def Signature(M, IDA, dA, PA): a = config.get_a() b = config.get_b() n = config.get_n() Gx = config.get_Gx() Gy = config.get_Gy() ZA = get_Z(IDA, PA) # A1：置M=ZA ∥ M M_ = ZA + M # A2：计算e = Hv(M)，按本文本第1部分4.2.3和4.2.2给出的细节将e的数据类型转换为整数 e = hash_function(M_) e = bytes_to_int(bits_to_bytes(e)) r = 0 k = 0 while(r==0 or r+k==n): # A3：用随机数发生器产生随机数k ∈[1,n-1] k = PRG_function(1, n-1) # A4：计算椭圆曲线点(x1,y1)=[k]G，按本文本第1部分4.2.7给出的细节将x1的数据类型转换为整 数 x1 = ECG_k_point(k, Point(Gx, Gy)).x x1 = bytes_to_int(ele_to_bytes(x1)) # A5：计算r=(e+x1) modn，若r=0或r+k=n则返回A3 r = (e+x1)%n # A6：计算s = ((1 + dA)−1 ·(k−r·dA)) modn，若s=0则返回A3 s = ( inverse(1+dA, n)*(k-r*dA) ) % n # A7：按本文本第1部分4.2.1给出的细节将r、s的数据类型转换为字节串，消息M 的签名为(r,s)。 #Sig = Point(int_to_bytes(r, math.ceil(n/256)), int_to_bytes(s, math.ceil(n/256))) #Sig = Point(int_to_bytes(r, math.ceil(math.log(n, 2)/8)), int_to_bytes(s, math.ceil(math.log(n, 2)/8))) r = int_to_bytes(r, math.ceil(math.log(n, 2)/8)) s = int_to_bytes(s, math.ceil(math.log(n, 2)/8)) Sig = r for i in s: Sig.append(i) return Sig
def Verification(M, Sig, IDA, PA):
a = config.get_a()
b = config.get_b()
n = config.get_n()
Gx = config.get_Gx()
Gy = config.get_Gy()
ZA = get_Z(IDA, PA)
r = Sig[0:int(len(Sig)/2)]
s = Sig[int(len(Sig)/2): len(Sig)]
r = bytes_to_int(r)
s = bytes_to_int(s)
if(r<1 or r>n-1 or s<1 or s>n-1):
#print("wrong signature: r,s wrong range")
return False
M_ = ZA + M
e = hash_function(M_)
e = bytes_to_int(bits_to_bytes(e))
t = (r + s) % n
if(t == 0):
#print("wrong signature : t is 0")
return False
x1 = ECG_ele_add( ECG_k_point(s, Point(Gx, Gy)), ECG_k_point(t, PA) ).x
R = (e + x1) % n
if R!=r:
#print("wrong signature: R unequal r")
return False
return True
def get_Z(ID, PA): a = config.get_a() a = bytes_to_bits(ele_to_bytes(a)) b = config.get_b() b = bytes_to_bits(ele_to_bytes(b)) n = config.get_n() Gx = config.get_Gx() Gx_ = bytes_to_bits(ele_to_bytes(Gx)) Gy = config.get_Gy() Gy_ = bytes_to_bits(ele_to_bytes(Gy)) ID = bytes_to_bits(str_to_bytes(ID)) ENTL = int_to_bytes(math.ceil((len(ID)-2)/8)*8, 2) ENTL = bytes_to_bits(ENTL) xA = bytes_to_bits(ele_to_bytes(PA.x)) yA = bytes_to_bits(ele_to_bytes(PA.y)) ZA = hash_function(ENTL+ID+a+b+Gx_+Gy_+xA+yA) return ZA
def Verification(M, signature, IDA, PA):
a = config.get_a()
b = config.get_b()
n = config.get_n()
Gx = config.get_Gx()
Gy = config.get_Gy()
ZA = get_Z(IDA, PA)
r = signature[0:int(len(signature) / 2)]
s = signature[int(len(signature) / 2):len(signature)]
r = bytes_to_int(r)
s = bytes_to_int(s)
#print("r:", r)
# print("s:", s)
if r < 1 or r > n - 1 or s < 1 or s > n - 1:
print("r或s的范围不对，验证不通过")
return False
M_ = ZA + M
M1 = M_ + M_ # Z1+M
e1 = hash_function(M1)
e1 = bytes_to_int(bits_to_bytes(e1))
# print("e1:", e1)
# e = hash_function(M_)
# e = bytes_to_int(bits_to_bytes(e))
t = (r + s) % n
