Python实现国密SM2密钥分配加解密、数字签名和SM3杂凑值

""" ALi 2017.12.23 for python3 """ """ 国家密码管理局推荐的曲线参数 椭圆曲线方程:y^2 = x^3+a*x+b 曲线参数: p=FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 FFFFFFFF FFFFFFFF a=FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 FFFFFFFF FFFFFFFC b=28E9FA9E 9D9F5E34 4D5A9E4B CF6509A7 F39789F5 15AB8F92 DDBCBD41 4D940E93 n=FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF 7203DF6B 21C6052B 53BBF409 39D54123 Gx=32C4AE2C 1F198119 5F990446 6A39C994 8FE30BBF F2660BE1 715A4589 334C74C7 Gy=BC3736A2 F4F6779C 59BDCEE3 6B692153 D0A9877C C62A4740 02DF32E5 2139F0A0 """ import random import math def SM2_Create(a, p, n, G):#SM2密钥对的生成 d_B = random.randint(1, n-2) P_B = SM2_Mulyipoint(d_B, G, a, p) return [d_B, P_B] def SM2_Encrypt(a, b, p, n, G, P_B, M):#加密 h = int((p**0.5+1)**2/n) klen = len(M)*8 t = "0" b = True while int(t, 2) == 0: k = random.randint(1, n-1) C_1 = SM2_Mulyipoint(k, G, a, p) C_1 = "00000100"+bin(C_1[0]).replace('0b', '').rjust(256, '0')+bin(C_1[1]).replace('0b', '').rjust(256, '0') S = SM2_Mulyipoint(h, P_B, a, p) if S == [float('inf'), float('inf')]: print("ERROR") C = "0000" break else: b = False [x_2, y_2] = SM2_Mulyipoint(k, P_B, a, p) t = SM2_KDF(bin(x_2).replace('0b', '').rjust(256, '0')+bin(y_2).replace('0b', '').rjust(256, '0'), klen) if b == False: M = "".join([bin(ord(i)).replace('0b', '').rjust(8, '0') for i in M]) C_2 = bin(int(M, 2) ^ int(t, 2)).replace('0b', '').rjust(klen, '0') C_3 = SM3(bin(x_2).replace('0b', '').rjust(256, '0')+M+bin(y_2).replace('0b', '').rjust(256, '0')) C = C_1+C_2+C_3 return C def SM2_Decrypt(a, b, p, n, G, d_B, C):#解密 h = int((p**0.5+1)**2/n) klen = len(C)-520-256 C_1 = C[0:520] C_2 = C[520:520+klen] C_3 = C[520+klen:776+klen] x_1 = int(C_1[8:264], 2) y_1 = int(C_1[264:520], 2) M = "\0" L = y_1**2%p R = (x_1**3+a*x_1+b)%p if L == R: S = SM2_Mulyipoint(h, [x_1, y_1], a, p) if S != [float('inf'), float('inf')]: [x_2, y_2] = SM2_Mulyipoint(d_B, [x_1, y_1], a, p) t = SM2_KDF(bin(x_2).replace('0b', '').rjust(256, '0')+bin(y_2).replace('0b', '').rjust(256, '0'), klen) if int(t, 2) != 0: M = bin(int(C_2, 2) ^ int(t, 2)).replace('0b', '').rjust(klen, '0') u = SM3(bin(x_2).replace('0b', '').rjust(256, '0')+M+bin(y_2).replace('0b', '').rjust(256, '0')) if u == C_3: M = "".join([chr(i) for i in [int(M[j:j+8], 2) for j in range(0, len(M), 8)]]) else: print("ERROR") else: