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ecc/logs/babygiantstep.py
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#!/usr/bin/env python3 | |
# This script makes use of another module: common.py, which can be | |
# found on GitHub: | |
# | |
# https://github.com/andreacorbellini/ecc/blob/master/logs/common.py | |
# | |
# You must place that module on the same directory of this script | |
# prior to running it. | |
import math | |
import random | |
from common import tinycurve as curve | |
def log(p, q): | |
assert curve.is_on_curve(p) | |
assert curve.is_on_curve(q) | |
sqrt_n = int(math.sqrt(curve.n)) + 1 | |
# Compute the baby steps and store them in the 'precomputed' hash table. | |
r = None | |
precomputed = {None: 0} | |
for a in range(1, sqrt_n): | |
r = curve.add(r, p) | |
precomputed[r] = a | |
# Now compute the giant steps and check the hash table for any | |
# matching point. | |
r = q | |
s = curve.mult(sqrt_n, curve.neg(p)) | |
for b in range(sqrt_n): | |
try: | |
a = precomputed[r] | |
except KeyError: | |
pass | |
else: | |
steps = sqrt_n + b | |
logarithm = a + sqrt_n * b | |
return logarithm, steps | |
r = curve.add(r, s) | |
raise AssertionError('logarithm not found') | |
def main(): | |
x = random.randrange(1, curve.n) | |
p = curve.g | |
q = curve.mult(x, p) | |
print('Curve: {}'.format(curve)) | |
print('Curve order: {}'.format(curve.n)) | |
print('p = (0x{:x}, 0x{:x})'.format(*p)) | |
print('q = (0x{:x}, 0x{:x})'.format(*q)) | |
print(x, '* p = q') | |
y, steps = log(p, q) | |
print('log(p, q) =', y) | |
print('Took', steps, 'steps') | |
assert x == y | |
if __name__ == '__main__': | |
main() |