In your favorite language (preferable in Python) create the following functions: 1. MRT →Use Miller-Rabin Primality Test to choose prime number with s=512 bits and check the primality test.
i dont know what im missing, project is due in a couple of hours and my output is just a blinking cursor. please help me. below is my source code and attatched is my project. please please help!
source code:
import random
def powMod_sm(base, exp, n):
exp_b=bin(exp)
value=base
for i in range(3, len(exp_b)):
value=(value**2)%n
if exp_b[i:i+1]=='1: ':
value = (value * base)% n
return value
# using the euclidean
def computeGCD(x, y):
while y:
x, y = y, x % y
return x
#Extended euclidean Algorithm method to calculate gcd and get the coefficient
def extendedGCD(a, b):
if a == 0:
return b, 0, 1
gcd, x1, y1 = extendedGCD(b % a, a)
x = y1 - (b // a)* x1
y = x1
return gcd, x, y
# calculating the modular inverse using EEA
def mod_Inv(b, n):
gcd, _, t = extendedGCD(n, b)
if gcd==1:
i = t % n
elif gcd!=1:
print("Inverse is undefined")
return i
#miller-rabin Primality test
def mrt(p):
if p == 2 or p == 3:
return True
if p<=1 or p%2==0:
return False
p1=p-1
t=15
u=0
r=p1
while r%2==0:
u=u+1
r=r/2
for i in range (1,t):
a=random.randint(2,p-2)
z=powMod_sm(a, int(r), p)
if z!=1 and z!=p1:
j=1
while j<u and z!=p1:
z=powMod_sm(z, 2, p)
if z==1:
return False
j+=1
if z!=p1:
return False
return True
# generating a random prime number given the bit length
def gen_prime(len):
n=random.getrandbits(len)
n|=(1<<len-1)|1
while not mrt(n):
n=random.getrandbits(len)
n|=(1<< len - 1)|1
return n
# using the random prime number generated above
# i will create a public and private rsa key
def rsa_key(p,q):
n=p*q
phi_n=(p-1) * (q-1)
for i in range (2,124):
if computeGCD(i, phi_n)==1:
e=i
break
d=mod_Inv(e,phi_n)
return n,e,d
# running main function and generating two prime number that are not =
def main():
p=gen_prime(60)
q=gen_prime(60)
while p==q:
q=gen_prime(60)
print ("prime number 1 is: ", p)
print ("prime number 2 is: ", q)
#generating private and public key
n,e,d=rsa_key(p,q)
print("public key is : ")
print("exponant e: ",e)
print("n : ", n )
print("private key is : ")
print("exponant d: ", d)
print("n : ", n)
#message to encrypt:
m= 8675390
print("The original message: ", m)
# encrypt using the powMod_sm method:
y=int(powMod_sm(m, e, n))
print("the encrypted message is: ", y)
#now decrypt the encrypted message using powMod_sm:
x=int(powMod_sm(y, int(d), n))
print("The original method after decryption: ", x)
main()
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