Java Card setExponent() method fails when exponent has more than 10 bytes

Question

I'm trying to implement the modPow function on Java Card using the build in RSA CryptoSystem. The code seems trivial but I have issued on implementation.

My code untill now :

    Cipher m_encryptCipherRSA = Cipher.getInstance(Cipher.ALG_RSA_NOPAD, false); // create the cipher
    RSAPublicKey m_rsaPublicKey = (RSAPublicKey) KeyBuilder.buildKey(KeyBuilder.TYPE_RSA_PUBLIC,KeyBuilder.LENGTH_RSA_1024,false);  // create the public key
    m_random = RandomData.getInstance(RandomData.ALG_SECURE_RANDOM);
    m_random.generateData(temp1, (short)0, MODULUS_LENGTH);
    m_rsaPublicKey.setModulus(temp1,(short)0, MODULUS_LENGTH); //generate modulus
    m_random.generateData(temp1,(short)0, (short) EXPONENT_LENGTH);
    m_rsaPublicKey.setExponent(temp1,(short)0, (short)EXPONENT_LENGTH);

The cod seems to work ok if EXPONENT_LENGTH has no more than 10 bytes.The Java Card I have has limited the dimension of public exponent. However my project is based on numbers up to 128bytes long.Is there a way to create a generic modpow function based on this hardware limitation? Is there another way I could implement the power exponentiation which is still feasible.

What happens when you use `EXPONENT_LENGTH > 10`? What status word do you get? — vojta, Apr 29 '16 at 11:28
Catch the thrown exception and tell us its type (use the instanceof operator) and its reason (output of getReason() method), please. — vojta, Apr 30 '16 at 17:16
@vojta I managed to solve the problem by using the private exponent instead of public one.Now I have the problem with dofinal method on Rsa when input is 1024 bits long and starts with an octet greater than 0x68. — Alberto12, May 01 '16 at 12:15
@vojta I started the new problem [here](http://stackoverflow.com/questions/36966764/rsa-cipher-java-card-error) with a detailed explanation — Alberto12, May 01 '16 at 12:43

score 1 · Accepted Answer · answered May 01 '16 at 12:26

I managed to solve the problem by using the private exponent ( which seems not be constraint by RSA cryptosystem).Below is the working code.

    public byte[] modPow(byte[] x,short xOffset,short xLength,byte[] y,short yOffset,short yLength)
{
    Util.arrayCopy(y, yOffset, tempBuffer, (short)(Configuration.TEMP_OFFSET_EXPONENT+4), yLength);
    Util.arrayFillNonAtomic(tempBuffer, Configuration.TEMP_OFFSET_EXPONENT, (byte)4,(byte)0x00);
    mRsaPrivateKeyModPow.setExponent(tempBuffer,Configuration.TEMP_OFFSET_EXPONENT, (short)(yLength+4));
    mRsaCipherModPow.init(mRsaPrivateKeyModPow, Cipher.MODE_DECRYPT);
    Util.arrayCopy(x,xOffset,tempBuffer, Configuration.TEMP_OFFSET_RSA, Configuration.LENGTH_RSAOBJECT_MODULUS);
    mRsaCipherModPow.doFinal(tempBuffer,Configuration.TEMP_OFFSET_RSA, (short) (Configuration.LENGTH_RSAOBJECT_MODULUS), tempBuffer,Configuration.TEMP_OFFSET_RSA);
    mRsaPrivateKeyModPow.clearKey();
    return tempBuffer;
}

score 1 · Answer 2 · edited May 23 '17 at 11:58

Well, I tried both RSAPublicKey and RSAPrivateKey for two different cards, and both worked fine:

package soqPack;

import javacard.framework.*;
import javacard.security.KeyBuilder;
import javacard.security.RSAPrivateKey;
import javacard.security.RSAPublicKey;
import javacard.security.RandomData;
import javacardx.biometry.BioBuilder;
import javacardx.crypto.Cipher;

public class modPowtest extends Applet {

    //Definition Of INS in APDU command
    public static final byte INS_MOD_POW = (byte) 0x00;

