def sign(sk, m, p, g, q):
r = randRelPrime(q)
s1 = modExp(g, r, p) % q
rI = multInv(r, q)
s2 = rI * (m + sk * s1) % q
return (s1, s2)
def verify(pk, m, s, p, q, g):
(s1, s2) = s
s2I = multInv(s2, q)
pks1 = modExp(pk, s1, p)
gm = modExp(g, m, p)
s1N = modExp(gm * pks1, s2I, p) % q
if (s1 == s1N):
return 1
else:
return 0
def keyGen(k):
p = 0
q = 0
while (p == q):
p = randPrime(int(k / 2))
q = randPrime(int(k / 2))
print("Found Prime p ", p)
print("Found Prime q ", q)
n = p * q
print("Calculate n ", n)
order = (p - 1) * (q - 1)
print("Calculate order ", order)
e = randRelPrime(order)
print("Calculate public key value e ", e)
d = multInv(e, order)
print("Calculate private key value d ", d)
pk = (n, e)
sk = (n, d)
return (pk, sk)
from RSA import keyGen, enc, dec, sign, verify
from helper import multInv
(pk, sk) = keyGen(10)
print("public key", pk)
print("private key", sk)
(n, e) = pk
m = 10
b = 5
print("signature of m should be " + str(sign(sk, m)))
blindsign = m * pow(b, e, n) % n
print("Blinded message " + str(blindsign))
sb = sign(sk, blindsign)
print("signed blind msg" + str(sb))
s = sb * multInv(b, n) % n
print("unblinded signature" + str(s))
print(verify(pk, m, s))
for i in range(2, 20):
print("IsPrime:", i, helper.isPrime(i, 64))
for i in range(2, 100):
result = helper.isPrime(i, 64)
if (result):
print(i)
print()
print("gcd(7,15)", helper.gcd(7, 15))
print("gcd(9,15)", helper.gcd(9, 15))
print("gcd(10,15)", helper.gcd(10, 15))
print("gcd(11,15)", helper.gcd(11, 15))
print()
print("multInv(7,1)", helper.multInv(7, 11))
print("multInv(1,11)", helper.multInv(1, 11))
print("multInv(3,11)", helper.multInv(3, 11))
print("multInv(8,11)", helper.multInv(8, 11))
print()
print("modexp(2,7,11)", helper.modExp(2, 7, 11))
print("modexp(5,17,11)", helper.modExp(5, 17, 11))
print("modexp(8,3,11)", helper.modExp(8, 3, 11))
print("modexp(4,8,11)", helper.modExp(4, 8, 11))
print("randprime", helper.randPrime(8))
print("randprime", helper.randPrime(40))
print("randprime", helper.randPrime(3))
print("randrelprime", helper.randRelPrime(9))
def dec(sk, c, p, q, g):
(a, b) = c
s = modExp(a, sk, p)
m = (b * multInv(s, p)) % p
#m = b*(modExp(a,multInv(sk,p),p)) % p
return m