feat: finish ecc add and mul

src/tpre.py

@@ -1,2 +1,158 @@
 from gmssl import * #pylint: disable = e0401 
-testtest
+from typing import Tuple, Callable
+
+# 生成密钥对模块
+class CurveFp:
+    def __init__(self, A, B, P, N, Gx, Gy, name):
+        self.A = A
+        self.B = B
+        self.P = P
+        self.N = N
+        self.Gx = Gx
+        self.Gy = Gy
+        self.name = name
+ 
+sm2p256v1 = CurveFp(
+    name="sm2p256v1",
+    A=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC,
+    B=0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93,
+    P=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF,
+    N=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123,
+    Gx=0x32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7,
+    Gy=0xBC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0
+)
+ 
+def multiply(a: Tuple[int, int], n: int) -> Tuple[int, int]:
+    N = sm2p256v1.N
+    A = sm2p256v1.A
+    P = sm2p256v1.P 
+    return fromJacobian(jacobianMultiply(toJacobian(a), n, N, A, P), P)
+
+def add(a: Tuple[int, int], b: Tuple[int, int], A: int, P: int) -> Tuple[int, int]:
+    A = sm2p256v1.A
+    P = sm2p256v1.P
+    return fromJacobian(jacobianAdd(toJacobian(a), toJacobian(b), A, P), P)
+ 
+def inv(a: int, n: int) -> int:
+    if a == 0:
+        return 0
+    lm, hm = 1, 0
+    low, high = a % n, n
+    while low > 1:
+        r = high // low
+        nm, new = hm - lm * r, high - low * r
+        lm, low, hm, high = nm, new, lm, low
+    return lm % n
+ 
+def toJacobian(Xp_Yp: Tuple[int, int]) -> Tuple[int, int, int]:
+    Xp, Yp = Xp_Yp
+    return (Xp, Yp, 1)
+
+def fromJacobian(Xp_Yp_Zp: Tuple[int, int, int], P: int) -> Tuple[int, int]:
+    Xp, Yp, Zp = Xp_Yp_Zp
+    z = inv(Zp, P)
+    return ((Xp * z ** 2) % P, (Yp * z ** 3) % P)
+ 
+def jacobianDouble(Xp_Yp_Zp: Tuple[int, int, int], A: int, P: int) -> Tuple[int, int, int]:
+    Xp, Yp, Zp = Xp_Yp_Zp
+    if not Yp:
+        return (0, 0, 0)
+    ysq = (Yp ** 2) % P
+    S = (4 * Xp * ysq) % P
+    M = (3 * Xp ** 2 + A * Zp ** 4) % P
+    nx = (M ** 2 - 2 * S) % P
+    ny = (M * (S - nx) - 8 * ysq ** 2) % P
+    nz = (2 * Yp * Zp) % P
+    return (nx, ny, nz)
+ 
+def jacobianAdd(
+    Xp_Yp_Zp: Tuple[int, int, int], 
+    Xq_Yq_Zq: Tuple[int, int, int], 
+    A: int, 
+    P: int
+) -> Tuple[int, int, int]:
+    Xp, Yp, Zp = Xp_Yp_Zp
+    Xq, Yq, Zq = Xq_Yq_Zq
+    if not Yp:
+        return (Xq, Yq, Zq)
+    if not Yq:
+        return (Xp, Yp, Zp)
+    U1 = (Xp * Zq ** 2) % P
+    U2 = (Xq * Zp ** 2) % P
+    S1 = (Yp * Zq ** 3) % P
+    S2 = (Yq * Zp ** 3) % P
+    if U1 == U2:
+        if S1 != S2:
+            return (0, 0, 1)
+        return jacobianDouble((Xp, Yp, Zp), A, P)
+    H = U2 - U1
+    R = S2 - S1
+    H2 = (H * H) % P
+    H3 = (H * H2) % P
+    U1H2 = (U1 * H2) % P
+    nx = (R ** 2 - H3 - 2 * U1H2) % P
+    ny = (R * (U1H2 - nx) - S1 * H3) % P
+    nz = (H * Zp * Zq) % P
+    return (nx, ny, nz)
+ 
+def jacobianMultiply(
+    Xp_Yp_Zp: Tuple[int, int, int], 
+    n: int, 
+    N: int, 
+    A: int, 
+    P: int
+    ) -> Tuple[int, int, int]:
+
+    Xp, Yp, Zp = Xp_Yp_Zp
+    if Yp == 0 or n == 0:
+        return (0, 0, 1)
+    if n == 1:
+        return (Xp, Yp, Zp)
+    if n < 0 or n >= N:
+        return jacobianMultiply((Xp, Yp, Zp), n % N, N, A, P)
+    if (n % 2) == 0:
+        return jacobianDouble(jacobianMultiply((Xp, Yp, Zp), n // 2, N, A, P), A, P)
+    if (n % 2) == 1:
+        return jacobianAdd(jacobianDouble(jacobianMultiply((Xp, Yp, Zp), n // 2, N, A, P), A, P), (Xp, Yp, Zp), A, P)
+    raise ValueError("jacobian Multiply error")
+        
+def Setup(sec: int) -> Tuple[int, int, int, Callable, Callable, Callable, Callable]:
+    '''
+    params:
+    sec: an init safety param
+    
+    return:
+    G: 
+    
+    '''
+    
+    return G, g, U, hash2, hash3, hash4, KDF
+
+def GenerateKeyPair(
+    lamda_parma: int, 
+    public_params: tuple
+    ) -> Tuple[Tuple[bytes, bytes], bytes]:
+    '''
+    params: 
+    lamda_param: an init safety param 
+    public_params: curve params
+    
+    return:
+    public_key, secret_key
+    '''
+    sm2 = Sm2Key()
+    sm2.generate_key()
+    public_key_x = bytes(sm2.public_key.x)
+    public_key_y = bytes(sm2.public_key.y)
+    public_key = (public_key_x, public_key_y)
+    secret_key = bytes(sm2.private_key)
+    print(private_key)
+    
+    
+    
+    
+    return public_key, secret_key
+    
+
+def Enc(pk, m):
+    pass