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Differential D2501 Diff 7257 test/functional/test_framework/schnorr.py

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test/functional/test_framework/schnorr.py

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#!/usr/bin/env python3
# Copyright 2019 The Bitcoin Developers
"""Schnorr secp256k1 using OpenSSL
WARNING: This module does not mlock() secrets; your private keys may end up on
disk in swap! Also, operations are not constant time. Use with caution!
Inspired by key.py from python-bitcoinlib.
"""
import ctypes
import ctypes.util
import hashlib
import hmac
import threading
ssl = ctypes.cdll.LoadLibrary(ctypes.util.find_library('ssl') or 'libeay32')
ssl.BN_new.restype = ctypes.c_void_p
ssl.BN_new.argtypes = []
ssl.BN_free.restype = None
ssl.BN_free.argtypes = [ctypes.c_void_p]
ssl.BN_bin2bn.restype = ctypes.c_void_p
ssl.BN_bin2bn.argtypes = [ctypes.c_char_p, ctypes.c_int, ctypes.c_void_p]
ssl.BN_CTX_new.restype = ctypes.c_void_p
ssl.BN_CTX_new.argtypes = []
ssl.BN_CTX_free.restype = None
ssl.BN_CTX_free.argtypes = [ctypes.c_void_p]
ssl.EC_GROUP_new_by_curve_name.restype = ctypes.c_void_p
ssl.EC_GROUP_new_by_curve_name.argtypes = [ctypes.c_int]
ssl.EC_POINT_new.restype = ctypes.c_void_p
ssl.EC_POINT_new.argtypes = [ctypes.c_void_p]
ssl.EC_POINT_free.restype = None
ssl.EC_POINT_free.argtypes = [ctypes.c_void_p]
ssl.EC_POINT_mul.restype = ctypes.c_int
ssl.EC_POINT_mul.argtypes = [ctypes.c_void_p, ctypes.c_void_p,
ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p]
ssl.EC_POINT_is_at_infinity.restype = ctypes.c_int
ssl.EC_POINT_is_at_infinity.argtypes = [ctypes.c_void_p, ctypes.c_void_p]
ssl.EC_POINT_point2oct.restype = ctypes.c_size_t
ssl.EC_POINT_point2oct.argtypes = [ctypes.c_void_p, ctypes.c_void_p,
ctypes.c_int, ctypes.c_void_p, ctypes.c_size_t, ctypes.c_void_p]
# point encodings for EC_POINT_point2oct
POINT_CONVERSION_COMPRESSED = 2
POINT_CONVERSION_UNCOMPRESSED = 4
SECP256K1_FIELDSIZE = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
SECP256K1_ORDER = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
SECP256K1_ORDER_HALF = SECP256K1_ORDER // 2
# this specifies the curve used
NID_secp256k1 = 714 # from openssl/obj_mac.h
group = ssl.EC_GROUP_new_by_curve_name(NID_secp256k1)
if not group:
raise RuntimeError("Cannot get secp256k1 group!")
class CTX:
"""Wrapper for a bignum context"""
def __init__(self):
self.ptr = ssl.BN_CTX_new()
assert(self.ptr)
def __del__(self):
ssl.BN_CTX_free(self.ptr)
_threadlocal = threading.local()
@classmethod
def ptr_for_this_thread(cls):
"""grab a pointer to per-thread ctx"""
try:
self = cls._threadlocal.ctxwrapper
except AttributeError:
self = cls()
cls._threadlocal.ctxwrapper = self
return self.ptr
def jacobi(a, n):
"""Jacobi symbol"""
# Based on the Handbook of Applied Cryptography (HAC), algorithm 2.149.
# This function has been tested by comparison with a small
# table printed in HAC, and by extensive use in calculating
# modular square roots.
# Borrowed from python ecdsa package (function originally from Peter Pearson)
# ... modified to use bitwise arithmetic when possible, for speed.
assert n >= 3
assert n & 1 == 1
a = a % n
if a == 0:
return 0
if a == 1:
return 1
a1, e = a, 0
while a1 & 1 == 0:
a1, e = a1 >> 1, e+1
if e & 1 == 0 or n & 7 == 1 or n & 7 == 7:
s = 1
else:
s = -1
if a1 == 1:
return s
if n & 3 == 3 and a1 & 3 == 3:
s = -s
return s * jacobi(n % a1, a1)
def nonce_function_rfc6979(privkeybytes, msg32, algo16=b'', ndata=b''):
# RFC6979 deterministic nonce generation, done in libsecp256k1 style.
# see nonce_function_rfc6979() in secp256k1.c; and details in hash_impl.h
assert len(privkeybytes) == 32
assert len(msg32) == 32
assert len(algo16) in (0, 16)
assert len(ndata) in (0, 32)
V = b'\x01'*32
K = b'\x00'*32
blob = bytes(privkeybytes) + msg32 + ndata + algo16
# initialize
K = hmac.HMAC(K, V+b'\x00'+blob, 'sha256').digest()
V = hmac.HMAC(K, V, 'sha256').digest()
K = hmac.HMAC(K, V+b'\x01'+blob, 'sha256').digest()
V = hmac.HMAC(K, V, 'sha256').digest()
# loop forever until an in-range k is found
k = 0
while True:
