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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.
/** * 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); } }