    //Switch cases to choose RSA Public key or RSA Private key for ModPow()
    //P1 in APDU command.
    public static final byte USE_PUB_KEY = (byte) 0x00;
    public static final byte USE_PRI_KEY = (byte) 0x01;

    //Required objects
    byte[] tempMem;
    Cipher myCipher;
    RSAPrivateKey rsaPriKey;
    RSAPublicKey rsaPubKey;
    RandomData random;

    public static void install(byte[] bArray, short bOffset, byte bLength) {
        new modPowtest();
    }

    protected modPowtest() {
        myCipher = Cipher.getInstance(Cipher.ALG_RSA_PKCS1, false);
        rsaPriKey = (RSAPrivateKey) KeyBuilder.buildKey(KeyBuilder.TYPE_RSA_PRIVATE, KeyBuilder.LENGTH_RSA_1024, false);
        rsaPubKey = (RSAPublicKey) KeyBuilder.buildKey(KeyBuilder.TYPE_RSA_PUBLIC, KeyBuilder.LENGTH_RSA_1024, false);
        tempMem = JCSystem.makeTransientByteArray((short) 0x80, JCSystem.CLEAR_ON_DESELECT);
        random = RandomData.getInstance(RandomData.ALG_PSEUDO_RANDOM);
        register();
    }

    public void process(APDU apdu) {
        if (selectingApplet()) {
            return;
        }

        byte[] buffer = apdu.getBuffer();
        switch (buffer[ISO7816.OFFSET_INS]) {
            case INS_MOD_POW:
                modPow(apdu);
                break;
            default:
                ISOException.throwIt(ISO7816.SW_INS_NOT_SUPPORTED);
        }
    }

    public void modPow(APDU apdu) {
        byte[] buffer = apdu.getBuffer();
        switch (buffer[ISO7816.OFFSET_P1]) {
            case USE_PUB_KEY:
                random.generateData(tempMem, (short) 0x00, (short) 0x80);
                rsaPubKey.setModulus(tempMem, (short) 0x00, (short) 0x80);
                random.generateData(tempMem, (short) 0x00, (short) 0x03);
                rsaPubKey.setExponent(tempMem, (short) 0x00, (short) 0x03);
                break;
            case USE_PRI_KEY:
                random.generateData(tempMem, (short) 0x00, (short) 0x80);
                rsaPriKey.setModulus(tempMem, (short) 0x00, (short) 0x80);
                random.generateData(tempMem, (short) 0x00, (short) 0x03);
                rsaPriKey.setExponent(tempMem, (short) 0x00, (short) 0x03);
                break;
            default:
                ISOException.throwIt(ISO7816.SW_INCORRECT_P1P2);
        }

    }
}

Works as below:

Download Cap begin...
Download Cap successful.
Install Applet begin...
Install Applet successful.
Select Applet begin...
Select Applet successful.

Send: 00 00 00 00 00
Recv: 90 00

Send: 00 00 01 00 00
Recv: 90 00

Update: (Related your new question in the comments and here):

I also, changed value of tempMem[0] just before the setModulus and setExponent methods to 0x69, and it still works fine.

I read that `setExponent()` may fail if the size of the exponent is greater than 4 bytes.From the oracle documentation I found this `All implementations must support exponent values up to 4 bytes in length. Implementations may also support exponent values greater than 4 bytes in length.` Here is the [link](http://www.win.tue.nl/pinpasjc/docs/apis/jc222/javacard/security/RSAPublicKey.html). — Alberto12, May 01 '16 at 13:03
I start [here](http://stackoverflow.com/questions/36966764/rsa-cipher-java-card-error) with the new problem.It seems to me a problem with the modulus vallue.I guess it is less than the x-value from RSA and the algorithm fails. — Alberto12, May 01 '16 at 13:08

Java Card setExponent() method fails when exponent has more than 10 bytes

2 Answers2