mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
59 lines
1.7 KiB
Python
59 lines
1.7 KiB
Python
"""
|
|
An RSA prime factor algorithm.
|
|
|
|
The program can efficiently factor RSA prime number given the private key d and
|
|
public key e.
|
|
Source: on page 3 of https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf
|
|
More readable source: https://www.di-mgt.com.au/rsa_factorize_n.html
|
|
large number can take minutes to factor, therefore are not included in doctest.
|
|
"""
|
|
|
|
from __future__ import annotations
|
|
|
|
import math
|
|
import random
|
|
|
|
|
|
def rsafactor(d: int, e: int, n: int) -> list[int]:
|
|
"""
|
|
This function returns the factors of N, where p*q=N
|
|
Return: [p, q]
|
|
|
|
We call N the RSA modulus, e the encryption exponent, and d the decryption exponent.
|
|
The pair (N, e) is the public key. As its name suggests, it is public and is used to
|
|
encrypt messages.
|
|
The pair (N, d) is the secret key or private key and is known only to the recipient
|
|
of encrypted messages.
|
|
|
|
>>> rsafactor(3, 16971, 25777)
|
|
[149, 173]
|
|
>>> rsafactor(7331, 11, 27233)
|
|
[113, 241]
|
|
>>> rsafactor(4021, 13, 17711)
|
|
[89, 199]
|
|
"""
|
|
k = d * e - 1
|
|
p = 0
|
|
q = 0
|
|
while p == 0:
|
|
g = random.randint(2, n - 1)
|
|
t = k
|
|
while True:
|
|
if t % 2 == 0:
|
|
t = t // 2
|
|
x = (g**t) % n
|
|
y = math.gcd(x - 1, n)
|
|
if x > 1 and y > 1:
|
|
p = y
|
|
q = n // y
|
|
break # find the correct factors
|
|
else:
|
|
break # t is not divisible by 2, break and choose another g
|
|
return sorted([p, q])
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|