"""
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