# print("t:", t)
if t == 0:
print("t等于0，验证不通过")
return False
x1 = ECG_ele_add(ECG_k_point(s, Point(Gx, Gy)), ECG_k_point(t, PA)).x
# print("x1:", x1)
R = (e1 + x1) % n
#print("R:", R)
if R == r:
# print("wrong signature: R unequal r")
# return False
print("R等于r，验证通过")
else:
print("R不等于r，验证不通过")
return True
def key_generation_2(ZA, ZB, r_self, R_self, R_opposite, d_self, P_self,
P_opposite, klen, is_send):
q = config.get_q()
a = config.get_a()
b = config.get_b()
n = config.get_n()
Gx = config.get_Gx()
Gy = config.get_Gy()
h = config.get_h()
w = math.ceil(math.ceil(math.log(n, 2)) / 2) - 1
# A4. 从R_self中取出域元素x_self，将x_self的数据类型转换为整数，计算x_self_ = 2w +(x_self&(2w−1))；
x_self = R_self.x
x_self = ele_to_int(x_self)
y_self = R_self.y
y_self = ele_to_int(y_self)
x_self_ = 2**w + (x_self & (2**w - 1))
# A5. 计算t_self = (d_self + ¯ x_self·r_self)modn
t_self = (d_self + x_self_ * r_self) % n
# A6.1 验证R_opposite是否满足椭圆曲线方程，若不满足则协商失败；
# A6.2 否则从R_opposite中取出域元素x_opposite，将x_opposite的数据类型转换为整数，计算x_opposite_ = 2w +(x_opposite&(2w−1))；
x_opposite = R_opposite.x
x_opposite = ele_to_int(x_opposite)
y_opposite = R_opposite.y
y_opposite = ele_to_int(y_opposite)
if (y_opposite**2) % q != (x_opposite**3 + a * x_opposite + b) % q:
print("keyExchange Fail: R_opposite do not satisfy the equation")
return -1
x_opposite_ = 2**w + (x_opposite & (2**w - 1))
# A7.1 计算椭圆曲线点U_self = [h·t_self](P_opposite +[x_opposite_]R_opposite) = (xU_self,yU_self)
# A7.2 若U_self是无穷远点，则A协商失败；否则将xU_self、yU_self的数据类型转换为比特串
U_self = ECG_k_point(
h * t_self,
ECG_ele_add(P_opposite, ECG_k_point(x_opposite_, R_opposite)))
xU_self = U_self.x
yU_self = U_self.y
xU_self = bytes_to_bits(ele_to_bytes(xU_self))
xU_self = remove_0b_at_beginning(xU_self)
yU_self = bytes_to_bits(ele_to_bytes(yU_self))
yU_self = remove_0b_at_beginning(yU_self)
# A8. 计算KA=KDF(xU_self ∥yU_self ∥ZA ∥ZB,klen)
k_self = KDF(xU_self + yU_self + ZA + ZB, klen)
# A9. 将R_self的坐标x_self、y_self 和R_opposite的坐标x_opposite、y_opposite的数据类型转换为比特串
# 计算S_test= Hash(0x02∥yU_self ∥Hash(xU_self ∥ZA ∥ZB ∥x_self ∥y_self ∥x_opposite ∥y_opposite))
# 并检验S_test=SB是否成立，若等式不成立则从B到A的密钥确认失败；
x_self = bytes_to_bits(ele_to_bytes(x_self))
x_self = remove_0b_at_beginning(x_self)
y_self = bytes_to_bits(ele_to_bytes(y_self))
y_self = remove_0b_at_beginning(y_self)
x_opposite = bytes_to_bits(ele_to_bytes(x_opposite))
x_opposite = remove_0b_at_beginning(x_opposite)
y_opposite = bytes_to_bits(ele_to_bytes(y_opposite))
y_opposite = remove_0b_at_beginning(y_opposite)
if is_send:
prefix = remove_0b_at_beginning(bytes_to_bits(int_to_bytes(2, 1)))
S_test = hash_function(prefix + yU_self +
hash_function(xU_self + ZA + ZB + x_opposite +
y_opposite + x_self + y_self))
else:
prefix = remove_0b_at_beginning(bytes_to_bits(int_to_bytes(3, 1)))
