Mukarram Mukhtar

Implementation of RSA

If you are a student of computer science and plan to take a course related to data security, then this article will be of particular interest of yours; because sooner or later you will have to implement RSA either in its trivial or more sophisticated form. Before I present the code of its implementation let me propound how UI of this implementation has been designed.

To run the application, of course you need Java Runtime installed on your machine (complete SDK is recommended), as well as PATH variables should also be set. Now when you see the following window, you can start clicking on the buttons on the left hand side of the window from top to bottom. The program will perform the following tasks:

  1. Create p: The program will create a random prime number of 512 bits, almost 150 digits.
  2. Create q: The program will create another random prime number of the same size as p.
  3. n = p x q: The program will calculate n = p x q.
  4. (p – 1) x (q – 1): The program will calculate Φ(n) = (p – 1) x (q – 1).
  5. Select d: Since d is the private key, we’ll select that of our own choice and then based upon that we’ll calculate e. The formula for calculating d is coming in short.
  6. Calculate e: This is the last step in key generation. The formula of calculating e is coming in short.
  7. Up till this step, our RSA key has been generated, now we are ready to enter plain text and apply encryption algorithms.
  8. After entering plain text, click on Call (OAEP) button to apply padding.
  9. Encrypt: The program will encrypt the number produced by OAEP routine.
  10. Decrypt: For verification that Encryption and Decryption routines are inverse of each other and that cipher text can be converted back to plain text, you can click on Decrypt button and you’ll see a congratulations message (hopefully, if everything goes alright).

Following is the window that you will see when you’ll run the java application.

General Formulas of RSA:

The first step of RSA implementation is its Key Generation, following are the steps:


Encryption and Decryption formulas are just sweet hearts; let’s have P as plaintext and C as ciphertext, and then the formulas will be as follows:

Now let’s take a look at the application, what does it do when we follow all the above given steps:

Up till that step your encryption is done, now to verify that encryption and decryption work inversely we need to click Decrypt button and get the following screen.

Okay, now I know what you guys want to say, I’ll just shut up and give you the source code, which is as follows, enjoy programming and have a great rest of the day  🙂

