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baby_step_giant_step.py
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baby_step_giant_step.py
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'''
Created on Dec 14, 2011
@author: andrewkittredge
'''
import math
from exponentiation import fast_exponentiation
from euclidean_algo import extended_euclidean_algorithm
def discrete_log(prime, public_key, primitive_root):
m = int(math.floor((prime - 1) ** .5))
base_exponents = {}
for j in xrange(0, m):
base_exponents[fast_exponentiation(primitive_root, j, prime)] = j
inverse_b = extended_euclidean_algorithm(primitive_root, prime) % prime
c = fast_exponentiation(inverse_b, m, prime)
x = public_key
for i in xrange(0, m):
if x in base_exponents:
return (m * i) + base_exponents[x]
else:
x = (x * c) % prime
import unittest
class BabyStepGiantStepTester(unittest.TestCase):
def test_dicrete_log(self):
self.assertEqual(5, discrete_log(29, 3, 2))
self.assertEqual(69, discrete_log(101, 3, 2))
self.assertEqual(237, discrete_log(1009, 482, 101))
self.assertEqual(2397011, discrete_log(prime=6876731,
public_key=3523346,
primitive_root=3422))
if __name__ == '__main__':
unittest.main()