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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 and up.
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package org.bouncycastle.crypto.test;

import java.io.IOException;
import java.security.SecureRandom;

import org.bouncycastle.crypto.modes.gcm.GCMExponentiator;
import org.bouncycastle.crypto.modes.gcm.GCMMultiplier;
import org.bouncycastle.crypto.modes.gcm.Tables1kGCMExponentiator;
import org.bouncycastle.crypto.modes.gcm.Tables4kGCMMultiplier;
import org.bouncycastle.util.Arrays;
import org.bouncycastle.util.Pack;
import org.bouncycastle.util.encoders.Hex;

import junit.framework.TestCase;

public class GCMReorderTest
    extends TestCase
{
    private static final byte[] H;
    private static final SecureRandom random = new SecureRandom(); 
    private static final GCMMultiplier mul = new Tables4kGCMMultiplier();
    private static final GCMExponentiator exp = new Tables1kGCMExponentiator();
    private static final byte[] EMPTY = new byte[0];

    static
    {
        H = new byte[16];
        random.nextBytes(H);
        mul.init(Arrays.clone(H));
        exp.init(Arrays.clone(H));
    }

    public void testCombine() throws Exception
    {
        for (int count = 0; count < 10; ++count)
        {
            byte[] A = randomBytes(1000);
            byte[] C = randomBytes(1000);

            byte[] ghashA_ = GHASH(A, EMPTY);
            byte[] ghash_C = GHASH(EMPTY, C);
            byte[] ghashAC = GHASH(A, C);

            byte[] ghashCombine = combine_GHASH(ghashA_, (long)A.length * 8, ghash_C, (long)C.length * 8);

            assertTrue(Arrays.areEqual(ghashAC, ghashCombine));
        }
    }

    public void testConcatAuth() throws Exception
    {
        for (int count = 0; count < 10; ++count)
        {
            byte[] P = randomBlocks(100);
            byte[] A = randomBytes(1000);
            byte[] PA = concatArrays(P, A);

            byte[] ghashP_ = GHASH(P, EMPTY);
            byte[] ghashA_ = GHASH(A, EMPTY);
            byte[] ghashPA_ = GHASH(PA, EMPTY);
            byte[] ghashConcat = concatAuth_GHASH(ghashP_, (long)P.length * 8, ghashA_, (long)A.length * 8);

            assertTrue(Arrays.areEqual(ghashPA_, ghashConcat));
        }
    }

    public void testConcatCrypt() throws Exception
    {
        for (int count = 0; count < 10; ++count)
        {
            byte[] P = randomBlocks(100);
            byte[] A = randomBytes(1000);
            byte[] PA = concatArrays(P, A);
    
            byte[] ghash_P = GHASH(EMPTY, P);
            byte[] ghash_A = GHASH(EMPTY, A);
            byte[] ghash_PA = GHASH(EMPTY, PA);
            byte[] ghashConcat = concatCrypt_GHASH(ghash_P, (long)P.length * 8, ghash_A, (long)A.length * 8);

            assertTrue(Arrays.areEqual(ghash_PA, ghashConcat));
        }
    }

    public void testExp()
    {
        {
            byte[] buf1 = new byte[16];
            buf1[0] = (byte)0x80;
    
            byte[] buf2 = new byte[16];
    
            for (int pow = 0; pow != 100; ++pow)
            {
                exp.exponentiateX(pow, buf2);
    
                assertTrue(Arrays.areEqual(buf1, buf2));

                mul.multiplyH(buf1);
            }
        }

        long[] testPow = new long[]{ 10, 1, 8, 17, 24, 13, 2, 13, 2, 3 };
        byte[][] testData = new byte[][]{
            Hex.decode("9185848a877bd87ba071e281f476e8e7"),
            Hex.decode("697ce3052137d80745d524474fb6b290"),
            Hex.decode("2696fc47198bb23b11296e4f88720a17"),
            Hex.decode("01f2f0ead011a4ae0cf3572f1b76dd8e"),
            Hex.decode("a53060694a044e4b7fa1e661c5a7bb6b"),
            Hex.decode("39c0392e8b6b0e04a7565c85394c2c4c"),
            Hex.decode("519c362d502e07f2d8b7597a359a5214"),
            Hex.decode("5a527a393675705e19b2117f67695af4"),
            Hex.decode("27fc0901d1d332a53ba4d4386c2109d2"),
            Hex.decode("93ca9b57174aabedf8220e83366d7df6"),
        };

        for (int i = 0; i != 10; ++i)
        {
            long pow = testPow[i];
            byte[] data = Arrays.clone(testData[i]);

            byte[] expected = Arrays.clone(data);
            for (int j = 0; j < pow; ++j)
            {
                mul.multiplyH(expected);
            }

            byte[] H_a = new byte[16];
            exp.exponentiateX(pow, H_a);
            byte[] actual = multiply(data, H_a);

            assertTrue(Arrays.areEqual(expected, actual));
        }
    }

    public void testMultiply()
    {
        byte[] expected = Arrays.clone(H);
        mul.multiplyH(expected);

        assertTrue(Arrays.areEqual(expected, multiply(H, H)));

        for (int count = 0; count < 10; ++count)
        {
            byte[] a = new byte[16];
            random.nextBytes(a);

            byte[] b = new byte[16];
            random.nextBytes(b);

            expected = Arrays.clone(a);
            mul.multiplyH(expected);
            assertTrue(Arrays.areEqual(expected, multiply(a, H)));
            assertTrue(Arrays.areEqual(expected, multiply(H, a)));

