sm2签名分析

Prompt

import secrets default_table = { 'n': 'FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123', 'p': 'FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF', 'g': '32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7' 'bc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0', 'a': 'FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC', 'b': '28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93', } class Crypt(): def __init__(self, private_key, public_key, mode=0): self.private_key = private_key if public_key.startswith("04"): self.public_key = public_key[2:] else: self.public_key = public_key self.para_len = len(default_table['n']) self.ecc_a3 = ( int(default_table['a'], base=16) + 3) % int(default_table['p'], base=16) assert mode in (0, 1), 'mode must be one of (0, 1)' self.mode = mode def _kg(self, k, Point): # kP运算 if k == 0: return None#无穷远点 Point = '%s%s' % (Point, '1') mask_str = '8' for i in range(self.para_len - 1): mask_str += '0' mask = int(mask_str, 16) Temp = Point flag = False for n in range(self.para_len * 4): if (flag): Temp = self._double_point(Temp) if (k & mask) != 0: if (flag): Temp = self._add_point(Temp, Point) else: flag = True Temp = Point k = k << 1 return self._convert_jacb_to_nor(Temp) def _double_point(self, Point): # 倍点 if Point is None: return None l = len(Point) len_2 = 2 * self.para_len if l < self.para_len * 2: return None else: x1 = int(Point[0:self.para_len], 16) y1 = int(Point[self.para_len:len_2], 16) if l == len_2: z1 = 1 else: z1 = int(Point[len_2:], 16) T6 = (z1 * z1) % int(default_table['p'], base=16) T2 = (y1 * y1) % int(default_table['p'], base=16) T3 = (x1 + T6) % int(default_table['p'], base=16) T4 = (x1 - T6) % int(default_table['p'], base=16) T1 = (T3 * T4) % int(default_table['p'], base=16) T3 = (y1 * z1) % int(default_table['p'], base=16) T4 = (T2 * 8) % int(default_table['p'], base=16) T5 = (x1 * T4) % int(default_table['p'], base=16) T1 = (T1 * 3) % int(default_table['p'], base=16) T6 = (T6 * T6) % int(default_table['p'], base=16) T6 = (self.ecc_a3 * T6) % int(default_table['p'], base=16) T1 = (T1 + T6) % int(default_table['p'], base=16) z3 = (T3 + T3) % int(default_table['p'], base=16) T3 = (T1 * T1) % int(default_table['p'], base=16) T2 = (T2 * T4) % int(default_table['p'], base=16) x3 = (T3 - T5) % int(default_table['p'], base=16) if (T5 % 2) == 1: T4 = (T5 + ((T5 + int(default_table['p'], base=16)) >> 1) - T3) % int( default_table['p'], base=16) else: T4 = (T5 + (T5 >> 1) - T3) % int(default_table['p'], base=16) T1 = (T1 * T4) % int(default_table['p'], base=16) y3 = (T1 - T2) % int(default_table['p'], base=16) form = '%%0%dx' % self.para_len form = form * 3 return form % (x3, y3, z3) def _add_point(self, P1, P2): # 点加函数，P2点为仿射坐标即z=1，P1为Jacobian加重射影坐标 if P1 is None: return P2 if P2 is None: return P1 len_2 = 2 * self.para_len l1 = len(P1) l2 = len(P2) if (l1 < len_2) or (l2 < len_2): return None else: X1 = int(P1[0:self.para_len], 16) Y1 = int(P1[self.para_len:len_2], 16) if (l1 == len_2): Z1 = 1 else: Z1 = int(P1[len_2:], 16) x2 = int(P2[0:self.para_len], 16) y2 = int(P2[self.para_len:len_2], 16) T1 = (Z1 * Z1) % int(default_table['p'], base=16) T2 = (y2 * Z1) % int(default_table['p'], base=16) T3 = (x2 * T1) % int(default_table['p'], base=16) T1 = (T1 * T2) % int(default_table['p'], base=16) T2 = (T3 - X1) % int(default_table['p'], base=16) T3 = (T3 + X1) % int(default_table['p'], base=16) T4 = (T2 * T2) % int(default_table['p'], base=16) T1 = (T1 - Y1) % int(default_table['p'], base=16) Z3 = (Z1 * T2) % int(default_table['p'], base=16) T2 = (T2 * T4) % int(default_table['p'], base=16) T3 = (T3 * T4) % int(default_table['p'], base=16) T5 = (T1 * T1) % int(default_table['p'], base=16) T4 = (X1 * T4) % int(default_table['p'], base=16) X3 = (T5 - T3) % int(default_table['p'], base=16) T2 = (Y1 * T2) % int(default_table['p'], base=16) T3 = (T4 - X3) % int(default_table['p'], base=16) T1 = (T1 * T3) % int(default_table['p'], base=16) Y3 = (T1 - T2) % int(default_table['p'], base=16) form = '%%0%dx' % self.para_len form = form * 3 return form % (X3, Y3, Z3) def _convert_jacb_to_nor(self, Point): # Jacobian加重射影坐标转换成仿射坐标 if Point is None: return None len_2 = 2 * self.para_len x = int(Point[0:self.para_len], 16) y = int(Point[self.para_len:len_2], 16) z = int(Point[len_2:], 16) z_inv = pow( z, int(default_table['p'], base=16) - 2, int(default_table['p'], base=16)) z_invSquar = (z_inv * z_inv) % int(default_table['p'], base=16) z_invQube = (z_invSquar * z_inv) % int(default_table['p'], base=16) x_new = (x * z_invSquar) % int(default_table['p'], base=16) y_new = (y * z_invQube) % int(default_table['p'], base=16) z_new = (z * z_inv) % int(default_table['p'], base=16) if z_new == 1: form = '%%0%dx' % self.para_len form = form * 2 return form % (x_new, y_new) else: return None def verify(self, Sign, data): if Sign is None or Sign == '': return None r = int(Sign[0:self.para_len], 16) s = int(Sign[self.para_len:2*self.para_len], 16) e = int(data.hex(), 16) # 参数合法性 if not (1 <= r < int(default_table['n'], base=16) and 1 <= s < int(default_table['n'], base=16)): return False t = r + s if t == 0: return False else: t = t % int(default_table['n'], base=16) if self.public_key is None or self.public_key == '': return None P1 = self._kg(s, default_table['g']) if P1 is None: return False P2 = self._kg(t, self.public_key) if P1 == P2: P1 = '%s%s' % (P1, 1) P1 = self._double_point(P1) else: P1 = '%s%s' % (P1, 1) P1 = self._add_point(P1, P2) P1 = self._convert_jacb_to_nor(P1) x = int(P1[0:self.para_len], 16) return r == ((e + x) % int(default_table['n'], base=16)) def sign(self, data): k = secrets.randbelow(int(default_table['n'], 16) - 1) + 1 if not (1 <= k <= int(default_table['n'], base=16)- 1): return None E = data.hex() e = int(E, 16) if self.private_key is None or self.private_key == '': return None d = int(self.private_key, 16) P1 = self._kg(k, default_table['g']) x = int(P1[0:self.para_len], 16) A = ((e + x) % int(default_table['n'], base=16)) if A == 0 or A + k == int(default_table['n'], base=16): return None d_1 = pow( d+1, int(default_table['n'], base=16) - 2, int(default_table['n'], base=16)) B = (d_1*(k + A) - A) % int(default_table['n'], base=16) if B == 0: return None else: return '%064x%064x' % (A, B) if __name__ == '__main__': crypt = Crypt( # 公钥格式为64字节的16进制字符串 public_key='', # 私钥格式为32字节的16进制字符串 private_key='' ) data = '919535c3ef53d3fa359196b5229c4bbb386ce209f5905d33fc7bcdff46ae27c2' sign = crypt.sign(bytes.fromhex(data)) print(sign) verify = crypt.verify(sign,bytes.fromhex(data)) print(verify)