Generating Prime Number with BigInteger Class

This section provides a tutorial example on how to generate probable prime numbers using the java.math.BigInteger class in Java.

The first thing I want to try with the java.Math.BigInteger Class is to generate probable prime numbers. I am interested how fast large prime numbers can be generated and how good they are. Here is my first Java program using the java.Math.BigInteger Class:

#- Copyright (c) 2013,, All Rights Reserved.
import java.math.BigInteger;
import java.util.Random;
class PrimeGenerator {
   public static void main(String[] a) {
      if (a.length<2) {
         System.out.println("java PrimeGenerator length certainty");
      int length = Integer.parseInt(a[0]);
      int certainty = Integer.parseInt(a[1]);
      Random rnd = new Random();

      long t1 = System.currentTimeMillis();
      BigInteger p = new BigInteger(length,certainty,rnd);
      long t2 = System.currentTimeMillis();
      boolean ok = p.isProbablePrime(certainty);
      long t3 = System.currentTimeMillis();
      BigInteger two = new BigInteger("2");
      System.out.println("Probable prime: "+p);
      System.out.println("Validation: "+ok);
      System.out.println("Bit length: "+length);
      System.out.println("Certainty: "+certainty);
      System.out.println("Probability (%): "
      System.out.println("Generation time (milliseconds): "+(t2-t1));
      System.out.println("Validation time (milliseconds): "+(t3-t2));

Compile and run it on my Windows 7 computer with JDK 1.6 starting with a small bit length and certainty to validate my program:


C:\herong>java PrimeGenerator 4 4
Probable prime: 13
Validation: true
Bit length: 4
Certainty: 4
Probability (%): 93.75
Generation time (milliseconds): 1
Validation time (milliseconds): 39

Reviewing the output, we can see that prime number generated by the program, 13, does meet specified criteria:

I think my program works correctly. What do you think?

Last update: 2013.

Table of Contents

 About This Book

 Cryptography Terminology

 Cryptography Basic Concepts

 Introduction to AES (Advanced Encryption Standard)

 Introduction to DES Algorithm

 DES Algorithm - Illustrated with Java Programs

 DES Algorithm Java Implementation

 DES Algorithm - Java Implementation in JDK JCE

 DES Encryption Operation Modes

 DES in Stream Cipher Modes

 PHP Implementation of DES - mcrypt

 Blowfish - 8-Byte Block Cipher

 Secret Key Generation and Management

 Cipher - Secret Key Encryption and Decryption

 Introduction of RSA Algorithm

RSA Implementation using java.math.BigInteger Class

 java.Math.BigInteger Class

Generating Prime Number with BigInteger Class

 Performance of Prime Number Generation

 RSA Encryption Implementation using BigInteger Class for RSA Key Generation

 RSA Keys Generated by for RSA Key Validation

 64-bit RSA Key Validated by

 Converting Byte Sequences to Positive Integers

 Cleartext Block Size for RSA Encryption

 Cleartext Message Padding and Revised Block Size

 Ciphertext Block Size for RSA Encryption for RSA Encryption Operation for RSA Decryption Operation

 Testing with a 16-bit Key

 Testing with a 64-bit Key

 Testing with a 3072-bit Key

 Introduction of DSA (Digital Signature Algorithm)

 Java Default Implementation of DSA

 Private key and Public Key Pair Generation

 PKCS#8/X.509 Private/Public Encoding Standards

 Cipher - Public Key Encryption and Decryption

 MD5 Mesasge Digest Algorithm

 SHA1 Mesasge Digest Algorithm

 OpenSSL Introduction and Installation

 OpenSSL Generating and Managing RSA Keys

 OpenSSL Managing Certificates

 OpenSSL Generating and Signing CSR

 OpenSSL Validating Certificate Path

 "keytool" and "keystore" from JDK

 "OpenSSL" Signing CSR Generated by "keytool"

 Migrating Keys from "keystore" to "OpenSSL" Key Files

 Certificate X.509 Standard and DER/PEM Formats

 Migrating Keys from "OpenSSL" Key Files to "keystore"

 Using Certificates in IE (Internet Explorer)

 Using Certificates in Firefox

 Using Certificates in Google Chrome

 Outdated Tutorials


 PDF Printing Version