| /* |
| * 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 |
| * under the terms of the GNU General Public License version 2 only, as |
| * 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. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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| * questions. |
| */ |
| |
| package sun.security.util.math.intpoly; |
| |
| import java.math.BigInteger; |
| |
| /** |
| * An IntegerFieldModuloP designed for use with the Curve448. |
| * The representation uses 16 signed long values. |
| */ |
| |
| public class IntegerPolynomial448 extends IntegerPolynomial { |
| |
| private static final int POWER = 448; |
| private static final int NUM_LIMBS = 16; |
| private static final int BITS_PER_LIMB = 28; |
| public static final BigInteger MODULUS |
| = TWO.pow(POWER).subtract(TWO.pow(POWER / 2)) |
| .subtract(BigInteger.valueOf(1)); |
| |
| public IntegerPolynomial448() { |
| super(BITS_PER_LIMB, NUM_LIMBS, 1, MODULUS); |
| } |
| |
| private void modReduceIn(long[] limbs, int index, long x) { |
| limbs[index - NUM_LIMBS] += x; |
| limbs[index - NUM_LIMBS / 2] += x; |
| } |
| |
| @Override |
| protected void finalCarryReduceLast(long[] limbs) { |
| long carry = limbs[numLimbs - 1] >> bitsPerLimb; |
| limbs[numLimbs - 1] -= carry << bitsPerLimb; |
| modReduceIn(limbs, numLimbs, carry); |
| } |
| |
| @Override |
| protected void reduce(long[] a) { |
| |
| // carry(14, 2) |
| long carry14 = carryValue(a[14]); |
| a[14] -= (carry14 << BITS_PER_LIMB); |
| a[15] += carry14; |
| |
| long carry15 = carryValue(a[15]); |
| a[15] -= (carry15 << BITS_PER_LIMB); |
| |
| // reduce(0, 1) |
| a[0] += carry15; |
| a[8] += carry15; |
| |
| // carry(0, 15) |
| carry(a, 0, 15); |
| } |
| |
| @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[0] * b[10]) + (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]) + (a[10] * b[0]); |
| long c11 = (a[0] * b[11]) + (a[1] * b[10]) + (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]) + (a[10] * b[1]) + (a[11] * b[0]); |
| long c12 = (a[0] * b[12]) + (a[1] * b[11]) + (a[2] * b[10]) + (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]) + (a[10] * b[2]) + (a[11] * b[1]) + (a[12] * b[0]); |
| long c13 = (a[0] * b[13]) + (a[1] * b[12]) + (a[2] * b[11]) + (a[3] * b[10]) + (a[4] * b[9]) + (a[5] * b[8]) + (a[6] * b[7]) + (a[7] * b[6]) + (a[8] * b[5]) + (a[9] * b[4]) + (a[10] * b[3]) + (a[11] * b[2]) + (a[12] * b[1]) + (a[13] * b[0]); |
| long c14 = (a[0] * b[14]) + (a[1] * b[13]) + (a[2] * b[12]) + (a[3] * b[11]) + (a[4] * b[10]) + (a[5] * b[9]) + (a[6] * b[8]) + (a[7] * b[7]) + (a[8] * b[6]) + (a[9] * b[5]) + (a[10] * b[4]) + (a[11] * b[3]) + (a[12] * b[2]) + (a[13] * b[1]) + (a[14] * b[0]); |
| long c15 = (a[0] * b[15]) + (a[1] * b[14]) + (a[2] * b[13]) + (a[3] * b[12]) + (a[4] * b[11]) + (a[5] * b[10]) + (a[6] * b[9]) + (a[7] * b[8]) + (a[8] * b[7]) + (a[9] * b[6]) + (a[10] * b[5]) + (a[11] * b[4]) + (a[12] * b[3]) + (a[13] * b[2]) + (a[14] * b[1]) + (a[15] * b[0]); |
