Simple RSA decryption error

Question

Hi All
I am trying a very simple RSA implementations. I am not able to decrypt the data correctly. Please find my code below,
import java.math.BigInteger;
import java.util.Random;
public class SimpleRSA {
     public static BigInteger p, q, N, v, k, d;
     public static void main(String[] args) {
          // p & q are prime numbers
          Random myRandom = new Random(0);
          p = BigInteger.probablePrime(32, myRandom);
          q = BigInteger.probablePrime(32, myRandom);
          System.out.println("Value of p:" + p);
          System.out.println("Value of q:" + q);
          // N = pq
          N = p.multiply(q);
          System.out.println("Value of N:" + N);
          // v = (p-1)*(q-1)
          v =
               (p.subtract(BigInteger.valueOf(1))).multiply(
                    q.subtract(BigInteger.valueOf(1)));
          System.out.println("Value of v:" + v);
          // Compute k such that gcd(k, v) = 1
          k = new BigInteger("3");
          while(v.gcd(k).intValue() > 1) k = k.add(new BigInteger("2"));
          System.out.println("Value of k:" + k);
          // Compute d such that (d * k)%v = 1
          d = k.modInverse(v);
          System.out.println("Value of d:" + d);
          System.out.println("Public Key (k,N): (" + k + "," + N + ")");
          System.out.println("Private Key (d,N): (" + d + "," + N + ")");
          // Encryption
          String text = "Welcome to Java";
          System.out.println("Sample text:" + text);
          byte[] cipherData = text.getBytes();
          BigInteger a = new BigInteger(cipherData);
          System.out.println("BigInteger a:" + a);          
          BigInteger b = a.modPow(k, N);
          System.out.println("Encrypted data:" + b);
          // Decryption
          BigInteger c = b.modPow(d, N);
          byte[] decryptedData = c.toByteArray();          
          String plainText = new String(decryptedData);
          System.out.println("Decrypted data:" + plainText);     
The answer I am getting is like this
Value of p:3139482721
Value of q:3180579707
Value of N:9985375032889742747
Value of v:9985375026569680320
Value of k:7
Value of d:4279446439958434423
Public Key (k,N): (7,9985375032889742747)
Private Key (d,N): (4279446439958434423,9985375032889742747)
Sample text:Welcome to Java
BigInteger a:1446156601937412646258
Encrypted data:9678387382297663676
Decrypted data:r��`�>B[/i]
Please help me in this regard.
Regards
Kathirvel

Answer 1

"m" (the integer rep of the message) must be strictly less than "N" (p*q). Look at the output - your p and q are too small for your data. Tryp = BigInteger.probablePrime(512, myRandom);
q = BigInteger.probablePrime(512, myRandom);and try again.
Then, go back and re-read the description of the RSA algorithm:
http://en.wikipedia.org/wiki/RSA
("Applied Cryptography" would be bettr - but Wikipedia is at least a good start...)
Grant