import java.awt.*;
import java.sql.*;
import javax.swing.*;
import java.applet.*;
import java.awt.event.*;
import java.math.*;
import java.util.*;
public class RSA extends JFrame implements ActionListener
     public static void main(String[] args)
           final RSA app = new RSA();
     // the whole constructor is for setting up the UI of the form
     public RSA()
           c = getContentPane();
           setBounds(50, 50, 1200, 400);
           setBackground(new Color(204, 204, 204));
           setTitle("Implementation of RSA");
           btnCreateP.setBounds(5, 10, 110, 25);
           btnCreateQ.setBounds(5, 40, 110, 25);
           btnCalculateN.setBounds(5, 70, 110, 25);
           btnCalculateN1.setBounds(5, 100, 110, 25);
           btnSelectE.setBounds(5, 160, 110, 25);
           btnCalculateD.setBounds(5, 130, 110, 25);
           btnCalculateOAEP.setBounds(5, 250, 110, 25);
           btnEncrypt.setBounds(5, 280, 110, 25);
           btnDecrypt.setBounds(5, 310, 110, 25);
           txtP.setBounds(120, 10, 1070, 25);
           txtQ.setBounds(120, 40, 1070, 25);
           txtN.setBounds(120, 70, 1070, 25);
           txtN1.setBounds(120, 100, 1070, 25);
           txtE.setBounds(120, 160, 1070, 25);
           txtD.setBounds(120, 130, 1070, 25);
           txtPlainText.setBounds(120, 220, 1070, 25);
           txtOAEP.setBounds(120, 250, 1070, 25);
           txtCipher.setBounds(120, 280, 1070, 25);
           txtDecipher.setBounds(120, 310, 1070, 25);
           lblAnnouncePrivatePublicKeys.setBounds(120, 190, 1070, 25);
           lblEnterPlainText.setBounds(5, 220, 310, 25);
           txtP.setBackground(new Color(255, 255, 255));
           txtQ.setBackground(new Color(255, 255, 255));
           txtN.setBackground(new Color(255, 255, 255));
           txtN1.setBackground(new Color(255, 255, 255));
           txtE.setBackground(new Color(255, 255, 255));
           txtD.setBackground(new Color(255, 255, 255));
           txtOAEP.setBackground(new Color(255, 255, 255));
           txtCipher.setBackground(new Color(255, 255, 255));
           txtDecipher.setBackground(new Color(255, 255, 255));
     // this method decides which method to call for any particular button click
     public void actionPerformed(ActionEvent e)
           Object source = e.getSource();
           if (source == btnCreateP)
           else if (source == btnCreateQ)
           else if (source == btnCalculateN)
           else if (source == btnCalculateN1)
           else if (source == btnSelectE)
           else if (source == btnCalculateD)
           else if (source == btnCalculateOAEP)
           else if (source == btnEncrypt)
           else if (source == btnDecrypt)
     public void CreateP_Click()
           // step 1.1 in Key Generation (see page # 303 in book, RSA Key Generation)
           // create a large prime p, of 512 bits, almost 150 digits
           bigP = BigInteger.probablePrime(512, new Random(rnd.nextInt()));
     public void btnCreateQ_Click()
           // step 1.2 in Key Generation (see page # 303 in book, RSA Key Generation)
           // create a large prime q, of 512 bits, almost 150 digits
           bigQ = BigInteger.probablePrime(512, new Random(rnd.nextInt()));
     public void btnCalculateN_Click()
           if (this.txtQ.getText().length() == 0 || this.txtP.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Create p' and 'Create q' buttons first.", "Warning", JOptionPane.ERROR_MESSAGE);
                // step 3 in Key Generation (see page # 303 in book, RSA Key Generation)
                // calculate n = p x q
                bigN = bigP.multiply(bigQ);
     public void btnCalculateN1_Click()
           if (this.txtQ.getText().length() == 0 || this.txtP.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Create p' and 'Create q' buttons first.", "Warning", JOptionPane.ERROR_MESSAGE);
                // step 4 in Key Generation (see page # 303 in book, RSA Key Generation)
                // calculate n' = (p - 1) x (q - 1)
                bigP = bigP.subtract(BigInteger.ONE);
                bigQ = bigQ.subtract(BigInteger.ONE);
                bigN1 = bigP.multiply(bigQ);
     public void btnSelectE_Click()
           if (this.txtN1.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click '(p - 1) x (q - 1)' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
           else if (this.txtD.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Select d' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
                bigE = bigD.modInverse(bigN1);            
     public void btnCalculateD_Click()
           bigD = BigInteger.probablePrime(256, new Random(rnd.nextInt()));
     public void btnCalculateOAEP_Click()
           if (this.txtPlainText.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please enter a valid numeric value in Plain Text field.", "Warning", JOptionPane.ERROR_MESSAGE);
           else if (this.txtPlainText.getText().length() > 15)
                JOptionPane.showMessageDialog(this, "Please enter a valid numeric value, 5 - 15 digits.", "Warning", JOptionPane.ERROR_MESSAGE);
           else if (!this.IsLong(this.txtPlainText.getText()))
                JOptionPane.showMessageDialog(this, "Please enter a valid numeric value, 5 - 15 digits.", "Warning", JOptionPane.ERROR_MESSAGE);
                // convert input text to integer
                BigInteger plainTextBigInt = new BigInteger(txtPlainText.getText());            
                // get bit length of input text
                int plainTextBitLength = plainTextBigInt.bitLength();
                // m bit message
                m = 50;             
                padding = m - plainTextBitLength;
                // create padded message M of bit length m
                BigInteger M = plainTextBigInt.shiftLeft(padding);             
                // Step 2 - # of bits for random number r
                k = 8;              
                // Step 2 - create new random variable r of k bits
                BigInteger r = new BigInteger(8, new Random(rnd.nextInt()));
                // Step 3 - create G(r) which is m bit integer from r bit integer
                BigInteger Gofr= r.shiftLeft(m - k);
                // Step 4 - create P1, first part of plain text which is M XOR G(r)
                BigInteger P1 = M.xor(Gofr);
                // Step 5 - create P2
                BigInteger HofP1 = P1.shiftRight(k - m);
                BigInteger P2 = HofP1.xor(r);
                // Step 6.1 - Concatenate P1 and P2
                String strTemp = P1.toString() + P2.toString();           
                p1Length = P1.toString().length();
                bigPlain = new BigInteger(strTemp);
                //txtOAEP.setText("P1: " + P1 + " P2: " + P2 + " P1 || P2: " + strTemp);
     public BigInteger OEAPDecryption(BigInteger P1, BigInteger P2)
           BigInteger r = (P1.shiftRight(k - m)).xor(P2);
           BigInteger M = (r.shiftLeft(m - k)).xor(P1);
           BigInteger plainTextBigInt = M.shiftRight(padding);
           return plainTextBigInt;
     public void btnEncrypt_Click()
           if (this.txtOAEP.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Cal ( OAEP )' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
           else if (this.txtN.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'n = p x q' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
           else if (this.txtE.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Calculate e' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
                // Encrypt the plain text entered.
                // CAUTION: Plain text should only be numeric and should not be a value bigger than 10 - 15 digits.
                bigCipher = bigPlain.modPow(bigE, bigN);
     public void btnDecrypt_Click()
           if (this.txtCipher.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Encrypt' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
           else if (this.txtD.getText().length() == 0)
                JOptionPane.showMessageDialog(this, "Please click 'Select d' button first.", "Warning", JOptionPane.ERROR_MESSAGE);
                // Decrypt the encrypted integer back to prove that encryption and decryption are inverse of each other.
                bigPlain = bigCipher.modPow(bigD, bigN);
                BigInteger P1 = new BigInteger(bigPlain.toString().substring(0, p1Length));
                BigInteger P2 = new BigInteger(bigPlain.toString().substring(p1Length));
                bigPlain = this.OEAPDecryption(P1, P2);             
                if (new BigInteger(this.txtPlainText.getText()).compareTo(bigPlain) == 0)
                     JOptionPane.showMessageDialog(this, "Since decrypted text is exactly equal to the plain text, hence proved
that encryption and decryption are inverse of each other.
\n\nRSA implementation completed successfully!", "Congratulations", JOptionPane.INFORMATION_MESSAGE);
     private boolean IsLong(String number)
           boolean isLong = true;
           catch (NumberFormatException nfe)
                isLong = false;
           return isLong;
     private int m, k, padding, p1Length;
     private JButton btnCreateP = new JButton("Create p");
     private JButton btnCreateQ = new JButton("Create q");
     private JButton btnCalculateN = new JButton("n = p x q");
     private JButton btnCalculateN1 = new JButton("(p -1) x (q -1)");
     private JButton btnSelectE = new JButton("Calculate e");
     private JButton btnCalculateD = new JButton("Select d");
     private JButton btnCalculateOAEP = new JButton("Call ( OAEP )");
     private JButton btnEncrypt = new JButton("Encrypt");
     private JButton btnDecrypt = new JButton("Decrypt");
     private JTextField txtP = new JTextField();
     private JTextField txtQ = new JTextField();
     private JTextField txtN = new JTextField();
     private JTextField txtN1 = new JTextField();
     private JTextField txtE = new JTextField();
     private JTextField txtD = new JTextField();
     private JTextField txtPlainText = new JTextField();
     private JTextField txtOAEP = new JTextField();
     private JTextField txtCipher = new JTextField();
     private JTextField txtDecipher = new JTextField();
     private JLabel lblAnnouncePrivatePublicKeys = new JLabel("To be announced publicly: e and n are public keys.
To be kept secret: d is private key.");
     private JLabel lblEnterPlainText = new JLabel("Enter Plain Text:");
     private Random rnd = new Random();
     private BigInteger bigP;
     private BigInteger bigQ;
     private BigInteger bigN;
     private BigInteger bigN1;
     private BigInteger bigE;
     private BigInteger bigD;
     private BigInteger bigPlain;
     private BigInteger bigCipher;
     private Container c;


