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

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.

Answer 1

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;
}

Answer 2

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.