Java Program to Implement Fermat Factorization Algorithm

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This is a Java Program to Implement Fermat Factorization Algorithm. Fermat’s factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a2 – b2. That difference is algebraically factorable as (a + b)(a – b); if neither factor equals one, it is a proper factorization of N.

Here is the source code of the Java Program to Implement Fermat Factorization Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

  1. /**
  2.  ** Java Program to implement Fermat Factorization Algorithm
  3.  **/
  4.  
  5. import java.util.Scanner;
  6.  
  7. public class FermatFactorization
  8. {
  9.     /** Fermat factor **/
  10.     public void FermatFactor(long N)
  11.     {
  12.         long a = (long) Math.ceil(Math.sqrt(N));
  13.         long b2 = a * a - N;
  14.         while (!isSquare(b2))
  15.         {
  16.             a++;
  17.             b2 = a * a - N;
  18.         }
  19.         long r1 = a - (long)Math.sqrt(b2);
  20.         long r2 = N / r1;
  21.         display(r1, r2);
  22.     }
  23.     /** function to display roots **/
  24.     public void display(long r1, long r2)
  25.     {
  26.         System.out.println("\nRoots = "+ r1 +" , "+ r2);    
  27.     }
  28.     /** function to check if N is a perfect square or not **/
  29.     public boolean isSquare(long N)
  30.     {
  31.         long sqr = (long) Math.sqrt(N);
  32.         if (sqr * sqr == N || (sqr + 1) * (sqr + 1) == N)
  33.             return true;
  34.         return false;
  35.     }
  36.     /** main method **/
  37.     public static void main(String[] args) 
  38.     {
  39.         Scanner scan = new Scanner(System.in);
  40.         System.out.println("Fermat Factorization Test\n");
  41.         System.out.println("Enter odd number");
  42.         long N = scan.nextLong();
  43.         FermatFactorization ff = new FermatFactorization();
  44.         ff.FermatFactor(N);
  45.     }
  46. }

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Fermat Factorization Test
 
Enter odd number
5959
 
Roots = 59 , 101
 
 
Fermat Factorization Test
 
Enter odd number
432633
 
Roots = 499 , 867

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter