RSA algorithm implementation not working properly in java

Question

Theoretically I know that if n=33, e(public key)=3 and d(private key)=7 I can encrypt a plaintext by using BigInteger class with modPow(e, n), and decrypt with modPow(d,n), but after decryption plaintext is not the same as first.

Here is my code:

  public class KeyTest {
private BigInteger n = new BigInteger("33");
private BigInteger e = new BigInteger("3");
private BigInteger d = new BigInteger("7");

public static void main(String[] args) {
    KeyTest test = new KeyTest();

    BigInteger plaintext = new BigInteger("55");
    System.out.println("Plain text: " + plaintext);

    BigInteger ciphertext = test.encrypt(plaintext);
    System.out.println("Ciphertext: " + ciphertext);

    BigInteger decrypted = test.decrypt(ciphertext);
    System.out.println("Plain text after decryption: " + decrypted);
}

public BigInteger encrypt(BigInteger plaintext) {

    return plaintext.modPow(e, n);
}

public BigInteger decrypt(BigInteger ciphertext) {

    return ciphertext.modPow(d, n);
}
}

The output is:

Plain text: 55 Ciphertext: 22 Plain text after decryption: 22

Your "plaintext=55" is greater than the "modulus=n=33" so what is actually getting encrypted is number 22 (55 mod 33). Also it so happens then 22 encrypted under modulus 33 is again 22. — Oleg Estekhin
– Oleg Estekhin, Commented Jun 17, 2014 at 14:11
The algorithm should be (pow(plaintext, pubKey) mod n), the first operation should be pow and then the mod operation is I'm not right? — M.Veli
– M.Veli, Commented Jun 17, 2014 at 14:19

durron597 · Accepted Answer · 2014-06-17 14:43:57Z

3

Your plaintext (55) is larger than the the modulus (33), so you can't actually encrypt the message. Consider the following slightly different example:

p = 11
q = 17
n = 187
phi(n) = 160
Choose e = 3
If d = 107 then e * d = 321 = 1 mod phi(n)

So change your code to:

  private BigInteger n = new BigInteger("187");
  private BigInteger e = new BigInteger("3");
  private BigInteger d = new BigInteger("107");

  public static void main(String[] args) {
    KeyTest test = new KeyTest();

    BigInteger plaintext = new BigInteger("55");
    System.out.println("Plain text: " + plaintext);

    BigInteger ciphertext = test.encrypt(plaintext);
    System.out.println("Ciphertext: " + ciphertext);

    BigInteger decrypted = test.decrypt(ciphertext);
    System.out.println("Plain text after decryption: " + decrypted);
  }

  public BigInteger encrypt(BigInteger plaintext) {

    return plaintext.modPow(e, n);
  }

  public BigInteger decrypt(BigInteger ciphertext) {

    return ciphertext.modPow(d, n);
  }
}

Output:

Plain text: 55
Ciphertext: 132
Plain text after decryption: 55

answered Jun 17, 2014 at 14:43

durron597

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1 Comment

M.Veli Over a year ago

I understand now why after decryption in my code i am getting "wrong" answer, because it is impossible to calculate bigger number than 33 after mod 33 operation.

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