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params.py
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params.py
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# !/usr/bin/env python
# -*- coding: utf-8 -*-
from future.utils import iteritems
from builtins import bytes
from past.builtins import basestring
from past.builtins import long
from functools import reduce
import json
import argparse
import logging
import coloredlogs
import base64
import hashlib
import sys
import os
import re
import math
import itertools
import binascii
import collections
import traceback
import datetime
from math import ceil, log
class DlogFprint(object):
"""
Discrete logarithm (dlog) fingerprinter for ROCA.
Exploits the mathematical prime structure described in the paper.
No external python dependencies are needed (for sake of compatibility).
Detection could be optimized using sympy / gmpy but that would add significant dependency overhead.
"""
def __init__(self, max_prime=167, generator=65537):
self.primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167]
self.max_prime = max_prime
self.generator = generator
self.m, self.phi_m = self.primorial(max_prime)
self.phi_m_decomposition = DlogFprint.small_factors(self.phi_m, max_prime)
self.generator_order = DlogFprint.element_order(generator, self.m, self.phi_m, self.phi_m_decomposition)
self.generator_order_decomposition = DlogFprint.small_factors(self.generator_order, max_prime)
self.n = 0x1db349e1f58f5d41f65aa5b0ffa6ae0cea80de6c170b2b4abf9c358d79494ca59cab008f5ee92759b91d497e2131701047f953935a163e91db5460c82566f4df0c05bca02a8576f7c4e916b274e2f307b56fc8a20ad452b1b54d3924726a3b2329da882c7b8e102379dfe7a8c6b01d62e7ff0fd58e1e9822f6e32b5b0486561fb
# self.order = 2 ** 4 * 3 ** 4 * 5 ** 2 * 7 * 11 * 13 * 17 * 23 * 29 * 37 * 41 * 83
self.order = 2454106387091158800
print self.order
print "log2order", log(self.order / 2, 2)
print "log2m", log(self.m, 2)
print "log2n/4", log(self.n, 2) / 4
mp = self.m
ordp = self.order
while True:
r = 0
pv = 0
ev = 0
mpcand = mp
for p, exp in self.small_factors(ordp, 167).iteritems():
for e in range(1, exp + 1):
candidate = p ** e
mpnew = self.algo2(mp, self.prime_factors(mp, 167), ordp / candidate)
reward = (log(ordp, 2) - log(ordp / candidate, 2)) / (log(mp, 2) - log(mpnew, 2))
if reward > r:
r = reward
pv = p
ev = e
mpcand = mpnew
if pv == 0:
break
if log(mpcand, 2) < (log(self.n, 2) / 4):
print "done"
break
print "eliminating %d^%d (reward %f)" % (pv, ev, r)
mp = mpcand
ordp = ordp / (pv ** ev)
# break
print "mp", mp
print "ordp", ordp
print self.small_factors(ordp, 167)
print "log2m", log(mp, 2)
print "log2n/4", log(self.n, 2) / 4
def algo2(self, m, m_decomposition, order):
mp = m
for prime in m_decomposition:
ord = self.ord(prime)
if order % ord != 0:
mp /= prime
# print "eliminated %d" % (prime)
return mp
def ord(self, modulus):
power = 1
while True:
if pow(65537, power, modulus) == 1:
return power
power += 1
def fprint(self, modulus):
"""
Returns True if fingerprint is present / detected.