print("ERROR") else: print("ERROR") else: print("ERROR") return M def SM2_KDF(Z, klen):#KDF c = "00000000000000000000000000000001" H = [] i = 0 while i < math.ceil(klen/256): H.append(SM3(Z+c)) c = bin((int(c, 2)+1)).replace('0b', '').rjust(32, '0') i += 1 if klen/32-math.ceil(klen/256) == 0: H_H = H[math.ceil(klen/256)-1] else: H_H = H[math.ceil(klen/256)-1][:klen-256*math.floor(klen/256)] H.pop() K = "" i = 0 while i < len(H): K = K+H[i] i += 1 K = K+H_H return K def SM2_Mulyipoint(k, P, a, p):#多倍点运算 k_b = bin(k).replace('0b', '')#按2^i分层逐层运算 i = len(k_b)-1 R = P if i > 0: k = k-2**i while i > 0: R = SM2_Pluspoint(R, R, a, p) i -= 1 if k > 0: R = SM2_Pluspoint(R, SM2_Mulyipoint(k, P, a, p), a, p) return R def SM2_Pluspoint(P, Q, a, p):#双倍点运算 if (math.isinf(P[0]) or math.isinf(P[1])) and (~math.isinf(Q[0]) and ~math.isinf(Q[1])):#OP = P R = Q elif (~math.isinf(P[0]) and ~math.isinf(P[1])) and (math.isinf(Q[0]) or math.isinf(Q[1])):#PO = P R = P elif (math.isinf(P[0]) or math.isinf(P[1])) and (math.isinf(Q[0]) or math.isinf(Q[1])):#OO = O R = [float('inf'), float('inf')] else: if P != Q: l = SM2__Mod_Decimal(Q[1]-P[1], Q[0]-P[0], p) else: l = SM2__Mod_Decimal(3*P[0]**2+a, 2*P[1], p) x = SM2_Mod(l**2-P[0]-Q[0], p) y = SM2_Mod (l*(P[0]-x)-P[1], p) R = [x, y] return R def SM2_Mod(a, b):#摸运算 if math.isinf(a): return float('inf') else: return a%b def SM2__Mod_Decimal(n, d, b):#小数的模运算 if d == 0: x = float('inf') elif n == 0: x = 0 else: a = bin(b-2).replace('0b', '') y = 1 i = 0 while i < len(a):#n/d = x mod b => x = n*d^(b-2) mod b y = (y**2)%b#快速指数运算 if a[i] == '1': y = (y*d)%b i += 1 x = (y*n)%b return x def SM3(m):#SM3杂凑算法，m是消息 m= SM3_Fill(m) V_n = SM3_Iterate(m) return V_n def SM3_Fill(m):#填充 l = len(m)#m转换成的01串的长度 k = (448-l-1)%512#k满足l+1+k = 448 mod 512的最小非负整数 l_b = bin(l).replace('0b', '').rjust(64, '0')#l的64位二进制表示 m = m+'1'+'0'*k+l_b#在消息后添加1个1、k个0和64位的l return m def SM3_Iterate(m):#迭代 IV = 0x7380166f4914b2b9172442d7da8a0600a96f30bc163138aae38dee4db0fb0e4e#初始值 IV_b = bin(IV).replace('0b', '').rjust(256, '0')#初始值转换为01串 n = int(len(m)/512)#n = (l+k+65)/512 B = [m[i:i+512] for i in range(0, 512*n, 512)]#填充后的消息按512比特分组B(0)B(1)...B(n-1) V = [IV_b]#V(0)的初值为IV i = 0 while i < n:#0 to n-1 V.append(SM3_CF(V[i], B[i]))#V(i+1) = CF(V(i), B(i)) CF是压缩函数 i += 1 return V[n] def SM3_W(B):#消息拓展 W = [B[i:i+32] for i in range(0, 512, 