  1. Really Really nice implementation yar. Great work

    Comment by Tamil Selvan — October 12, 2010 @ 5:57 pm

    • Thanks for appreciation 🙂

      Comment by Mukarram Mukhtar — October 15, 2010 @ 2:57 pm

  2. In btnDecrypt_Click() you are using p1Length which is calculated in the encryption phase. How do you calculate that if you don’t know the plain text?

    Comment by Magnus — December 13, 2010 @ 10:10 am

    • Beats me!
      I could go back and study and answer your question, but frankly speaking I’m crazy busy these days, therefore, I encourage you to put some of your own effort and find out. Perhaps the application that is creating cipher code could pass P1Length as a parameter to the other application which is deciphering. Lastly, OAEP is not an essential part of RSA, you can skip OAEP and still implement RSA. Good luck!

      Comment by Mukarram Mukhtar — December 14, 2010 @ 2:37 pm

      • Sounds very strange to me, the code that performs the decryption doesn’t know any data from the encryption phase, if it did it could just use the original plain text directly 😉

        I will try to find it out but I am unfortunately not an expert on this.

        Comment by Magnus — December 14, 2010 @ 3:42 pm

  3. WOooow! That’s great man:) Thanks alot for your link.
    Have a great spring.
    Good luck

    Comment by Bahar — April 7, 2011 @ 7:23 pm

    • You are very welcome, I hope it helps.

      Comment by Mukarram Mukhtar — April 7, 2011 @ 7:50 pm

  4. Its Realy nice and Great Work for the End users,new commer in programming.
    Thanks alot, love you

    Comment by Usman Tariq — May 17, 2011 @ 7:58 am

  5. Please in conect.

    Comment by Usman Tariq — May 17, 2011 @ 7:59 am

  6. how decrease random number size from 512 to 4

    Comment by magid tatai — December 10, 2012 @ 6:32 am

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