add carmichael integer factorization algorithm

Author: daedalus

carmichael.py

@@ -0,0 +1,26 @@
+from gmpy2 import *
+
+def factor(N):
+  """
+  Algorithm described in the wagstaf-joy of factoring book.
+  """
+  f = N1 = N - 1
+  while f & 1 == 0: f >>= 1
+  a = 2
+  while a <= N1:
+    r1 = powmod(a, f << 1, N) 
+    if r1 == 1:
+      r = powmod(a, f, N) 
+      p = gcd(r - 1, N)
+      q = gcd(r + 1, N)
+      if (q > p > 1): #and (p * q == N):
+        return factor(p) + factor(q)
+    a = next_prime(a)
+  return [N]
+
+def tests():
+  for n in [561,6601, 8911,23224518901,1901 * 3701,6601 * 8911,52193 * 3701]:
+    print(n, factor(n))
+
+if __name__ == "__main__":
+  tests()