Added Shor Algorithm for RSA n factorization

quantum/shor_algorithm.py

@@ -0,0 +1,64 @@
+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.
+"""
+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) -> list[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))
+            
+            
+            
+