Somsuk algorithm

Author: daedalus

somsuk.py

@@ -0,0 +1,61 @@
+#!/usr/bin/env python3
+# Author Dario Clavijo 2022
+
+from gmpy2 import isqrt, gcd, sqrt, powmod, isqrt_rem, is_square
+import random
+import time
+
+def fermat(n):
+    a, rem = isqrt_rem(n)
+    b2 = -rem
+    c0 = (a << 1) + 1
+    c = c0
+    while not is_square(b2):
+        b2 += c
+        c += 2
+    a = (c - 1) >> 1
+    b = isqrt(b2)
+    return a - b, a + b
+
+
+def somsuk(n):
+  """
+  Implementation based on Kritsanapong Somsuk paper: 
+  The new integer factorization algorithm based on fermat’s
+  factorization algorithm and euler’s theorem (2020).
+  ISSN: 2088-8708, DOI: 10.11591/ijece.v10i2.pp1469-1476
+  """
+  u = isqrt(n) << 1
+  c = n
+  while gcd(c, n) > 1:
+    c = random.randrange(2, n - 1)
+  a = powmod(c, -1, n)
+  s = powmod(c, 2, n)
+  phi_aprox = n - u  + 1
+  t = powmod(a, phi_aprox, n)
+  while True:
+    if t == 1:
+      x = u >> 1
+      y = isqrt(x * x - n)
+      return x - y, x + y
+    t = (t*s) % n
+    u += 2
+
+def timeit(f,n):
+  t0 = time.time()
+  r = f(n)
+  t1 = time.time()
+  print(str(f).split(" ")[1],"(", n , ") =", r,"time:",round(t1-t0,5))
+
+def test():
+  timeit(somsuk, 340213)
+  timeit(fermat, 340213)
+  timeit(somsuk, 788582867650121563)
+  timeit(fermat, 788582867650121563)
+  timeit(somsuk, 1047329636821139813)
+  timeit(fermat, 1047329636821139813)
+
+if __name__ == "__main__":
+  test()
+
+