mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
66 lines
1.9 KiB
Python
66 lines
1.9 KiB
Python
import math
|
|
import random
|
|
|
|
"""
|
|
Shor Algorithm is one of the basic quantum computing algorithm
|
|
that is used in breaking the RSA cryptography protocol, by finding the
|
|
prime numbers that are used to create the public key value, n
|
|
|
|
In this implementation, I have used a very simple construct without
|
|
the use of qiskit or cirq to help understand how Shor algorithm's
|
|
idea actually works.
|
|
|
|
Website referred for shor algorithm:
|
|
https://www.geeksforgeeks.org/shors-factorization-algorithm/
|
|
"""
|
|
|
|
|
|
class Shor:
|
|
def period_find(self, num: int, number: int) -> int:
|
|
"""
|
|
Find the period of a^x mod N.
|
|
|
|
>>> shor = Shor()
|
|
>>> shor.period_find(2, 15)
|
|
4
|
|
>>> shor.period_find(3, 7)
|
|
6
|
|
"""
|
|
start: int = 1
|
|
while pow(num, start, number) != 1:
|
|
start += 1
|
|
return start
|
|
|
|
def shor_algorithm(self, number:int) -> tuple[int, int]:
|
|
"""
|
|
Run Shor's algorithm to factor a number.
|
|
>>> shor = Shor()
|
|
>>> random.seed(0)
|
|
>>> factors = shor.shor_algorithm(15)
|
|
>>> isinstance(factors, tuple) and len(factors) == 2
|
|
True
|
|
>>> factors
|
|
(3, 5)
|
|
"""
|
|
if number % 2 == 0:
|
|
return 2, number // 2
|
|
while True:
|
|
random.seed(0)
|
|
num: int = random.randint(2, number - 1)
|
|
gcd_number_num: int = math.gcd(number, num)
|
|
if gcd_number_num > 1:
|
|
return gcd_number_num, number // gcd_number_num
|
|
|
|
result: int = self.period_find(num, number)
|
|
if not result % 2:
|
|
start: int = pow(num, result // 2, number)
|
|
if start != number - 1:
|
|
p_value: int = math.gcd(start - 1, number)
|
|
q_value: int = math.gcd(start + 1, number)
|
|
if p_value > 1 and q_value > 1:
|
|
return p_value, q_value
|
|
|
|
|
|
shor = Shor()
|
|
print(shor.shor_algorithm(15))
|