Implemented arbitrary-sized Pollard Rho function and added test program.

Author: netromdk

src/Common.cpp

@@ -3,7 +3,7 @@
 #include "Common.h"
 
 namespace Math {
-  bool isPropPrime(mpz_t n) {
+  bool isPropPrime(const mpz_t n) {
     return mpz_probab_prime_p(n, 10) > 0;
   }
 

src/Common.h

@@ -5,7 +5,7 @@
 #include <string>
 
 namespace Math {
-  bool isPropPrime(mpz_t n);  
+  bool isPropPrime(const mpz_t n);  
   bool isPropPrime(int n);
   void dump(mpz_t n, std::string msg = "", bool newline = true);
 }

src/PollardRho.cpp

@@ -7,13 +7,61 @@
 namespace Math {
   namespace Fac {
     namespace {
-      int fI(int x, int a, int n) {
+      void func(mpz_t r, const mpz_t x, const mpz_t a, const mpz_t n) {
+        mpz_mul(r, x, x);
+        mpz_add(r, r, a);
+        mpz_mod(r, r, n);
+      }
+      
+      int funcI(int x, int a, int n) {
         return mod(x * x + a, n);
       }
     }
+
+    void pollardRho(const mpz_t n, mpz_t f) {
+      // Return n as the factor if it's a probable-prime.      
+      if (isPropPrime(n)) {
+        mpz_set(f, n);
+        return;
+      }
+
+      mpz_t a, s, g, u, v, one, zero, tmp;
+      mpz_inits(a, s, g, u, v, one, zero, tmp, NULL);
+      mpz_set_ui(zero, 0);      
+      mpz_set_ui(one, 1);
+      mpz_sub_ui(tmp, n, 3);
+      randRange(a, one, tmp); // a in [1, n - 3]
+
+      mpz_sub_ui(tmp, n, 1);      
+      randRange(s, zero, tmp); // s in [0, n - 1]
+
+      // u = v = s
+      mpz_set(u, s);
+      mpz_set(v, s);
+
+      do {
+        func(u, u, a, n);
+        func(v, v, a, n);
+        func(v, v, a, n);
+
+        // g = gcd((u - v) mod n, n)
+        mpz_sub(tmp, u, v);
+        mpz_mod(tmp, tmp, n);
+        mpz_gcd(g, tmp, n);
+      } while (mpz_cmp(g, one) == 0);
+
+      // Failed: g == n
+      if (mpz_cmp(g, n) == 0) {
+        mpz_clears(a, s, g, u, v, one, zero, tmp, NULL);
+        pollardRho(n, f);
+      }
+
+      // Found factor.
+      mpz_set(f, g);
+      mpz_clears(a, s, g, u, v, one, zero, tmp, NULL);
+    }
 
     int pollardRhoI(int n) {
-      // Return n if n is a probable-prime.
       if (isPropPrime(n)) return n;
 
       Random rnd;
@@ -24,8 +72,8 @@ namespace Math {
       u = v = s;
 
       do {
-        u = fI(u, a, n);
-        v = fI(fI(v, a, n), a, n);
+        u = funcI(u, a, n);
+        v = funcI(funcI(v, a, n), a, n);
         g = gcd(mod(u - v, n), n);
       } while (g == 1);
 

src/PollardRho.h

@@ -1,12 +1,21 @@
 #ifndef MATH_POLLARD_RHO_H
 #define MATH_POLLARD_RHO_H
 
+#include <gmp.h>
+
 namespace Math {
   namespace Fac {
     namespace {
-      int fI(int x, int a, int n);
+      void func(mpz_t r, const mpz_t x, const mpz_t a, const mpz_t n);
+      int funcI(int x, int a, int n);
     }
 
+    /**
+     * Finds a nontrivial factor of composite number n of arbitrary
+     * size and writes the result to f.
+     */
+    void pollardRho(const mpz_t n, mpz_t f);    
+
     /**
      * Finds a nontrivial factor of composite number n.
      */

test/CMakeLists.txt

@@ -9,3 +9,6 @@ INCLUDE_DIRECTORIES( ${PROJECT_SOURCE_DIR}/src )
 ADD_EXECUTABLE( PollardRhoI PollardRhoI.cpp ) 
 TARGET_LINK_LIBRARIES( PollardRhoI ${CORELIBS} )
 
+ADD_EXECUTABLE( PollardRho PollardRho.cpp ) 
+TARGET_LINK_LIBRARIES( PollardRho ${CORELIBS} )
+

test/PollardRho.cpp

@@ -0,0 +1,39 @@
+#include <gmp.h>
+#include <sstream>
+#include <iostream>
+using namespace std;
+
+#include "Common.h"
+#include "PollardRho.h"
+using namespace Math;
+using namespace Math::Fac;
+
+#include "TestCommon.h"
+
+void usage(char **argv) {
+  cout << "Usage: " << argv[0] << " <num>" << endl
+       << "Find a nontrivial prime factor of <num>." << endl;
+}
+
+int main(int argc, char **argv) {
+  if (argc != 2) {
+    usage(argv);
+    return -1;
+  }
+
+  mpz_t num, g;
+  mpz_init(num);
+  if (mpz_set_str(num, argv[1], 10) == -1) {
+    mpz_clear(num);
+    usage(argv);
+    return -1;
+  }
+  
+  mpz_init(g);
+  pollardRho(num, g);
+  dump(num, "A factor of", false);
+  dump(g, " is");
+
+  mpz_clears(num, g, NULL);
+  return 0;
+}