32)]#B(i)划分为16个字W(0)W(1)...W(15) i = 16 while i < 68:#j = 16 to 63 W.append(SM3_NOR(SM3_NOR(SM3_P1(SM3_NOR(SM3_NOR(W[i-16], W[i-9]), SM3_ROL(W[i-3], 15))), SM3_ROL(W[i-13], 7)), W[i-6]))#W(j) = P1(W(j-16)^W(j-9)^(W(j-3)<<<15))^(W(j-13)<<<7)^W(j-6) i += 1 W_W = [] i = 0 while i < 64:#j = 0 to 63 W_W.append(SM3_NOR(W[i], W[i+4]))#W'(j) = W(j)^W(j+4) i += 1 return [W, W_W] def SM3_CF(V, B):#压缩函数V(i+1) = CF(V(i), B(i)) T_0_15 = 0x79cc4519 T_16_63 = 0x7a879d8a T_0_15_b = bin(T_0_15).replace('0b', '').rjust(32, '0') T_16_63_b = bin(T_16_63).replace('0b', '').rjust(32, '0') [W, W_W] = SM3_W(B) A = V[0:32] B = V[32:64] C = V[64:96] D = V[96:128] E = V[128:160] F = V[160:192] G = V[192:224] H = V[224:256]#ABCDEFGH = V(i) SS1 = "00000000000000000000000000000000" SS2 = "00000000000000000000000000000000" TT1 = "00000000000000000000000000000000" TT2 = "00000000000000000000000000000000" j = 0 while j < 64:#j = 0 to 63 if 0 <= j <= 15:#T_j T_b = T_0_15_b else: T_b = T_16_63_b SS1 = SM3_ROL(SM3_PLUS(SM3_PLUS(SM3_ROL(A, 12), E), SM3_ROL(T_b, j)), 7)#SS1 = ((A<<<12)+E(T(j)<<<j))<<<7 SS2 = SM3_NOR(SS1, SM3_ROL(A, 12))#SS2 = SS1^(A<<<12) TT1 = SM3_PLUS(SM3_PLUS(SM3_PLUS(SM3_FF(A, B, C, j), D), SS2), W_W[j])#TT1 = FF_j(A, b, C)+D+SS2+W'(j) TT2 = SM3_PLUS(SM3_PLUS(SM3_PLUS(SM3_GG(E, F, G, j), H), SS1), W[j])#TT2 = GG_j(E. F, G)+H+SS1+W(j) D = C C = SM3_ROL(B, 9)#C = B<<<9 B = A A = TT1 H = G G = SM3_ROL(F, 19)#G = F<<<19 F = E E = SM3_P0(TT2)#E = P0(TT2) j += 1 V = bin(int(A+B+C+D+E+F+G+H, 2) ^ int(V, 2)).replace('0b', '').rjust(256, '0') return V#V(i+1) = ABCDEFGH^V(i) def SM3_FF(X, Y, Z, j):#FF_j(X, Y, Z) if 0 <= j <=15: R = SM3_NOR(SM3_NOR(X, Y), Z) else: R = SM3_OR(SM3_OR(SM3_AND(X, Y), SM3_AND(X, Z)), SM3_AND(Y, Z)) return R def SM3_GG(X, Y, Z, j):#GG_j(X, Y, Z) if 0 <= j <=15: R = SM3_NOR(SM3_NOR(X, Y), Z) else: R = SM3_OR(SM3_AND(X, Y), SM3_AND(SM3_NOT(X), Z)) return R def SM3_P0(X):#P0(X) return SM3_NOR(SM3_NOR(X, SM3_ROL(X, 9)), SM3_ROL(X, 17)) def SM3_P1(X):#P1(X) return SM3_NOR(SM3_NOR(X, SM3_ROL(X, 15)), SM3_ROL(X, 23)) def SM3_ROL(X, n):#<<< return (X+X[0:n%32])[n%32:32+n%32] def SM3_PLUS(X, Y):#+ return bin((int(X, 2)+int(Y, 2))%4294967296).replace('0b', '').rjust(32, '0') def SM3_NOR(X, Y):#^ return bin(int(X, 2) ^ int(Y, 2)).replace('0b', '').rjust(32, '0') def SM3_AND(X, Y):#∧ return bin(int(X, 2) & int(Y, 2)).replace('0b', '').rjust(32, '0') def SM3_O