1. 1 Java Program to Implement RSA Algorithm Yu-Li Chen April, 2002

2. 2 RSA: public key cryptographic system algorithm of RSA is openly published much slower than encrypting with a secret key provides both confidentiality and digital signing functions mostly used for authentication and exchanging a secret key

3. 3 The RSA algorithm: Key generation Encryption with public key Decryption with private key

4. 4 Key generation Select p,qp and q both prime Calculate n = p*q Calculate  (n)=(p-1)(q-1) Select integergcd (  (n),e)=1; 1<e<  (n) Calculate de*d=1 mod  (n) Public key K public ={e,n} Private keyK privarte ={d,n}

5. 5 Encryption Plaintext:M<n e Ciphertext:C=Mmode n

6. 6 Decryption Ciphertext:C d Plaintext:M=Cmode n

7. 7 Objectives: Write a Java program to implement RSA algorithm After public key and private key been generated, use Alice/Bob application over TCP to demonstrate encryption and decryption process.

8. 8 Method: Alice class: Generate the public key pair (1024 bit) and send to Bob. Decrypt the message received from Bob Bob class: Receive public key from Alice Use the public key to encrypt the message Send the ciphertext to Alice.

9. 9 Alice: bitLength = 512; certainty = 50; rnd = new SecureRandom(); p = new BigInteger(bitLength, certainty, rnd); q = new BigInteger(bitLength,certainty,rnd); n= p.multiply(q); one= new BigInteger("1"); x = p.subtract(one).multiply(q.subtract(one)); e = new BigInteger("65537"); d = e.modInverse(x);

10. 10 Alice: Socket clientSocket = new Socket(hostname, 6789); DataOutputStream outToBob =new DataOutputStream(clientSocket.getOutputStream()); outToBob.writeBytes(publicKey + '\n'); clientSocket.close();

11. 11 Bob: ServerSocket welcomeSocket = new ServerSocket(6789); while(true) { Socket connectionSocket = welcomeSocket.accept(); BufferedReader inFromAlice =new BufferedReader(new InputStreamReader(connectionSocket.getInputStream())); publicKey = inFromAlice.readLine(); publickyText.setText(publicKey); }

12. 12 Bob: n= new BigInteger(publicKey); e = new BigInteger("65537"); plaintext=plainText.getText(); m= new BigInteger(plaintext); c = m.modPow(e,n); ciphertext=c.toString();

13. 13 Bob: Socket clientSocket = new Socket(hostname, 2345); DataOutputStream outToAlice = new DataOutputStream( clientSocket.getOutputStream()); outToAlice.writeBytes(ciphertext); clientSocket.close();

14. 14 Alice: ServerSocket welcomeSocket = new ServerSocket(2345); while(true) { Socket connectionSocket= welcomeSocket.accept(); BufferedReader inFromBob = new BufferedReader(new InputStreamReader(connectionSocket.getInputStream())); cipher=inFromBob.readLine(); cipherText.setText(cipher); c= new BigInteger(cipher); m=c.modPow(d,n);

15. 15

16. 16