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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
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package org.bouncycastle.crypto.engines;

import java.math.BigInteger;
import java.security.SecureRandom;

import org.bouncycastle.crypto.AsymmetricBlockCipher;
import org.bouncycastle.crypto.CipherParameters;
import org.bouncycastle.crypto.CryptoServicesRegistrar;
import org.bouncycastle.crypto.DataLengthException;
import org.bouncycastle.crypto.constraints.ConstraintUtils;
import org.bouncycastle.crypto.constraints.DefaultServiceProperties;
import org.bouncycastle.crypto.params.ElGamalKeyParameters;
import org.bouncycastle.crypto.params.ElGamalPrivateKeyParameters;
import org.bouncycastle.crypto.params.ElGamalPublicKeyParameters;
import org.bouncycastle.crypto.params.ParametersWithRandom;
import org.bouncycastle.util.BigIntegers;

/**
 * this does your basic ElGamal algorithm.
 */
public class ElGamalEngine
    implements AsymmetricBlockCipher
{
    private ElGamalKeyParameters    key;
    private SecureRandom            random;
    private boolean                 forEncryption;
    private int                     bitSize;

    private static final BigInteger ZERO = BigInteger.valueOf(0);
    private static final BigInteger ONE = BigInteger.valueOf(1);
    private static final BigInteger TWO = BigInteger.valueOf(2);

    /**
     * initialise the ElGamal engine.
     *
     * @param forEncryption true if we are encrypting, false otherwise.
     * @param param the necessary ElGamal key parameters.
     */
    public void init(
        boolean             forEncryption,
        CipherParameters    param)
    {
        if (param instanceof ParametersWithRandom)
        {
            ParametersWithRandom    p = (ParametersWithRandom)param;

            this.key = (ElGamalKeyParameters)p.getParameters();
            this.random = p.getRandom();
        }
        else
        {
            this.key = (ElGamalKeyParameters)param;
            this.random = CryptoServicesRegistrar.getSecureRandom();
        }

        this.forEncryption = forEncryption;

        BigInteger p = key.getParameters().getP();

        bitSize = p.bitLength();

        if (forEncryption)
        {
            if (!(key instanceof ElGamalPublicKeyParameters))
            {
                throw new IllegalArgumentException("ElGamalPublicKeyParameters are required for encryption.");
            }
        }
        else
        {
            if (!(key instanceof ElGamalPrivateKeyParameters))
            {
                throw new IllegalArgumentException("ElGamalPrivateKeyParameters are required for decryption.");
            }
        }

        CryptoServicesRegistrar.checkConstraints(new DefaultServiceProperties("RSA", ConstraintUtils.bitsOfSecurityFor(key.getParameters().getP()), key, Utils.getPurpose(forEncryption)));
    }

    /**
     * Return the maximum size for an input block to this engine.
     * For ElGamal this is always one byte less than the size of P on
     * encryption, and twice the length as the size of P on decryption.
     *
     * @return maximum size for an input block.
     */
    public int getInputBlockSize()
    {
        if (forEncryption)
        {
            return (bitSize - 1) / 8;
        }

        return 2 * ((bitSize + 7) / 8);
    }

    /**
     * Return the maximum size for an output block to this engine.
     * For ElGamal this is always one byte less than the size of P on
     * decryption, and twice the length as the size of P on encryption.
     *
     * @return maximum size for an output block.
     */
    public int getOutputBlockSize()
    {
        if (forEncryption)
        {
            return 2 * ((bitSize + 7) / 8);
        }

        return (bitSize - 1) / 8;
    }

    /**
     * Process a single block using the basic ElGamal algorithm.
     *
     * @param in the input array.
     * @param inOff the offset into the input buffer where the data starts.
     * @param inLen the length of the data to be processed.
     * @return the result of the ElGamal process.
     * @exception DataLengthException the input block is too large.
     */
    public byte[] processBlock(
        byte[]  in,
        int     inOff,
        int     inLen)
    {
        if (key == null)
        {
            throw new IllegalStateException("ElGamal engine not initialised");
        }

        int maxLength = forEncryption
            ?   (bitSize - 1 + 7) / 8
            :   getInputBlockSize();

        if (inLen > maxLength)
        {
            throw new DataLengthException("input too large for ElGamal cipher.\n");
        }

        BigInteger  p = key.getParameters().getP();

        if (key instanceof ElGamalPrivateKeyParameters) // decryption
        {
            byte[]  in1 = new byte[inLen / 2];
            byte[]  in2 = new byte[inLen / 2];

            System.arraycopy(in, inOff, in1, 0, in1.length);
            System.arraycopy(in, inOff + in1.length, in2, 0, in2.length);

            BigInteger  gamma = new BigInteger(1, in1);
            BigInteger  phi = new BigInteger(1, in2);

            ElGamalPrivateKeyParameters  priv = (ElGamalPrivateKeyParameters)key;
            // a shortcut, which generally relies on p being prime amongst other things.
            // if a problem with this shows up, check the p and g values!
            BigInteger  m = gamma.modPow(p.subtract(ONE).subtract(priv.getX()), p).multiply(phi).mod(p);

            return BigIntegers.asUnsignedByteArray(m);
        }
        else // encryption
        {
            byte[] block;
            if (inOff != 0 || inLen != in.length)
            {
                block = new byte[inLen];

                System.arraycopy(in, inOff, block, 0, inLen);
            }
            else
            {
                block = in;
            }

            BigInteger input = new BigInteger(1, block);

            if (input.compareTo(p) >= 0)
            {
                throw new DataLengthException("input too large for ElGamal cipher.\n");
            }

            ElGamalPublicKeyParameters  pub = (ElGamalPublicKeyParameters)key;

            int                         pBitLength = p.bitLength();
            BigInteger                  k = BigIntegers.createRandomBigInteger(pBitLength, random);

            while (k.equals(ZERO) || (k.compareTo(p.subtract(TWO)) > 0))
            {
                k = BigIntegers.createRandomBigInteger(pBitLength, random);
            }

            BigInteger  g = key.getParameters().getG();
            BigInteger  gamma = g.modPow(k, p);
            BigInteger  phi = input.multiply(pub.getY().modPow(k, p)).mod(p);

            byte[]  out1 = gamma.toByteArray();
            byte[]  out2 = phi.toByteArray();
            byte[]  output = new byte[this.getOutputBlockSize()];

            if (out1.length > output.length / 2)
            {
                System.arraycopy(out1, 1, output, output.length / 2 - (out1.length - 1), out1.length - 1);
            }
            else
            {
                System.arraycopy(out1, 0, output, output.length / 2 - out1.length, out1.length);
            }

            if (out2.length > output.length / 2)
            {
                System.arraycopy(out2, 1, output, output.length - (out2.length - 1), out2.length - 1);
            }
            else
            {
                System.arraycopy(out2, 0, output, output.length - out2.length, out2.length);
            }

            return output;
        }
    }
}