RsaKeyGenerator.java for RSA Key Generation

Cryptography Tutorials - Herong's Tutorial Examples

∟RSA Implementation using java.math.BigInteger Class

∟RsaKeyGenerator.java for RSA Key Generation

This section describes the initial draft of a RSA public key and private key generation implementation using the java.math.BigInteger class.

The first step of RSA public key encryption implementation is to write a program to generate a pair of public key and private key. Here is my initial draft using the java.math.BigInteger class:

/* RsaKeyGenerator.java
#- Copyright (c) 2013, HerongYang.com, All Rights Reserved.
 */
import java.math.BigInteger;
import java.util.Random;
class RsaKeyGenerator {
   public static void main(String[] a) {
      if (a.length<1) {
         System.out.println("Usage:");
         System.out.println("java RsaKeyGenerator size");
         return;
      }
      int size = Integer.parseInt(a[0]);

      Random rnd = new Random();
      BigInteger p = BigInteger.probablePrime(size/2,rnd);
      BigInteger q = p.nextProbablePrime();
      BigInteger n = p.multiply(q);
      BigInteger m = (p.subtract(BigInteger.ONE)).multiply(
         q.subtract(BigInteger.ONE));
      BigInteger e = getCoprime(m);
      BigInteger d = e.modInverse(m);

      System.out.println("p: "+p);
      System.out.println("q: "+q);
      System.out.println("m: "+m);
      System.out.println("Modulus: "+n);
      System.out.println("Key size: "+n.bitLength());
      System.out.println("Public key: "+e);
      System.out.println("Private key: "+d);
   }
   public static BigInteger getCoprime(BigInteger m) {
      Random rnd = new Random();
      int length = m.bitLength()-1;
      BigInteger e = BigInteger.probablePrime(length,rnd);
      while (! (m.gcd(e)).equals(BigInteger.ONE) ) {
      	 e = BigInteger.probablePrime(length,rnd);
      }
      return e;
   }
}

Some notes on RsaKeyGenerator.java:

probablePrime() method uses the default certainty value of 100. This ensures that the probability of the resulting value being a prime number is 100-100/(2**100) percent.
When generating the first prime number "p", I specified the bit length to be "size/2", This ensures that the bit length of the modulus "n", which the RSA key size, to be the requested value "size". The bit length of "n" is about 2 times of the bit length of "p".
When calling probablePrime(), it requires a random number generator. I used a java.util,Random constructor to created a random number generator. Another option is to use a java.security.SecureRandom contrustor.
To generate the second prime number "q", I used the p.nextProbablePrime() method, which returns the next prime number bigger than "p". This ensures that "q" is different than "p".
To find a public key "e", I used a "while" loop to test different possible "e" until (m.gcd(e)).equals(BigInteger.ONE).

See the next tutorial for testing result of this program.

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

►RsaKeyGenerator.java for RSA Key Generation

RSA Keys Generated by RsaKeyGenerator.java

RsaKeyValidator.java for RSA Key Validation

64-bit RSA Key Validated by RsaKeyValidator.java

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

RsaKeyEncryption.java for RSA Encryption Operation

RsaKeyDecryption.java for RSA Decryption Operation

Testing RsaKeyEncryption.java with a 16-bit Key

Testing RsaKeyEncryption.java with a 64-bit Key

Testing RsaKeyEncryption.java 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