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src/secp256k1/src/ecmult_gen.h

/********************************************************************** /**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille * * Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying * * Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.* * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/ **********************************************************************/
#ifndef SECP256K1_ECMULT_GEN_H #ifndef SECP256K1_ECMULT_GEN_H
#define SECP256K1_ECMULT_GEN_H #define SECP256K1_ECMULT_GEN_H
#include "scalar.h" #include "scalar.h"
#include "group.h" #include "group.h"
#if ECMULT_GEN_PREC_BITS != 2 && ECMULT_GEN_PREC_BITS != 4 && ECMULT_GEN_PREC_BITS != 8
# error "Set ECMULT_GEN_PREC_BITS to 2, 4 or 8."
#endif
#define ECMULT_GEN_PREC_B ECMULT_GEN_PREC_BITS
#define ECMULT_GEN_PREC_G (1 << ECMULT_GEN_PREC_B)
#define ECMULT_GEN_PREC_N (256 / ECMULT_GEN_PREC_B)
typedef struct { typedef struct {
/* For accelerating the computation of a*G: /* For accelerating the computation of a*G:
* To harden against timing attacks, use the following mechanism: * To harden against timing attacks, use the following mechanism:
* * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63. * * Break up the multiplicand into groups of PREC_B bits, called n_0, n_1, n_2, ..., n_(PREC_N-1).
* * Compute sum(n_i * 16^i * G + U_i, i=0..63), where: * * Compute sum(n_i * (PREC_G)^i * G + U_i, i=0 ... PREC_N-1), where:
* * U_i = U * 2^i (for i=0..62) * * U_i = U * 2^i, for i=0 ... PREC_N-2
* * U_i = U * (1-2^63) (for i=63) * * U_i = U * (1-2^(PREC_N-1)), for i=PREC_N-1
* where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0. * where U is a point with no known corresponding scalar. Note that sum(U_i, i=0 ... PREC_N-1) = 0.
* For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is * For each i, and each of the PREC_G possible values of n_i, (n_i * (PREC_G)^i * G + U_i) is
* precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63). * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0 ... PREC_N-1).
* None of the resulting prec group elements have a known scalar, and neither do any of * None of the resulting prec group elements have a known scalar, and neither do any of
* the intermediate sums while computing a*G. * the intermediate sums while computing a*G.
*/ */
secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */ secp256k1_ge_storage (*prec)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G]; /* prec[j][i] = (PREC_G)^j * i * G + U_i */
secp256k1_scalar blind; secp256k1_scalar blind;
secp256k1_gej initial; secp256k1_gej initial;
} secp256k1_ecmult_gen_context; } secp256k1_ecmult_gen_context;
static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE; static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE;
static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx); static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, void **prealloc); static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, void **prealloc);
static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context* src); static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context* src);
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