# see RFC6979 3.2.h.2 : we take a shortcut and don't build T in
# multiple steps since the first step is always the right size for
# our purpose.
V = hmac.HMAC(K, V, 'sha256').digest()
T = V
assert len(T) >= 32
k = int.from_bytes(T, 'big')
if k > 0 and k < SECP256K1_ORDER:
break
K = hmac.HMAC(K, V+b'\x00', 'sha256').digest()
V = HMAC_K(V)
return k
def sign(privkeybytes, msg32):
"""Create Schnorr signature (BIP-Schnorr convention)."""
assert len(privkeybytes) == 32
assert len(msg32) == 32
k = nonce_function_rfc6979(
privkeybytes, msg32, algo16=b"Schnorr+SHA256 ")
ctx = CTX.ptr_for_this_thread()
# calculate R point and pubkey point, and get them in
# uncompressed/compressed formats respectively.
R = ssl.EC_POINT_new(group)
assert R
pubkey = ssl.EC_POINT_new(group)
assert pubkey
kbn = ssl.BN_bin2bn(k.to_bytes(32, 'big'), 32, None)
assert kbn
privbn = ssl.BN_bin2bn(privkeybytes, 32, None)
assert privbn
assert ssl.EC_POINT_mul(group, R, kbn, None, None, ctx)
assert ssl.EC_POINT_mul(group, pubkey, privbn, None, None, ctx)
# buffer for uncompressed R coord
Rbuf = ctypes.create_string_buffer(65)
assert 65 == ssl.EC_POINT_point2oct(
group, R, POINT_CONVERSION_UNCOMPRESSED, Rbuf, 65, ctx)
# buffer for compressed pubkey
pubkeybuf = ctypes.create_string_buffer(33)
assert 33 == ssl.EC_POINT_point2oct(
group, pubkey, POINT_CONVERSION_COMPRESSED, pubkeybuf, 33, ctx)
ssl.BN_free(kbn)
ssl.BN_free(privbn)
ssl.EC_POINT_free(R)
ssl.EC_POINT_free(pubkey)
Ry = int.from_bytes(Rbuf[33:65], 'big') # y coord
if jacobi(Ry, SECP256K1_FIELDSIZE) == -1:
k = SECP256K1_ORDER - k
rbytes = Rbuf[1:33] # x coord big-endian
e = int.from_bytes(hashlib.sha256(
rbytes + pubkeybuf + msg32).digest(), 'big')
privkey = int.from_bytes(privkeybytes, 'big')
s = (k + e*privkey) % SECP256K1_ORDER
return rbytes + s.to_bytes(32, 'big')
def getpubkey(privkeybytes, compressed=True):
assert len(privkeybytes) == 32
encoding = POINT_CONVERSION_COMPRESSED if compressed else POINT_CONVERSION_UNCOMPRESSED
ctx = CTX.ptr_for_this_thread()
pubkey = ssl.EC_POINT_new(group)
assert pubkey
privbn = ssl.BN_bin2bn(privkeybytes, 32, None)
assert privbn
assert ssl.EC_POINT_mul(group, pubkey, privbn, None, None, ctx)
assert not ssl.EC_POINT_is_at_infinity(group, pubkey)
# first call (with nullptr for buffer) gets us the size
size = ssl.EC_POINT_point2oct(group, pubkey, encoding, None, 0, ctx)
pubkeybuf = ctypes.create_string_buffer(size)
ret = ssl.EC_POINT_point2oct(group, pubkey, encoding, pubkeybuf, size, ctx)
assert ret == size
ssl.BN_free(privbn)
ssl.EC_POINT_free(pubkey)
return bytes(pubkeybuf)
if __name__ == '__main__':
# Test Schnorr implementation.
# duplicate the deterministic sig test from src/test/key_tests.cpp
private_key = bytes.fromhex(
"12b004fff7f4b69ef8650e767f18f11ede158148b425660723b9f9a66e61f747")
pubkey = getpubkey(private_key, compressed=True)
assert pubkey == bytes.fromhex(
"030b4c866585dd868a9d62348a9cd008d6a312937048fff31670e7e920cfc7a744")
def sha(b):
return hashlib.sha256(b).digest()
msg = b"Very deterministic message"
msghash = sha(sha(msg))
assert msghash == bytes.fromhex(
"5255683da567900bfd3e786ed8836a4e7763c221bf1ac20ece2a5171b9199e8a")
sig = sign(private_key, msghash)
assert sig == bytes.fromhex(
"2c56731ac2f7a7e7f11518fc7722a166b02438924ca9d8b4d1113"
"47b81d0717571846de67ad3d913a8fdf9d8f3f73161a4c48ae81c"
"b183b214765feb86e255ce")
print("ok")