| /* |
| * Copyright (c) 2018, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
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| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
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| */ |
| |
| package sun.security.util.math.intpoly; |
| |
| import java.math.BigInteger; |
| |
| /** |
| * An IntegerFieldModuloP designed for use with the Curve25519. |
| * The representation uses 10 signed long values. |
| */ |
| |
| public class IntegerPolynomial25519 extends IntegerPolynomial { |
| |
| private static final int POWER = 255; |
| private static final int SUBTRAHEND = 19; |
| private static final int NUM_LIMBS = 10; |
| private static final int BITS_PER_LIMB = 26; |
| public static final BigInteger MODULUS |
| = TWO.pow(POWER).subtract(BigInteger.valueOf(SUBTRAHEND)); |
| |
| // BITS_PER_LIMB does not divide POWER, so reduction is a bit complicated |
| // The constants below help split up values during reduction |
| private static final int BIT_OFFSET = NUM_LIMBS * BITS_PER_LIMB - POWER; |
| private static final int LIMB_MASK = -1 >>> (64 - BITS_PER_LIMB); |
| private static final int RIGHT_BIT_OFFSET = BITS_PER_LIMB - BIT_OFFSET; |
| |
| public IntegerPolynomial25519() { |
| super(BITS_PER_LIMB, NUM_LIMBS, 1, MODULUS); |
| } |
| |
| @Override |
| protected void finalCarryReduceLast(long[] limbs) { |
| |
| long reducedValue = limbs[numLimbs - 1] >> RIGHT_BIT_OFFSET; |
| limbs[numLimbs - 1] -= reducedValue << RIGHT_BIT_OFFSET; |
| limbs[0] += reducedValue * SUBTRAHEND; |
| } |
| |
| @Override |
| protected void reduce(long[] a) { |
| |
| // carry(8, 2) |
| long carry8 = carryValue(a[8]); |
| a[8] -= (carry8 << BITS_PER_LIMB); |
| a[9] += carry8; |
| |
| long carry9 = carryValue(a[9]); |
| a[9] -= (carry9 << BITS_PER_LIMB); |
| |
| // reduce(0, 1) |
| long reducedValue10 = (carry9 * SUBTRAHEND); |
| a[0] += ((reducedValue10 << BIT_OFFSET) & LIMB_MASK); |
| a[1] += reducedValue10 >> RIGHT_BIT_OFFSET; |
| |
| // carry(0, 9) |
| carry(a, 0, 9); |
| } |
| |
| @Override |
| 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[0] * b[5]) + (a[1] * b[4]) + (a[2] * b[3]) + (a[3] * b[2]) + (a[4] * b[1]) + (a[5] * b[0]); |
| long c6 = (a[0] * b[6]) + (a[1] * b[5]) + (a[2] * b[4]) + (a[3] * b[3]) + (a[4] * b[2]) + (a[5] * b[1]) + (a[6] * b[0]); |
| long c7 = (a[0] * b[7]) + (a[1] * b[6]) + (a[2] * b[5]) + (a[3] * b[4]) + (a[4] * b[3]) + (a[5] * b[2]) + (a[6] * b[1]) + (a[7] * b[0]); |
| long c8 = (a[0] * b[8]) + (a[1] * b[7]) + (a[2] * b[6]) + (a[3] * b[5]) + (a[4] * b[4]) + (a[5] * b[3]) + (a[6] * b[2]) + (a[7] * b[1]) + (a[8] * b[0]); |
| long c9 = (a[0] * b[9]) + (a[1] * b[8]) + (a[2] * b[7]) + (a[3] * b[6]) + (a[4] * b[5]) + (a[5] * b[4]) + (a[6] * b[3]) + (a[7] * b[2]) + (a[8] * b[1]) + (a[9] * b[0]); |
| long c10 = (a[1] * b[9]) + (a[2] * b[8]) + (a[3] * b[7]) + (a[4] * b[6]) + (a[5] * b[5]) + (a[6] * b[4]) + (a[7] * b[3]) + (a[8] * b[2]) + (a[9] * b[1]); |
| long c11 = (a[2] * b[9]) + (a[3] * b[8]) + (a[4] * b[7]) + (a[5] * b[6]) + (a[6] * b[5]) + (a[7] * b[4]) + (a[8] * b[3]) + (a[9] * b[2]); |
| long c12 = (a[3] * b[9]) + (a[4] * b[8]) + (a[5] * b[7]) + (a[6] * b[6]) + (a[7] * b[5]) + (a[8] * b[4]) + (a[9] * b[3]); |
| long c13 = (a[4] * b[9]) + (a[5] * b[8]) + (a[6] * b[7]) + (a[7] * b[6]) + (a[8] * b[5]) + (a[9] * b[4]); |
| long c14 = (a[5] * b[9]) + (a[6] * b[8]) + (a[7] * b[7]) + (a[8] * b[6]) + (a[9] * b[5]); |
| long c15 = (a[6] * b[9]) + (a[7] * b[8]) + (a[8] * b[7]) + (a[9] * b[6]); |