| long c16 = (a[1] * b[15]) + (a[2] * b[14]) + (a[3] * b[13]) + (a[4] * b[12]) + (a[5] * b[11]) + (a[6] * b[10]) + (a[7] * b[9]) + (a[8] * b[8]) + (a[9] * b[7]) + (a[10] * b[6]) + (a[11] * b[5]) + (a[12] * b[4]) + (a[13] * b[3]) + (a[14] * b[2]) + (a[15] * b[1]); |
| long c17 = (a[2] * b[15]) + (a[3] * b[14]) + (a[4] * b[13]) + (a[5] * b[12]) + (a[6] * b[11]) + (a[7] * b[10]) + (a[8] * b[9]) + (a[9] * b[8]) + (a[10] * b[7]) + (a[11] * b[6]) + (a[12] * b[5]) + (a[13] * b[4]) + (a[14] * b[3]) + (a[15] * b[2]); |
| long c18 = (a[3] * b[15]) + (a[4] * b[14]) + (a[5] * b[13]) + (a[6] * b[12]) + (a[7] * b[11]) + (a[8] * b[10]) + (a[9] * b[9]) + (a[10] * b[8]) + (a[11] * b[7]) + (a[12] * b[6]) + (a[13] * b[5]) + (a[14] * b[4]) + (a[15] * b[3]); |
| long c19 = (a[4] * b[15]) + (a[5] * b[14]) + (a[6] * b[13]) + (a[7] * b[12]) + (a[8] * b[11]) + (a[9] * b[10]) + (a[10] * b[9]) + (a[11] * b[8]) + (a[12] * b[7]) + (a[13] * b[6]) + (a[14] * b[5]) + (a[15] * b[4]); |
| long c20 = (a[5] * b[15]) + (a[6] * b[14]) + (a[7] * b[13]) + (a[8] * b[12]) + (a[9] * b[11]) + (a[10] * b[10]) + (a[11] * b[9]) + (a[12] * b[8]) + (a[13] * b[7]) + (a[14] * b[6]) + (a[15] * b[5]); |
| long c21 = (a[6] * b[15]) + (a[7] * b[14]) + (a[8] * b[13]) + (a[9] * b[12]) + (a[10] * b[11]) + (a[11] * b[10]) + (a[12] * b[9]) + (a[13] * b[8]) + (a[14] * b[7]) + (a[15] * b[6]); |
| long c22 = (a[7] * b[15]) + (a[8] * b[14]) + (a[9] * b[13]) + (a[10] * b[12]) + (a[11] * b[11]) + (a[12] * b[10]) + (a[13] * b[9]) + (a[14] * b[8]) + (a[15] * b[7]); |
| long c23 = (a[8] * b[15]) + (a[9] * b[14]) + (a[10] * b[13]) + (a[11] * b[12]) + (a[12] * b[11]) + (a[13] * b[10]) + (a[14] * b[9]) + (a[15] * b[8]); |
| long c24 = (a[9] * b[15]) + (a[10] * b[14]) + (a[11] * b[13]) + (a[12] * b[12]) + (a[13] * b[11]) + (a[14] * b[10]) + (a[15] * b[9]); |
| long c25 = (a[10] * b[15]) + (a[11] * b[14]) + (a[12] * b[13]) + (a[13] * b[12]) + (a[14] * b[11]) + (a[15] * b[10]); |
| long c26 = (a[11] * b[15]) + (a[12] * b[14]) + (a[13] * b[13]) + (a[14] * b[12]) + (a[15] * b[11]); |
| long c27 = (a[12] * b[15]) + (a[13] * b[14]) + (a[14] * b[13]) + (a[15] * b[12]); |
| long c28 = (a[13] * b[15]) + (a[14] * b[14]) + (a[15] * b[13]); |
| long c29 = (a[14] * b[15]) + (a[15] * b[14]); |
| long c30 = (a[15] * b[15]); |
| |
| carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, |
| c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, |
| c26, c27, c28, c29, c30); |
| } |
| |
| 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, |
| long c19, long c20, long c21, long c22, long c23, |
| long c24, long c25, long c26, long c27, long c28, |
| long c29, long c30) { |
| |
| // reduce(8, 7) |
| c8 += c24; |
| c16 += c24; |
| |
| c9 += c25; |
| c17 += c25; |
| |
| c10 += c26; |
| c18 += c26; |
| |
| c11 += c27; |
| c19 += c27; |
| |
| c12 += c28; |
| c20 += c28; |
| |
| c13 += c29; |
| c21 += c29; |
