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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.generators;

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

import org.bouncycastle.crypto.AsymmetricCipherKeyPair;
import org.bouncycastle.crypto.AsymmetricCipherKeyPairGenerator;
import org.bouncycastle.crypto.KeyGenerationParameters;
import org.bouncycastle.crypto.params.DSAKeyGenerationParameters;
import org.bouncycastle.crypto.params.DSAParameters;
import org.bouncycastle.crypto.params.DSAPrivateKeyParameters;
import org.bouncycastle.crypto.params.DSAPublicKeyParameters;
import org.bouncycastle.math.ec.WNafUtil;
import org.bouncycastle.util.BigIntegers;

/**
 * a DSA key pair generator.
 *
 * This generates DSA keys in line with the method described 
 * in FIPS 186-3 B.1 FFC Key Pair Generation.
 */
public class DSAKeyPairGenerator
    implements AsymmetricCipherKeyPairGenerator
{
    private static final BigInteger ONE = BigInteger.valueOf(1);

    private DSAKeyGenerationParameters param;

    public void init(
        KeyGenerationParameters param)
    {
        this.param = (DSAKeyGenerationParameters)param;
    }

    public AsymmetricCipherKeyPair generateKeyPair()
    {
        DSAParameters dsaParams = param.getParameters();

        BigInteger x = generatePrivateKey(dsaParams.getQ(), param.getRandom());
        BigInteger y = calculatePublicKey(dsaParams.getP(), dsaParams.getG(), x);

        return new AsymmetricCipherKeyPair(
            new DSAPublicKeyParameters(y, dsaParams),
            new DSAPrivateKeyParameters(x, dsaParams));
    }

    private static BigInteger generatePrivateKey(BigInteger q, SecureRandom random)
    {
        // B.1.2 Key Pair Generation by Testing Candidates
        int minWeight = q.bitLength() >>> 2;
        for (;;)
        {
            // TODO Prefer this method? (change test cases that used fixed random)
            // B.1.1 Key Pair Generation Using Extra Random Bits
//            BigInteger x = new BigInteger(q.bitLength() + 64, random).mod(q.subtract(ONE)).add(ONE);

            BigInteger x = BigIntegers.createRandomInRange(ONE, q.subtract(ONE), random);
            if (WNafUtil.getNafWeight(x) >= minWeight)
            {
                return x;
            }
        }
    }

    private static BigInteger calculatePublicKey(BigInteger p, BigInteger g, BigInteger x)
    {
        return g.modPow(x, p);
    }
}