fix implementation errors. (#1568)

I revised my implementation and found out that I have miss a inner loop for t.  x and y should be recalculated everytime when t is divisble by 2. I have also included a more readble source for this algorithm.

ciphers/rsa_factorization.py

@@ -4,6 +4,7 @@ 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.
 """
 import math
@@ -35,6 +36,7 @@ def rsafactor(d: int, e: int, N: int) -> List[int]:
     while p == 0:
         g = random.randint(2, N - 1)
         t = k
+        while True:
             if t % 2 == 0:
                 t = t // 2
                 x = (g ** t) % N
@@ -42,6 +44,9 @@ def rsafactor(d: int, e: int, N: int) -> List[int]:
                 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])