     CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
     CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
 
     EC_KEY_free(ec_key);
 }
 
 void run_ecdsa_openssl(void) {
     int i;
     for (i = 0; i < 10*count; i++) {
         test_ecdsa_openssl();
     }
 }
 #endif
 
 #ifdef ENABLE_MODULE_ECDH
 # include "modules/ecdh/tests_impl.h"
 #endif
 
 #ifdef ENABLE_MODULE_MULTISET
 # include "modules/multiset/tests_impl.h"
 #endif
 
 #ifdef ENABLE_MODULE_RECOVERY
 # include "modules/recovery/tests_impl.h"
 #endif
 
 #ifdef ENABLE_MODULE_SCHNORR
 # include "modules/schnorr/tests_impl.h"
 #endif
 
 int main(int argc, char **argv) {
     unsigned char seed16[16] = {0};
     unsigned char run32[32] = {0};
     /* find iteration count */
     if (argc > 1) {
         count = strtol(argv[1], NULL, 0);
     }
 
     /* find random seed */
     if (argc > 2) {
         int pos = 0;
         const char* ch = argv[2];
         while (pos < 16 && ch[0] != 0 && ch[1] != 0) {
             unsigned short sh;
             if (sscanf(ch, "%2hx", &sh)) {
                 seed16[pos] = sh;
             } else {
                 break;
             }
             ch += 2;
             pos++;
         }
     } else {
         FILE *frand = fopen("/dev/urandom", "r");
         if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) {
             uint64_t t = time(NULL) * (uint64_t)1337;
             fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n");
             seed16[0] ^= t;
             seed16[1] ^= t >> 8;
             seed16[2] ^= t >> 16;
             seed16[3] ^= t >> 24;
             seed16[4] ^= t >> 32;
             seed16[5] ^= t >> 40;
             seed16[6] ^= t >> 48;
             seed16[7] ^= t >> 56;
         }
         if (frand) {
             fclose(frand);
         }
     }
     secp256k1_rand_seed(seed16);
 
     printf("test count = %i\n", count);
     printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
 
     /* initialize */
     run_context_tests();
     run_scratch_tests();
     ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
     if (secp256k1_rand_bits(1)) {
         secp256k1_rand256(run32);
         CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
     }
 
     run_rand_bits();
     run_rand_int();
 
     run_sha256_tests();
     run_hmac_sha256_tests();
     run_rfc6979_hmac_sha256_tests();
 
 #ifndef USE_NUM_NONE
     /* num tests */
     run_num_smalltests();
 #endif
 
     /* scalar tests */
     run_scalar_tests();
 
     /* field tests */
     run_field_inv();
     run_field_inv_var();
     run_field_inv_all_var();
     run_field_misc();
     run_field_convert();
     run_sqr();
     run_sqrt();
 
     /* group tests */
     run_ge();
     run_group_decompress();
 
     /* ecmult tests */
     run_wnaf();
     run_point_times_order();
     run_ecmult_chain();
     run_ecmult_constants();
     run_ecmult_gen_blind();
     run_ecmult_const_tests();
     run_ecmult_multi_tests();
     run_ec_combine();
 
     /* endomorphism tests */
 #ifdef USE_ENDOMORPHISM
     run_endomorphism_tests();
 #endif
 
     /* EC point parser test */
     run_ec_pubkey_parse_test();
 
     /* EC key edge cases */
     run_eckey_edge_case_test();
 
 #ifdef ENABLE_MODULE_ECDH
     /* ecdh tests */
     run_ecdh_tests();
 #endif
 
     /* ecdsa tests */
     run_random_pubkeys();
     run_ecdsa_der_parse();
     run_ecdsa_sign_verify();
     run_ecdsa_end_to_end();
     run_ecdsa_edge_cases();
 #ifdef ENABLE_OPENSSL_TESTS
     run_ecdsa_openssl();
 #endif
 
 #ifdef ENABLE_MODULE_MULTISET
     run_multiset_tests();
 #endif
 
 #ifdef ENABLE_MODULE_RECOVERY
     /* ECDSA pubkey recovery tests */
     run_recovery_tests();
 #endif
 
 #ifdef ENABLE_MODULE_SCHNORR
     /* Schnorr signature tests */
     run_schnorr_tests();
 #endif
 
     secp256k1_rand256(run32);
     printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
 
     /* shutdown */
     secp256k1_context_destroy(ctx);
 
     printf("no problems found\n");
     return 0;
 }