ECDSA.py

"""
待验证
"""
# ECDSA椭圆曲线数字签名算法
from random import choice
from gmssl import sm3, func
# 根据SM2椭圆曲线公钥密码算法推荐曲线参数进行初始化
# 椭圆曲线方程:y^2=x^3+a*x+b
a = int('FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC', 16)
b = int('28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93', 16)
p = int('FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF', 16)
n = int('FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123', 16)
# 基点G:x||y
G = '32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0'

# 随机产生指定长度的字符串,OK


def random_string(strlen):
    letterlist = ['0', '1', '2', '3', '4', '5', '6',
                  '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F']
    strl = ""
    for i in range(strlen):
        temp = choice(letterlist)
        strl += temp
    return strl
# 椭圆曲线点计算

# 倍点,OK


def doublepoint(point, length):
    l = len(point)
    len_2 = 2*length
    if l < len_2:
        return None
    else:
        x1 = int(point[0:length], 16)
        y1 = int(point[length:len_2], 16)
        if l == len_2:
            z1 = 1
        else:
            z1 = int(point[len_2:], 16)
        T6 = (z1*z1) % p
        T2 = (y1*y1) % p
        T3 = (x1+T6) % p
        T4 = (x1-T6) % p
        T1 = (T3*T4) % p
        T3 = (y1*z1) % p
        T4 = (T2*8) % p
        T5 = (x1*T4) % p
        T1 = (T1*3) % p
        T6 = (T6*T6) % p
        T6 = (((a+3) % p)*T6) % p
        T1 = (T1+T6) % p
        z3 = (T3+T3) % p
        T3 = (T1*T1) % p
        T2 = (T2*T4) % p
        x3 = (T3-T5) % p
        if (T5 % 2) == 1:
            T4 = (T5+((T5+p) >> 1)-T3) % p
        else:
            T4 = (T5+(T5 >> 1)-T3) % p
        T1 = (T1*T4) % p
        y3 = (T1-T2) % p
        form = '%%0%dx' % length
        form = form*3
        return form % (x3, y3, z3)

# 点加,OK


def addpoint(p1, p2, length):
    len_2 = 2*length
    l1 = len(p1)
    l2 = len(p2)
    if (l1 < len_2) or (l2 < len_2):
        return None
    else:
        x1 = int(p1[0:length], 16)
        y1 = int(p1[length:len_2], 16)
        if (l1 == len_2):
            z1 = 1
        else:
            z1 = int(p1[len_2:], 16)
        x2 = int(p2[0:length], 16)
        y2 = int(p2[length:len_2], 16)
        T1 = (z1*z1) % p
        T2 = (y2*z1) % p
        T3 = (x2*T1) % p
        T1 = (T1*T2) % p
        T2 = (T3-x1) % p
        T3 = (T3+x1) % p
        T4 = (T2*T2) % p
        T1 = (T1-y1) % p
        z3 = (z1*T2) % p
        T2 = (T2*T4) % p
        T3 = (T3*T4) % p
        T5 = (T1*T1) % p
        T4 = (x1*T4) % p
        x3 = (T5-T3) % p
        T2 = (y1*T2) % p
        T3 = (T4-x3) % p
        T1 = (T1*T3) % p
        y3 = (T1-T2) % p
        form = '%%0%dx' % length
        form = form*3
        return form % (x3, y3, z3)

# Jacobian加重射影坐标转换成仿射坐标,OK


def convertJacb2Nor(point, length):
    len_2 = length*2
    x = int(point[0:length], 16)
    y = int(point[length:len_2], 16)
    z = int(point[len_2:], 16)
    z_inv = pow(z, p-2, p)
    z_invSquar = (z_inv*z_inv) % p
    z_invQube = (z_invSquar*z_inv) % p
    x_new = (x*z_invSquar) % p
    y_new = (y*z_invQube) % p
    z_new = (z*z_inv) % p
    if z_new == 1:
        form = '%%0%dx' % length
        form = form*2
        return form % (x_new, y_new)
    else:
        print("point at infinity!!!")
        return None
    '''form='%%0%dx'%length
    form=form*2
    return form%(x_new,y_new)'''

# 点乘kp   k:数字，倍数  point:点坐标


def kp(k, point, length):
    point = '%s%s' % (point, '1')
    # print("point",point)
    mask_str = '8'
    for i in range(length-1):
        mask_str += '0'
    # print("mask_str",mask_str)
    mask = int(mask_str, 16)
    temp = point
    flag = False
    for n in range(length*4):
        if (flag):
            temp = doublepoint(temp, length)
        if (k & mask) != 0:
            if (flag):
                temp = addpoint(temp, point, length)
            else:
                flag = True
                temp = point
        k = k << 1
    return convertJacb2Nor(temp, length)

# 签名算法
# 十六进制转换为byte数组


def hex_byte(msg):
    ml = len(msg)
    if ml % 2 != 0:
        msg = '0'+msg
    ml = int(len(msg)/2)
    msg_byte = []
    for i in range(ml):
        msg_byte.append(int(msg[i*2:i*2+2], 16))
    return msg_byte
# 预处理1,计算z值


def pre1(PA):
    data = '001031323334353637383132333435363738'
    data += str(a)
    data += str(b)
    data += QA
    data += PA
    # print("data",data)
    data_byte = hex_byte(data)
    return sm3.sm3_hash(data_byte)
# 预处理2,得到杂凑值H,z：z值  m:消息


def pre2(z, m):
    data = z+m
    data_byte = hex_byte(data)
    return sm3.sm3_hash(data_byte)
# 生成签名，E:消息的hash值，dA:签名者的私钥，K：随机数


def sign(E, dA, K, length, hexstr=0):
    if hexstr:
        e = int(E, 16)
    else:
        E = E.encode('utf-8')
        E = E.hex()
        e = int(E, 16)
    d = int(dA, 16)
    k = int(K, 16)
    p1 = kp(k, QA, length)
    x = int(p1[0:length], 16)
    R = ((e+x) % n)
    if R == 0 or R+k == n:
        return None
    d_1 = pow(d+1, n-2, n)
    S = (d_1*(k+R)-R) % n
    if S == 0:
        return None
    else:
        return '%064x%064x' % (R, S)
# 验证签名,sign：签名R||S,E:消息的hash值，PA：公钥


def verify(sign, E, PA, length):
    r = int(sign[0:length], 16)
    s = int(sign[length:2*length], 16)
    e = int(E, 16)
    t = (r+s) % n
    if t == 0:
        return None
    p1 = kp(s, QA, length)
    p2 = kp(t, PA, length)
    if p1 == p2:
        p1 = '%s%s' % (p1, 1)
        p1 = doublepoint(p1, length)
    else:
        p1 = '%s%s' % (p1, 1)
        p1 = addpoint(p1, p2, length)
        p1 = convertJacb2Nor(p1, length)
    x = int(p1[0:length], 16)
    return (r == ((e+x) % n))


if __name__ == '__main__':
    # 私钥dA
    dA = random_string(64)
    # 公钥QA=dA*G
    QA = kp(int(dA, 16), G, 64)
    # k:随机数
    k = random_string(64)
    Pa = kp(int(dA, 16), QA, 64)
    z1 = pre1(Pa)
    m = '665165adbcfe5'
    hash_M = pre2(z1, m)
    sig = sign(hash_M, dA, k, 64, 1)
    print("sig:", sig)
    print("verify:", verify(sig, hash_M, Pa, 64))