mirror of
https://github.com/billbuchanan/appliedcrypto.git
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123 lines
2.3 KiB
Python
123 lines
2.3 KiB
Python
import sys
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import random
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import hashlib
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n=997
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text="Hello"
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g= 3
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def extended_euclidean_algorithm(a, b):
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"""
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Returns a three-tuple (gcd, x, y) such that
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a * x + b * y == gcd, where gcd is the greatest
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common divisor of a and b.
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This function implements the extended Euclidean
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algorithm and runs in O(log b) in the worst case.
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"""
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s, old_s = 0, 1
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t, old_t = 1, 0
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r, old_r = b, a
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while r != 0:
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quotient = old_r // r
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old_r, r = r, old_r - quotient * r
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old_s, s = s, old_s - quotient * s
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old_t, t = t, old_t - quotient * t
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return old_r, old_s, old_t
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def inverse_of(n, p):
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"""
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Returns the multiplicative inverse of
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n modulo p.
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This function returns an integer m such that
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(n * m) % p == 1.
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"""
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gcd, x, y = extended_euclidean_algorithm(n, p)
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assert (n * x + p * y) % p == gcd
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if gcd != 1:
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# Either n is 0, or p is not a prime number.
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raise ValueError(
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'{} has no multiplicative inverse '
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'modulo {}'.format(n, p))
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else:
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return x % p
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def pickg(p):
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for x in range (1,p):
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rand = x
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exp=1
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next = rand % p
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while (next <> 1 ):
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next = (next*rand) % p
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exp = exp+1
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if (exp==p-1):
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return rand
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v = random.randint(1,n)
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c = random.randint(1,n)
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if (len(sys.argv)>1):
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text=str(sys.argv[1])
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if (len(sys.argv)>2):
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v=int(sys.argv[2])
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if (len(sys.argv)>3):
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c=int(sys.argv[3])
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if (len(sys.argv)>4):
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n=int(sys.argv[4])
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print "Password:\t",text
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x = int(hashlib.md5(text).hexdigest()[:8], 16) % n
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g=pickg(n)
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y= pow(g,x,n)
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t = pow(g,v,n)
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r = (v - c * x)
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if (r<0):
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Result = ( inverse_of(pow(g,-r,n),n) * pow(y,c,n)) % n
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else:
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Result = ( pow(g,r,n) * pow(y,c,n)) % n
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print '\n======Agreed parameters============'
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print 'P=',n,'\t(Prime number)'
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print 'G=',g,'\t(Generator)'
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print '\n======The secret=================='
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print 'x=',x,'\t(Alice\'s secret)'
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print '\n======Random values==============='
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print 'c=',c,'\t(Bob\'s random value)'
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print 'v=',v,'\t(Alice\'s random value)'
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print '\n======Shared value==============='
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print 'g^x mod P=\t',y
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print 'r=\t\t',r
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print '\n=========Results==================='
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print 't=g**v % n =\t\t',t
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print '( (g**r) * (y**c) )=\t',Result
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if (t==Result):
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print 'Alice has proven she knows password'
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else:
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print 'Alice has not proven she knows x'
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