:param modulus:
:return:
"""
d = DlogFprint.discrete_log(modulus, self.generator,
self.generator_order, self.generator_order_decomposition, self.m)
return d is not None
def primorial(self, max_prime=167):
"""
Returns primorial (and its totient) with max prime inclusive - product of all primes below the value
:param max_prime:
:param dummy:
:return: primorial, phi(primorial)
"""
mprime = max(self.primes)
if max_prime > mprime:
raise ValueError('Current primorial implementation does not support values above %s' % mprime)
primorial = 1
phi_primorial = 1
for prime in self.primes:
primorial *= prime
phi_primorial *= prime - 1
return primorial, phi_primorial
@staticmethod
def prime3(a):
"""
Simple trial division prime detection
:param a:
:return:
"""
if a < 2:
return False
if a == 2 or a == 3:
return True # manually test 2 and 3
if a % 2 == 0 or a % 3 == 0:
return False # exclude multiples of 2 and 3
max_divisor = int(math.ceil(a ** 0.5))
d, i = 5, 2
while d <= max_divisor:
if a % d == 0:
return False
d += i
i = 6 - i # this modifies 2 into 4 and vice versa
return True
@staticmethod
def is_prime(a):
return DlogFprint.prime3(a)
@staticmethod
def prime_factors(n, limit=None):
"""
Simple trial division factorization
:param n:
:param limit:
:return:
"""
num = []
# add 2, 3 to list or prime factors and remove all even numbers(like sieve of ertosthenes)
while n % 2 == 0:
num.append(2)
n = n // 2
while n % 3 == 0:
num.append(3)
n = n // 3
max_divisor = int(math.ceil(n ** 0.5)) if limit is None else limit
d, i = 5, 2
while d <= max_divisor:
while n % d == 0:
num.append(d)
n = n // d
d += i
i = 6 - i # this modifies 2 into 4 and vice versa
# if no is > 2 i.e no is a prime number that is only divisible by itself add it
if n > 2:
num.append(n)
return num
@staticmethod
def factor_list_to_map(factors):
"""
Factor list to map factor -> power
:param factors:
:return:
"""
ret = {}
for k, g in itertools.groupby(factors):
ret[k] = len(list(g))
return ret
@staticmethod
def element_order(element, modulus, phi_m, phi_m_decomposition):
"""
Returns order of the element in Zmod(modulus)
:param element:
:param modulus:
:param phi_m: phi(modulus)
:param phi_m_decomposition: factorization of phi(modulus)
:return:
"""
if element == 1:
return 1 # by definition
if pow(element, phi_m, modulus) != 1:
return None # not an element of the group
order = phi_m
for factor, power in list(phi_m_decomposition.items()):
for p in range(1, power + 1):
next_order = order // factor
if pow(element, next_order, modulus) == 1:
order = next_order
else:
break
return order
@staticmethod
def chinese_remainder(n, a):
"""
Solves CRT for moduli and remainders
:param n:
:param a:
:return:
"""
sum = 0
prod = reduce(lambda a, b: a * b, n)
for n_i, a_i in zip(n, a):
p = prod // n_i
s = a_i * DlogFprint.mul_inv(p, n_i) * p
sum += s
return sum % prod
@staticmethod
def mul_inv(a, b):
"""
Modular inversion a mod b
:param a:
:param b:
:return:
"""
b0 = b
x0, x1 = 0, 1
if b == 1:
return 1
while a > 1:
q = a // b
a, b = b, a % b
x0, x1 = x1 - q * x0, x0
if x1 < 0:
x1 += b0
return x1
@staticmethod
def small_factors(x, max_prime):
"""
Factorizing x up to max_prime limit.
:param x:
:param max_prime:
:return:
"""
factors = DlogFprint.prime_factors(x, limit=max_prime)
return DlogFprint.factor_list_to_map(factors)
@staticmethod
def discrete_log(element, generator, generator_order, generator_order_decomposition, modulus):
"""
Simple discrete logarithm
:param element:
:param generator:
:param generator_order:
:param generator_order_decomposition:
:param modulus:
:return:
"""
if pow(element, generator_order, modulus) != 1:
# logger.debug('Powmod not one')
return None
moduli = []
remainders = []
for prime, power in list(generator_order_decomposition.items()):
prime_to_power = prime ** power
order_div_prime_power = generator_order // prime_to_power # g.div(generator_order, prime_to_power)
g_dash = pow(generator, order_div_prime_power, modulus)
h_dash = pow(element, order_div_prime_power, modulus)
found = False
for i in range(0, prime_to_power):
if pow(g_dash, i, modulus) == h_dash:
remainders.append(i)
moduli.append(prime_to_power)
found = True
break
if not found:
# logger.debug('Not found :(')
return None
ccrt = DlogFprint.chinese_remainder(moduli, remainders)
return ccrt
def main():
DlogFprint()
if __name__ == '__main__':
main()