def egVerification(p, m, a, r, s, y):
if r < 1 or r >= p:
return False
v1 = (expm(p, y, r) * expm(p, r, s)) % p
v2 = expm(p, a, m)
return v1 == v2
def egEnc(p, a, y, m):
if m < 0 or m >= p:
raise Exception('m is outside range: 0 <= m < p')
k = randbelow(p - 1)
while k < 1:
k = randbelow(p - 1)
c1 = expm(p, a, k)
c2 = m * expm(p, y, k) % p
return (c1, c2)
def order(p, f, a):
t = p - 1
for pi in f:
if expm(p, a, t // pi) == 1:
t = t // pi
return t
def egKey(s):
p, a = pair(s)
x = randbelow(p - 1)
while x < 1:
x = randbelow(p - 1)
y = expm(p, a, x)
return (p, a, x, y)
def egSignature(p, m, a, x):
# if m < 0 or m >= p - 1:
# raise Exception('m is outside range: 0 <= m < p-1')
k = randbelow(p - 1)
while k < 1 or gcd(k, p - 1) != 1:
k = randbelow(p - 1)
r = expm(p, a, k)
s = invm(p - 1, k) * (m - x * r) % (p - 1)
return (r, s)
def egDec(p, x, c1, c2):
return expm(p, c1, (p - 1 - x)) * c2 % p
def log(p, a, x):
i = 0
while expm(p, a, i) != x:
i += 1
return i
def rsaAppValidate(n, s, e, m):
m = hashlib.sha1(str(m).encode('utf-8'))
return int(m.hexdigest(), 16) == expm(n, s, e)
def rsaAppSignature(n, d, m):
m = hashlib.sha1(str(m).encode('utf-8'))
sha1 = int(m.hexdigest(), 16)
return expm(n, sha1, d)
def rsaRecVerification(m, n, s, e, k):
return okSimple(len(bin(m)[2:]), k, expm(n, s, e))
def rsaRecRecovery(n, s, e, k):
x = expm(n, s, e)
m_len = len(bin(x)[2:]) - k
return removeSimple(m_len, k, x)
def rsaRecSignature(n, d, m, k):
m_len = len(bin(m)[2:])
return expm(n, addSimple(m_len, k, m), d)