| long c16 = (a[7] * b[9]) + (a[8] * b[8]) + (a[9] * b[7]); |
| long c17 = (a[8] * b[9]) + (a[9] * b[8]); |
| long c18 = a[9] * b[9]; |
| |
| carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8, |
| c9, c10, c11, c12, c13, c14, c15, c16, c17, c18); |
| |
| } |
| |
| private void carryReduce(long[] r, long c0, long c1, long c2, |
| long c3, long c4, long c5, long c6, |
| long c7, long c8, long c9, long c10, |
| long c11, long c12, long c13, long c14, |
| long c15, long c16, long c17, long c18) { |
| // reduce(7,2) |
| long reducedValue17 = (c17 * SUBTRAHEND); |
| c7 += (reducedValue17 << BIT_OFFSET) & LIMB_MASK; |
| c8 += reducedValue17 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue18 = (c18 * SUBTRAHEND); |
| c8 += (reducedValue18 << BIT_OFFSET) & LIMB_MASK; |
| c9 += reducedValue18 >> RIGHT_BIT_OFFSET; |
| |
| // carry(8,2) |
| long carry8 = carryValue(c8); |
| r[8] = c8 - (carry8 << BITS_PER_LIMB); |
| c9 += carry8; |
| |
| long carry9 = carryValue(c9); |
| r[9] = c9 - (carry9 << BITS_PER_LIMB); |
| c10 += carry9; |
| |
| // reduce(0,7) |
| long reducedValue10 = (c10 * SUBTRAHEND); |
| r[0] = c0 + ((reducedValue10 << BIT_OFFSET) & LIMB_MASK); |
| c1 += reducedValue10 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue11 = (c11 * SUBTRAHEND); |
| r[1] = c1 + ((reducedValue11 << BIT_OFFSET) & LIMB_MASK); |
| c2 += reducedValue11 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue12 = (c12 * SUBTRAHEND); |
| r[2] = c2 + ((reducedValue12 << BIT_OFFSET) & LIMB_MASK); |
| c3 += reducedValue12 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue13 = (c13 * SUBTRAHEND); |
| r[3] = c3 + ((reducedValue13 << BIT_OFFSET) & LIMB_MASK); |
| c4 += reducedValue13 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue14 = (c14 * SUBTRAHEND); |
| r[4] = c4 + ((reducedValue14 << BIT_OFFSET) & LIMB_MASK); |
| c5 += reducedValue14 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue15 = (c15 * SUBTRAHEND); |
| r[5] = c5 + ((reducedValue15 << BIT_OFFSET) & LIMB_MASK); |
| c6 += reducedValue15 >> RIGHT_BIT_OFFSET; |
| |
| long reducedValue16 = (c16 * SUBTRAHEND); |
| r[6] = c6 + ((reducedValue16 << BIT_OFFSET) & LIMB_MASK); |
| r[7] = c7 + (reducedValue16 >> RIGHT_BIT_OFFSET); |
| |
| // carry(0,9) |
| carry(r, 0, 9); |
| } |
| |
| @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 = a[1] * a[1] + 2 * a[0] * a[2]; |
| long c3 = 2 * (a[0] * a[3] + a[1] * a[2]); |
| long c4 = a[2] * a[2] + 2 * (a[0] * a[4] + a[1] * a[3]); |
| long c5 = 2 * (a[0] * a[5] + a[1] * a[4] + a[2] * a[3]); |
| long c6 = a[3] * a[3] + 2 * (a[0] * a[6] + a[1] * a[5] + a[2] * a[4]); |
| long c7 = 2 * (a[0] * a[7] + a[1] * a[6] + a[2] * a[5] + a[3] * a[4]); |
| long c8 = a[4] * a[4] + 2 * (a[0] * a[8] + a[1] * a[7] + a[2] * a[6] + a[3] * a[5]); |
| long c9 = 2 * (a[0] * a[9] + a[1] * a[8] + a[2] * a[7] + a[3] * a[6] + a[4] * a[5]); |
| long c10 = a[5] * a[5] + 2 * (a[1] * a[9] + a[2] * a[8] + a[3] * a[7] + a[4] * a[6]); |
| long c11 = 2 * (a[2] * a[9] + a[3] * a[8] + a[4] * a[7] + a[5] * a[6]); |
| long c12 = a[6] * a[6] + 2 * (a[3] * a[9] + a[4] * a[8] + a[5] * a[7]); |
| long c13 = 2 * (a[4] * a[9] + a[5] * a[8] + a[6] * a[7]); |
| long c14 = a[7] * a[7] + 2 * (a[5] * a[9] + a[6] * a[8]); |
| long c15 = 2 * (a[6] * a[9] + a[7] * a[8]); |
| long c16 = a[8] * a[8] + 2 * a[7] * a[9]; |
| long c17 = 2 * a[8] * a[9]; |
| long c18 = a[9] * a[9]; |
| |
| carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8, |
| c9, c10, c11, c12, c13, c14, c15, c16, c17, c18); |
| } |
| |
| |
| } |