| |
| c14 += c30; |
| c22 += c30; |
| |
| // reduce(4, 4) |
| r[4] = c4 + c20; |
| r[12] = c12 + c20; |
| |
| r[5] = c5 + c21; |
| r[13] = c13 + c21; |
| |
| r[6] = c6 + c22; |
| c14 += c22; |
| |
| r[7] = c7 + c23; |
| c15 += c23; |
| |
| //carry(14, 2) |
| long carry14 = carryValue(c14); |
| r[14] = c14 - (carry14 << BITS_PER_LIMB); |
| c15 += carry14; |
| |
| long carry15 = carryValue(c15); |
| r[15] = c15 - (carry15 << BITS_PER_LIMB); |
| c16 += carry15; |
| |
| // reduce(0, 4) |
| r[0] = c0 + c16; |
| r[8] = c8 + c16; |
| |
| r[1] = c1 + c17; |
| r[9] = c9 + c17; |
| |
| r[2] = c2 + c18; |
| r[10] = c10 + c18; |
| |
| r[3] = c3 + c19; |
| r[11] = c11 + c19; |
| |
| // carry(0, 15) |
| carry(r, 0, 15); |
| } |
| |
| @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[0] * a[10] + a[1] * a[9] + a[2] * a[8] + a[3] * a[7] + a[4] * a[6]); |
| long c11 = 2 * (a[0] * a[11] + a[1] * a[10] + a[2] * a[9] + a[3] * a[8] + a[4] * a[7] + a[5] * a[6]); |
| long c12 = a[6] * a[6] + 2 * (a[0] * a[12] + a[1] * a[11] + a[2] * a[10] + a[3] * a[9] + a[4] * a[8] + a[5] * a[7]); |
| long c13 = 2 * (a[0] * a[13] + a[1] * a[12] + a[2] * a[11] + a[3] * a[10] + a[4] * a[9] + a[5] * a[8] + a[6] * a[7]); |
| long c14 = a[7] * a[7] + 2 * (a[0] * a[14] + a[1] * a[13] + a[2] * a[12] + a[3] * a[11] + a[4] * a[10] + a[5] * a[9] + a[6] * a[8]); |
| long c15 = 2 * (a[0] * a[15] + a[1] * a[14] + a[2] * a[13] + a[3] * a[12] + a[4] * a[11] + a[5] * a[10] + a[6] * a[9] + a[7] * a[8]); |
| long c16 = a[8] * a[8] + 2 * (a[1] * a[15] + a[2] * a[14] + a[3] * a[13] + a[4] * a[12] + a[5] * a[11] + a[6] * a[10] + a[7] * a[9]); |
| long c17 = 2 * (a[2] * a[15] + a[3] * a[14] + a[4] * a[13] + a[5] * a[12] + a[6] * a[11] + a[7] * a[10] + a[8] * a[9]); |
| long c18 = a[9] * a[9] + 2 * (a[3] * a[15] + a[4] * a[14] + a[5] * a[13] + a[6] * a[12] + a[7] * a[11] + a[8] * a[10]); |
| long c19 = 2 * (a[4] * a[15] + a[5] * a[14] + a[6] * a[13] + a[7] * a[12] + a[8] * a[11] + a[9] * a[10]); |
| long c20 = a[10] * a[10] + 2 * (a[5] * a[15] + a[6] * a[14] + a[7] * a[13] + a[8] * a[12] + a[9] * a[11]); |
| long c21 = 2 * (a[6] * a[15] + a[7] * a[14] + a[8] * a[13] + a[9] * a[12] + a[10] * a[11]); |
| long c22 = a[11] * a[11] + 2 * (a[7] * a[15] + a[8] * a[14] + a[9] * a[13] + a[10] * a[12]); |
| long c23 = 2 * (a[8] * a[15] + a[9] * a[14] + a[10] * a[13] + a[11] * a[12]); |
| long c24 = a[12] * a[12] + 2 * (a[9] * a[15] + a[10] * a[14] + a[11] * a[13]); |
| long c25 = 2 * (a[10] * a[15] + a[11] * a[14] + a[12] * a[13]); |
| long c26 = a[13] * a[13] + 2 * (a[11] * a[15] + a[12] * a[14]); |
| long c27 = 2 * (a[12] * a[15] + a[13] * a[14]); |
| long c28 = a[14] * a[14] + 2 * a[13] * a[15]; |
| long c29 = 2 * a[14] * a[15]; |
| long c30 = a[15] * a[15]; |
| |
| carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, |
| c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, |
| c26, c27, c28, c29, c30); |
| |
| } |
| |
| |
| } |