def elGamalEncrypt(A, b, r_s, p_s, message):
B = modexp(r_s, b, p_s)
encrypted = modexp(message * modexp(A, b, p_s), 1, p_s)
print("[B, encrypted]")
print([B, encrypted])
return ([B, encrypted])
def elGamalDecrypt(B, a, p_s, encrypted):
R = modexp(B, a, p_s)
invR = multinv(R, p_s)
decrypted = modexp(encrypted * invR, 1, p_s)
print("[decrypted]")
print([decrypted])
return ([decrypted])
def request(a, m_s, N_s, prime1, prime2, e_s, r_r, p_r):
A = modexp(r_r, a, p_r)
d = multinv(e_s, (prime1 - 1) * (prime2 - 1))
signature = modexp(m_s, d, N_s)
print("[A, Ns, es, ms^ds] =")
print([A, N_s, e_s, signature])
return ([A, N_s, e_s, signature])
def probableprime(n, t):
random.seed()
for _ in range(t): # t tries
a = random.randint(2, n - 1)
assert a >= 2
assert a < n
x = modexp(a, n - 1, n)
if 1 != x:
return False
return True
def primality(N):
'''
Input: Positive integer N
Output: yes/no
'''
# Pick a positive integer a < N at random
random.seed(time.time())
a = random.randint(1, N - 1)
if modexp.modexp(a, N - 1, N) == 1:
return True
else:
return False
def primality2(N):
'''
Input: Positive integer N
Output: yes/no
'''
# Pick a positive integer a1, a2, ..., ak < N at random
k = 8
for i in range(8):
random.seed(time.time())
a = random.randint(1, N - 1)
if modexp.modexp(a, N - 1, N) == 1:
continue
else:
return False
return True
def testNumber(a,n):
if isprime(n):
return True
res = modexp(a, n-1, n)
return res != 1
def checkDigitalSignature(A, N, e, S, m_s):
signature = modexp(S, e, N)
if signature != m_s:
print("Signature check fails.")
else:
print("Signature check success.")