Diffie-Hellman

difhel.py

#!/usr/bin/python                                                                                                                                                                   

from sys import argv
from math import sqrt
from random import randint

def potMod(b,p,m):
    bits = p
    res = 1
    temp = b
    while bits > 0:
        if bits%2==1:
            res = (res*temp)%m
        temp = (temp*temp)%m
        bits = bits >> 1
    return res

def secret(mod,base):
    exp = randint(1,mod)
    return potMod(base,exp,mod),exp

def eveHack(A,B,prime,generator):
    for it in range(prime):
        if potMod(generator,it,prime) == A:
            alicePriv = it
        if potMod(generator,it,prime) == B:
            bobPriv = it
    return alicePriv,bobPriv

def main():
    prime = int(argv[1])
    generator = int(argv[2])
    A,secrNumA = secret(prime,generator)
    B,secrNumB = secret(prime,generator)
    print 'Alice generated: %d, using %d ^ %d mod %d'%(A,generator,secrNumA,prime)
    print 'Bob generated: %d, using %d ^ %d mod %d'%(B,generator,secrNumB,prime)
    print 'Alice\'s key: %d ^ %d mod %d = %d'%(B,secrNumA,prime,potMod(B,secrNumA,prime))
    print 'Bob\'s key: %d ^ %d mod %d = %d'%(A,secrNumB,prime,potMod(A,secrNumB,prime))
    aPr,bPr = eveHack(A,B,prime,generator)
    print 'Eve\'s key using bob\'s private number: %d'%(potMod(A,bPr,prime))
    print 'Eve\'s key using alice\'s private number: %d'%(potMod(B,aPr,prime))

main()

Ex.sh

$ python difhel.py 997 258
Alice generated: 531, using 258 ^ 91 mod 997
Bob generated: 550, using 258 ^ 46 mod 997
Alice's key: 550 ^ 91 mod 997 = 682
Bob's key: 531 ^ 46 mod 997 = 682
Eve's key using bob's private number: 682
Eve's key using alice's private number: 682

hack.py

def eveHack(A,B,prime,generator):
    for it in range(prime):
        if potMod(generator,it,prime) == A:
            alicePriv = it
        if potMod(generator,it,prime) == B:
            bobPriv = it
    return alicePriv,bobPriv

use.sh

$ python difhel.py primo generador