feat: add GenerateRekey

src/tpre.py

@@ -22,6 +22,9 @@ sm2p256v1 = CurveFp(
     Gx=0x32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7,
     Gy=0xBC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0
 )
+
+# sec需要重新设置
+sec = 256  
  
 def multiply(a: Tuple[int, int], n: int) -> Tuple[int, int]:
     N = sm2p256v1.N
@@ -146,7 +149,7 @@ def Setup(sec: int) -> Tuple[CurveFp, Tuple[int, int],
         sm3 = Sm3() #pylint: disable=e0602
         for i in double_G:
             for j in i:
-                sm3.update(j.to_bytes())
+                sm3.update(j.to_bytes(32))
         digest = sm3.digest()
         digest = int.from_bytes(digest,'big') % sm2p256v1.P
         return digest
@@ -157,7 +160,7 @@ def Setup(sec: int) -> Tuple[CurveFp, Tuple[int, int],
         sm3 = Sm3() #pylint: disable=e0602
         for i in triple_G:
             for j in i:
-                sm3.update(j.to_bytes())
+                sm3.update(j.to_bytes(32))
         digest = sm3.digest()
         digest = int.from_bytes(digest,'big') % sm2p256v1.P
         return digest
@@ -169,8 +172,8 @@ def Setup(sec: int) -> Tuple[CurveFp, Tuple[int, int],
         sm3 = Sm3() #pylint: disable=e0602
         for i in triple_G:
             for j in i:
-                sm3.update(j.to_bytes())
+                sm3.update(j.to_bytes(32))
-        sm3.update(Zp.to_bytes())
+        sm3.update(Zp.to_bytes(32))
         digest = sm3.digest()
         digest = int.from_bytes(digest,'big') % sm2p256v1.P
         return digest
@@ -211,8 +214,80 @@ def Enc(pk: Tuple[int, int], m: int) -> Tuple[Tuple[
     capsule = enca[1]
     
     sm4_enc = Sm4Cbc(key, iv, DO_ENCRYPT) #pylint: disable=e0602
-    plain_Data = m.to_bytes()
+    plain_Data = m.to_bytes(32)
     enc_Data = sm4_enc.update(plain_Data)
     enc_Data += sm4_enc.finish()
     enc_message = (capsule, enc_Data)
-    return enc_message
+    return enc_message
+
+# GenerateRekey
+def H5(id: int, D: int) -> int:
+    sm3 = Sm3()
+    sm3.update(id.to_bytes(32))
+    sm3.update(D.to_bytes(32))
+    hash = sm3.digest()
+    hash = int.from_bytes(hash,'big') % G.P
+    return hash
+
+def H6(triple_G: Tuple[Tuple[int, int], 
+                              Tuple[int, int],
+                              Tuple[int, int]]) -> int:
+        sm3 = Sm3() #pylint: disable=e0602
+        for i in triple_G:
+            for j in i:
+                sm3.update(j.to_bytes(32))
+        hash = sm3.digest()
+        hash = int.from_bytes(hash,'big') % G.P
+        return hash
+
+def f(x: int, f_modulus: list, T: int) -> int:
+    res = 0
+    for i in range(T):
+        res += f_modulus[i] * pow(x, i)
+    return res
+
+def GenerateReKey(N: int, T: int) -> list:
+    '''
+    param: skA, pkB, N(节点总数), T(阈值)
+    return rki(0 <= i <= N-1)
+    '''
+    g_a, a = GenerateKeyPair(0, ())
+    g_b, b = GenerateKeyPair(0, ())
+    # 计算临时密钥对(x_A, X_A)
+    x_A = random.randint(0, G.P - 1)
+    X_A = multiply(g, x_A)                
+
+    # d是Bob的密钥对与临时密钥对的非交互式Diffie-Hellman密钥交换的结果
+    d = hash3((X_A, multiply(g, b), multiply(g, b * x_A)))   
+    
+    # 计算多项式系数, 确定代理节点的ID(一个点)
+    f_modulus = []
+    # 计算f0
+    f0 = (a * inv(d, G.P)) % G.P
+    f_modulus.append(f0)
+    # 计算fi(1 <= i <= T - 1)
+    for i in range(1, T):
+        f_modulus.append(random.randint(0, G.P - 1))
+
+    # 计算D
+    D = H6((X_A, multiply(g, b), multiply(g, b * a)))
+
+    # 计算KF
+    KF = []
+    for i in range(N):
+        y = random.randint(0, G.P - 1)
+        Y = multiply(g, y)
+        s_x = H5(i, D)         # id需要设置
+        r_k = f(s_x, f_modulus, T)
+        U1 = multiply(U, r_k)   
+        kFrag = (i, r_k, X_A, U1)
+        KF.append(kFrag)
+
+    return KF
+
+# 测试GenerateReky函数
+# G, g, U, hash2, hash3, hash4, KDF = Setup(sec)
+# KF = GenerateReKey(30, 20)
+# for i in KF:
+#     for j in i:
+#         print(j)