math/intpoly/IntegerPolynomial1305.java

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package sun.security.util.math.intpoly;

import java.lang.invoke.MethodHandles;
import java.lang.invoke.VarHandle;
import java.math.BigInteger;
import java.nio.*;

/**
 * An IntegerFieldModuloP designed for use with the Poly1305 authenticator.
 * The representation uses 5 signed long values.
 */

public class IntegerPolynomial1305 extends IntegerPolynomial {

    protected static final int SUBTRAHEND = 5;
    protected static final int NUM_LIMBS = 5;
    private static final int POWER = 130;
    private static final int BITS_PER_LIMB = 26;
    private static final BigInteger MODULUS
        = TWO.pow(POWER).subtract(BigInteger.valueOf(SUBTRAHEND));

    public IntegerPolynomial1305() {
        super(BITS_PER_LIMB, NUM_LIMBS, 1, MODULUS);
    }

    protected void mult(long[] a, long[] b, long[] r) {

        // Use grade-school multiplication into primitives to avoid the
        // temporary array allocation. This is equivalent to the following
        // code:
        //  long[] c = new long[2 * NUM_LIMBS - 1];
        //  for(int i = 0; i < NUM_LIMBS; i++) {
        //      for(int j - 0; j < NUM_LIMBS; j++) {
        //          c[i + j] += a[i] * b[j]
        //      }
        //  }

        long c0 = (a[0] * b[0]);
        long c1 = (a[0] * b[1]) + (a[1] * b[0]);
        long c2 = (a[0] * b[2]) + (a[1] * b[1]) + (a[2] * b[0]);
        long c3 = (a[0] * b[3]) + (a[1] * b[2]) + (a[2] * b[1]) + (a[3] * b[0]);
        long c4 = (a[0] * b[4]) + (a[1] * b[3]) + (a[2] * b[2]) + (a[3] * b[1]) + (a[4] * b[0]);
        long c5 = (a[1] * b[4]) + (a[2] * b[3]) + (a[3] * b[2]) + (a[4] * b[1]);
        long c6 = (a[2] * b[4]) + (a[3] * b[3]) + (a[4] * b[2]);
        long c7 = (a[3] * b[4]) + (a[4] * b[3]);
        long c8 = (a[4] * b[4]);

        carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8);
    }

    private void carryReduce(long[] r, long c0, long c1, long c2, long c3,
                             long c4, long c5, long c6, long c7, long c8) {
        //reduce(2, 2)
        r[2] = c2 + (c7 * SUBTRAHEND);
        c3 += (c8 * SUBTRAHEND);

        // carry(3, 2)
        long carry3 = carryValue(c3);
        r[3] = c3 - (carry3 << BITS_PER_LIMB);
        c4 += carry3;

        long carry4 = carryValue(c4);
        r[4] = c4 - (carry4 << BITS_PER_LIMB);
        c5 += carry4;

        // reduce(0, 2)
        r[0] = c0 + (c5 * SUBTRAHEND);
        r[1] = c1 + (c6 * SUBTRAHEND);

        // carry(0, 4)
        carry(r);
    }

    @Override
    protected void square(long[] a, long[] r) {
        // Use grade-school multiplication with a simple squaring optimization.
        // Multiply into primitives to avoid the temporary array allocation.
        // This is equivalent to the following code:
        //  long[] c = new long[2 * NUM_LIMBS - 1];
        //  for(int i = 0; i < NUM_LIMBS; i++) {
        //      c[2 * i] = a[i] * a[i];
        //      for(int j = i + 1; j < NUM_LIMBS; j++) {
        //          c[i + j] += 2 * a[i] * a[j]
        //      }
        //  }

        long c0 = (a[0] * a[0]);
        long c1 = 2 * (a[0] * a[1]);
        long c2 = 2 * (a[0] * a[2]) + (a[1] * a[1]);
        long c3 = 2 * (a[0] * a[3] + a[1] * a[2]);
        long c4 = 2 * (a[0] * a[4] + a[1] * a[3]) + (a[2] * a[2]);
        long c5 = 2 * (a[1] * a[4] + a[2] * a[3]);
        long c6 = 2 * (a[2] * a[4]) + (a[3] * a[3]);
        long c7 = 2 * (a[3] * a[4]);
        long c8 = (a[4] * a[4]);

        carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8);
    }

    @Override
    protected void encode(ByteBuffer buf, int length, byte highByte,
                          long[] result) {
        if (length == 16) {
            long low = buf.getLong();
            long high = buf.getLong();
            encode(high, low, highByte, result);
        } else {
            super.encode(buf, length, highByte, result);
        }
    }

    protected void encode(long high, long low, byte highByte, long[] result) {
        result[0] = low & 0x3FFFFFFL;
        result[1] = (low >>> 26) & 0x3FFFFFFL;
        result[2] = (low >>> 52) + ((high & 0x3FFFL) << 12);
        result[3] = (high >>> 14) & 0x3FFFFFFL;
        result[4] = (high >>> 40) + (highByte << 24L);
    }

    private static final VarHandle AS_LONG_LE = MethodHandles
        .byteArrayViewVarHandle(long[].class, ByteOrder.LITTLE_ENDIAN);

    protected void encode(byte[] v, int offset, int length, byte highByte,
                          long[] result) {
        if (length == 16) {
            long low = (long) AS_LONG_LE.get(v, offset);
            long high = (long) AS_LONG_LE.get(v, offset + 8);
            encode(high, low, highByte, result);
        } else {
            super.encode(v, offset, length, highByte, result);
        }
    }

    @Override
    protected void reduceIn(long[] limbs, long x, int index) {
        // this only works when BITS_PER_LIMB * NUM_LIMBS = POWER exactly
        long reducedValue = (x * SUBTRAHEND);
        limbs[index - NUM_LIMBS] += reducedValue;
    }

    @Override
    protected void finalCarryReduceLast(long[] limbs) {
        long carry = limbs[numLimbs - 1] >> bitsPerLimb;
        limbs[numLimbs - 1] -= carry << bitsPerLimb;
        reduceIn(limbs, carry, numLimbs);
    }

    protected final void modReduce(long[] limbs, int start, int end) {

        for (int i = start; i < end; i++) {
            reduceIn(limbs, limbs[i], i);
            limbs[i] = 0;
        }
    }

    protected void modReduce(long[] limbs) {

        modReduce(limbs, NUM_LIMBS, NUM_LIMBS - 1);
    }

    @Override
    protected long carryValue(long x) {
        // This representation has plenty of extra space, so we can afford to
        // do a simplified carry operation that is more time-efficient.

        return x >> BITS_PER_LIMB;
    }

    @Override
    protected void postEncodeCarry(long[] v) {
        // not needed because carry is unsigned
    }

    @Override
    protected void reduce(long[] limbs) {
        long carry3 = carryOut(limbs, 3);
        long new4 = carry3 + limbs[4];

        long carry4 = carryValue(new4);
        limbs[4] = new4 - (carry4 << BITS_PER_LIMB);

        reduceIn(limbs, carry4, 5);
        carry(limbs);
    }

}