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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.signers;

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

import org.bouncycastle.crypto.CipherParameters;
import org.bouncycastle.crypto.DSA;
import org.bouncycastle.crypto.params.GOST3410KeyParameters;
import org.bouncycastle.crypto.params.GOST3410Parameters;
import org.bouncycastle.crypto.params.GOST3410PrivateKeyParameters;
import org.bouncycastle.crypto.params.GOST3410PublicKeyParameters;
import org.bouncycastle.crypto.params.ParametersWithRandom;

/**
 * GOST R 34.10-94 Signature Algorithm
 */
public class GOST3410Signer
        implements DSA
{
        GOST3410KeyParameters key;

        SecureRandom    random;

        public void init(
            boolean                 forSigning,
            CipherParameters        param)
        {
            if (forSigning)
            {
                if (param instanceof ParametersWithRandom)
                {
                    ParametersWithRandom rParam = (ParametersWithRandom)param;

                    this.random = rParam.getRandom();
                    this.key = (GOST3410PrivateKeyParameters)rParam.getParameters();
                }
                else
                {
                    this.random = new SecureRandom();
                    this.key = (GOST3410PrivateKeyParameters)param;
                }
            }
            else
            {
                this.key = (GOST3410PublicKeyParameters)param;
            }
        }

        /**
         * generate a signature for the given message using the key we were
         * initialised with. For conventional GOST3410 the message should be a GOST3411
         * hash of the message of interest.
         *
         * @param message the message that will be verified later.
         */
        public BigInteger[] generateSignature(
            byte[] message)
        {
            byte[] mRev = new byte[message.length]; // conversion is little-endian
            for (int i = 0; i != mRev.length; i++)
            {
                mRev[i] = message[mRev.length - 1 - i];
            }
            
            BigInteger      m = new BigInteger(1, mRev);
            GOST3410Parameters   params = key.getParameters();
            BigInteger      k;

            do
            {
                k = new BigInteger(params.getQ().bitLength(), random);
            }
            while (k.compareTo(params.getQ()) >= 0);

            BigInteger  r = params.getA().modPow(k, params.getP()).mod(params.getQ());

            BigInteger  s = k.multiply(m).
                                add(((GOST3410PrivateKeyParameters)key).getX().multiply(r)).
                                    mod(params.getQ());

            BigInteger[]  res = new BigInteger[2];

            res[0] = r;
            res[1] = s;

            return res;
        }

        /**
         * return true if the value r and s represent a GOST3410 signature for
         * the passed in message for standard GOST3410 the message should be a
         * GOST3411 hash of the real message to be verified.
         */
        public boolean verifySignature(
            byte[]      message,
            BigInteger  r,
            BigInteger  s)
        {
            byte[] mRev = new byte[message.length]; // conversion is little-endian
            for (int i = 0; i != mRev.length; i++)
            {
                mRev[i] = message[mRev.length - 1 - i];
            }
            
            BigInteger           m = new BigInteger(1, mRev);
            GOST3410Parameters params = key.getParameters();
            BigInteger           zero = BigInteger.valueOf(0);

            if (zero.compareTo(r) >= 0 || params.getQ().compareTo(r) <= 0)
            {
                return false;
            }

            if (zero.compareTo(s) >= 0 || params.getQ().compareTo(s) <= 0)
            {
                return false;
            }

            BigInteger  v = m.modPow(params.getQ().subtract(new BigInteger("2")),params.getQ());

            BigInteger  z1 = s.multiply(v).mod(params.getQ());
            BigInteger  z2 = (params.getQ().subtract(r)).multiply(v).mod(params.getQ());
            
            z1 = params.getA().modPow(z1, params.getP());
            z2 = ((GOST3410PublicKeyParameters)key).getY().modPow(z2, params.getP());

            BigInteger  u = z1.multiply(z2).mod(params.getP()).mod(params.getQ());

            return u.equals(r);
        }
}