            expected = Arrays.clone(b);
            mul.multiplyH(expected);
            assertTrue(Arrays.areEqual(expected, multiply(b, H)));
            assertTrue(Arrays.areEqual(expected, multiply(H, b)));

            assertTrue(Arrays.areEqual(multiply(a, b), multiply(b, a)));
        }
    }

    private byte[] randomBlocks(int upper)
    {
        byte[] bs = new byte[16 * random.nextInt(upper)];
        random.nextBytes(bs);
        return bs;
    }

    private byte[] randomBytes(int upper)
    {
        byte[] bs = new byte[random.nextInt(upper)];
        random.nextBytes(bs);
        return bs;
    }

    private byte[] concatArrays(byte[] a, byte[] b) throws IOException
    {
        byte[] ab = new byte[a.length + b.length];
        System.arraycopy(a, 0, ab, 0, a.length);
        System.arraycopy(b, 0, ab, a.length, b.length);
        return ab;
    }

    private byte[] combine_GHASH(byte[] ghashA_, long bitlenA, byte[] ghash_C, long bitlenC)
    {
        // Note: bitlenA must be aligned to the block size

        long c = (bitlenC + 127) >>> 7;

        byte[] H_c = new byte[16];
        exp.exponentiateX(c, H_c);

        byte[] tmp1 = lengthBlock(bitlenA, 0);
        mul.multiplyH(tmp1);

        byte[] ghashAC = Arrays.clone(ghashA_);
        xor(ghashAC, tmp1);
        ghashAC = multiply(ghashAC, H_c);
        // No need to touch the len(C) part (second 8 bytes)
        xor(ghashAC, tmp1);
        xor(ghashAC, ghash_C);

        return ghashAC;
    }

    private byte[] concatAuth_GHASH(byte[] ghashP, long bitlenP, byte[] ghashA, long bitlenA)
    {
        // Note: bitlenP must be aligned to the block size

        long a = (bitlenA + 127) >>> 7;

        byte[] tmp1 = lengthBlock(bitlenP, 0);
        mul.multiplyH(tmp1);

        byte[] tmp2 = lengthBlock(bitlenA ^ (bitlenP + bitlenA), 0);
        mul.multiplyH(tmp2);

        byte[] H_a = new byte[16];
        exp.exponentiateX(a, H_a);
        
        byte[] ghashC = Arrays.clone(ghashP);
        xor(ghashC, tmp1);
        ghashC = multiply(ghashC, H_a);
        xor(ghashC, tmp2);
        xor(ghashC, ghashA);
        return ghashC;
    }

    private byte[] concatCrypt_GHASH(byte[] ghashP, long bitlenP, byte[] ghashA, long bitlenA)
    {
        // Note: bitlenP must be aligned to the block size

        long a = (bitlenA + 127) >>> 7;

        byte[] tmp1 = lengthBlock(0, bitlenP);
        mul.multiplyH(tmp1);

        byte[] tmp2 = lengthBlock(0, bitlenA ^ (bitlenP + bitlenA));
        mul.multiplyH(tmp2);

        byte[] H_a = new byte[16];
        exp.exponentiateX(a, H_a);
        
        byte[] ghashC = Arrays.clone(ghashP);
        xor(ghashC, tmp1);
        ghashC = multiply(ghashC, H_a);
        xor(ghashC, tmp2);
        xor(ghashC, ghashA);
        return ghashC;
    }

    private byte[] GHASH(byte[] A, byte[] C)
    {
        byte[] X = new byte[16];

        {
            for (int pos = 0; pos < A.length; pos += 16)
            {
                byte[] tmp = new byte[16];
                int num = Math.min(A.length - pos, 16);
                System.arraycopy(A, pos, tmp, 0, num);
                xor(X, tmp);
                mul.multiplyH(X);
            }
        }

        {
            for (int pos = 0; pos < C.length; pos += 16)
            {
                byte[] tmp = new byte[16];
                int num = Math.min(C.length - pos, 16);
                System.arraycopy(C, pos, tmp, 0, num);
                xor(X, tmp);
                mul.multiplyH(X);
            }
        }

        {
            xor(X, lengthBlock((long)A.length * 8, (long)C.length * 8));
            mul.multiplyH(X);
        }

        return X;
    }

    private static byte[] lengthBlock(long bitlenA, long bitlenC)
    {
        byte[] tmp = new byte[16];
        Pack.longToBigEndian(bitlenA, tmp, 0);
        Pack.longToBigEndian(bitlenC, tmp, 8);
        return tmp;
    }

    private static void xor(byte[] block, byte[] val)
    {
        for (int i = 15; i >= 0; --i)
        {
            block[i] ^= val[i];
        }
    }

    private static byte[] multiply(byte[] a, byte[] b)
    {
        byte[] c = new byte[16];
        byte[] tmp = Arrays.clone(b);

        for (int i = 0; i < 16; ++i)
        {
            byte bits = a[i];
            for (int j = 7; j >= 0; --j)
            {
                if ((bits & (1 << j)) != 0)
                {
                    xor(c, tmp);
                }

                boolean lsb = (tmp[15] & 1) != 0;
                shiftRight(tmp);
                if (lsb)
                {
                    // R = new byte[]{ 0xe1, ... };
//                    GCMUtil.xor(v, R);
                    tmp[0] ^= (byte)0xe1;
                }
            }
        }

        return c;
    }

    private static void shiftRight(byte[] block)
    {
        int i = 0;
        int bit = 0;
        for (;;)
        {
            int b = block[i] & 0xff;
            block[i] = (byte) ((b >>> 1) | bit);
            if (++i == 16)
            {
                break;
            }
            bit = (b & 1) << 7;
        }
    }
}