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