S_test = hash_function(prefix + yU_self +
hash_function(xU_self + ZA + ZB + x_self +
y_self + x_opposite + y_opposite))
S_test = remove_0b_at_beginning(S_test)
# A10. (选项)计算S_target= Hash(0x03∥yU_self ∥Hash(xU_self ∥ZA ∥ZB ∥x_self ∥y_self ∥x_opposite ∥y_opposite))，并将S_target发送给用户B
if is_send:
prefix = remove_0b_at_beginning(bytes_to_bits(int_to_bytes(3, 1)))
S_target = hash_function(prefix + yU_self +
hash_function(xU_self + ZA + ZB + x_opposite +
y_opposite + x_self + y_self))
else:
prefix = remove_0b_at_beginning(bytes_to_bits(int_to_bytes(2, 1)))
S_target = hash_function(prefix + yU_self +
hash_function(xU_self + ZA + ZB + x_self +
y_self + x_opposite +
y_opposite))
S_target = remove_0b_at_beginning(S_target)
return k_self, S_target, S_test, x_self_, t_self, x_opposite_, U_self
def Signature(M, IDA, dA, PA, d1, d2):
a = config.get_a()
b = config.get_b()
n = config.get_n()
Gx = config.get_Gx()
Gy = config.get_Gy()
ZA = get_Z(IDA, PA)
# A1：置M=ZA ∥ M
M_ = ZA + M
# A2：计算e = Hv(M)，按本文本第1部分4.2.3和4.2.2给出的细节将e的数据类型转换为整数
# e = hash_function(M_)
# e = bytes_to_int(bits_to_bytes(e))
M1 = M_ + M_ # Z1+M
e1 = hash_function(M1)
e1 = bytes_to_int(bits_to_bytes(e1))
# print("e1:", e1)
r = 0
k = 0
k1 = 0
k2 = 0
k3 = 0
while (r == 0) or (r + k == n):
# A3：用随机数发生器产生随机数k ∈[1,n-1]
k = PRG_function(1, n - 1)
# A4：计算椭圆曲线点(x1,y1)=[k]G，按本文本第1部分4.2.7给出的细节将x1的数据类型转换为整 数
k1 = PRG_function(1, n - 1)
print("1:随机选取k1:", k1)
k2 = PRG_function(1, n - 1)
k3 = PRG_function(1, n - 1)
Q1 = ECG_k_point(k1, Point(Gx, Gy))
print("1:计算Q1=k1*G，并把Q1发送给用户2")
print("2:Q1:", Q1)
print("2:随机选取k2，k3:", k2, k3)
Q2 = ECG_k_point(k2, Point(Gx, Gy))
print("2:计算Q2=k2*G，Q2:", Q2)
# print("k1:", k1)
# print("k2:", k2)
# print("k3:", k3)
# x1 = ECG_k_point(k1, Point(Gx, Gy)).x
# x1 = bytes_to_int(ele_to_bytes(x1))
# A5：计算r=(e+x1) modn，若r=0或r+k=n则返回A3
temp = k1 * k3 + k2
# print("temp:", temp)
rx = ECG_k_point(temp, Point(Gx, Gy)).x # (k1*k3 + k2)*G
rx = bytes_to_int(ele_to_bytes(rx))
print("2:利用k3,Q1,Q2计算得到rx:", rx)
r = (rx + e1) % n
print("2:利用rx和待签名文件的哈希值计算r")
# print("r:", r)
# r = (e+x1) % n
# A6：计算s = ((1 + dA)−1 ·(k−r·dA)) modn，若s=0则返回A3
# s = (inverse(1+dA, n)*(k-r*dA)) % n
s2 = (d2 * k3) % n
s3 = (d2 * (r + k2)) % n
print("2:根据d2,k2,k3计算得到s2,s3,并将r,s2,s3发送给用户1")
print("1:r:", r)
print("1:s2:", s2)
print("1:s3:", s3)
s = (d1 * k1 * s2 + d1 * s3 - r) % n
print("1:根据d1,k1,r,s2,s3计算s:", s)
# print("s:", s)
# A7：按本文本第1部分4.2.1给出的细节将r、s的数据类型转换为字节串，消息M 的签名为(r,s)。
#Sig = Point(int_to_bytes(r, math.ceil(n/256)), int_to_bytes(s, math.ceil(n/256)))
#Sig = Point(int_to_bytes(r, math.ceil(math.log(n, 2)/8)), int_to_bytes(s, math.ceil(math.log(n, 2)/8)))
r = int_to_bytes(r, math.ceil(math.log(n, 2) / 8))
s = int_to_bytes(s, math.ceil(math.log(n, 2) / 8))
Sig = r
for i in s:
Sig.append(i)
return Sig