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/*
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* Copyright (c) 2018, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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package sun.security.ec;
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import sun.security.util.math.IntegerFieldModuloP;
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import sun.security.util.math.ImmutableIntegerModuloP;
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import sun.security.util.math.IntegerModuloP;
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import sun.security.util.math.MutableIntegerModuloP;
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import sun.security.util.math.SmallValue;
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import sun.security.util.math.intpoly.IntegerPolynomial25519;
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import sun.security.util.math.intpoly.IntegerPolynomial448;
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import java.math.BigInteger;
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import java.security.ProviderException;
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import java.security.SecureRandom;
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public class XECOperations {
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private final XECParameters params;
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private final IntegerFieldModuloP field;
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private final ImmutableIntegerModuloP zero;
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private final ImmutableIntegerModuloP one;
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private final SmallValue a24;
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private final ImmutableIntegerModuloP basePoint;
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public XECOperations(XECParameters c) {
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this.params = c;
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BigInteger p = params.getP();
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this.field = getIntegerFieldModulo(p);
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this.zero = field.getElement(BigInteger.ZERO).fixed();
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this.one = field.get1().fixed();
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this.a24 = field.getSmallValue(params.getA24());
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this.basePoint = field.getElement(
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BigInteger.valueOf(c.getBasePoint()));
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}
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public XECParameters getParameters() {
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return params;
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}
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public byte[] generatePrivate(SecureRandom random) {
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byte[] result = new byte[this.params.getBytes()];
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random.nextBytes(result);
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return result;
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}
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/**
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* Compute a public key from an encoded private key. This method will
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* modify the supplied array in order to prune it.
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*/
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public BigInteger computePublic(byte[] k) {
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pruneK(k);
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return pointMultiply(k, this.basePoint).asBigInteger();
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}
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/**
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*
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* Multiply an encoded scalar with a point as a BigInteger and return an
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* encoded point. The array k holding the scalar will be pruned by
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* modifying it in place.
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*
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* @param k an encoded scalar
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* @param u the u-coordinate of a point as a BigInteger
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* @return the encoded product
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*/
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public byte[] encodedPointMultiply(byte[] k, BigInteger u) {
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pruneK(k);
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ImmutableIntegerModuloP elemU = field.getElement(u);
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return pointMultiply(k, elemU).asByteArray(params.getBytes());
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}
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/**
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*
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* Multiply an encoded scalar with an encoded point and return an encoded
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* point. The array k holding the scalar will be pruned by
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* modifying it in place.
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*
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* @param k an encoded scalar
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* @param u an encoded point
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* @return the encoded product
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*/
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public byte[] encodedPointMultiply(byte[] k, byte[] u) {
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pruneK(k);
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ImmutableIntegerModuloP elemU = decodeU(u);
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return pointMultiply(k, elemU).asByteArray(params.getBytes());
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}
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/**
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* Return the field element corresponding to an encoded u-coordinate.
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* This method prunes u by modifying it in place.
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*
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* @param u
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* @param bits
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* @return
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*/
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private ImmutableIntegerModuloP decodeU(byte[] u, int bits) {
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maskHighOrder(u, bits);
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return field.getElement(u);
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}
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/**
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* Mask off the high order bits of an encoded integer in an array. The
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* array is modified in place.
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*
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* @param arr an array containing an encoded integer
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* @param bits the number of bits to keep
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* @return the number, in range [1,8], of bits kept in the highest byte
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*/
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private static byte maskHighOrder(byte[] arr, int bits) {
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int lastByteIndex = arr.length - 1;
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byte bitsMod8 = (byte) (bits % 8);
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byte highBits = bitsMod8 == 0 ? 8 : bitsMod8;
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byte msbMaskOff = (byte) ((1 << highBits) - 1);
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arr[lastByteIndex] &= msbMaskOff;
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return highBits;
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}
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/**
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* Prune an encoded scalar value by modifying it in place. The extra
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* high-order bits are masked off, the highest valid bit it set, and the
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* number is rounded down to a multiple of the cofactor.
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*
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* @param k an encoded scalar value
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* @param bits the number of bits in the scalar
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* @param logCofactor the base-2 logarithm of the cofactor
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*/
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private static void pruneK(byte[] k, int bits, int logCofactor) {
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int lastByteIndex = k.length - 1;
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// mask off unused high-order bits
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byte highBits = maskHighOrder(k, bits);
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// set the highest bit
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byte msbMaskOn = (byte) (1 << (highBits - 1));
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k[lastByteIndex] |= msbMaskOn;
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// round down to a multiple of the cofactor
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byte lsbMaskOff = (byte) (0xFF << logCofactor);
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k[0] &= lsbMaskOff;
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}
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private void pruneK(byte[] k) {
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pruneK(k, params.getBits(), params.getLogCofactor());
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}
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private ImmutableIntegerModuloP decodeU(byte [] u) {
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return decodeU(u, params.getBits());
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}
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// Constant-time conditional swap
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private static void cswap(int swap, MutableIntegerModuloP x1,
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MutableIntegerModuloP x2) {
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x1.conditionalSwapWith(x2, swap);
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}
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private static IntegerFieldModuloP getIntegerFieldModulo(BigInteger p) {
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if (p.equals(IntegerPolynomial25519.MODULUS)) {
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return new IntegerPolynomial25519();
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}
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else if (p.equals(IntegerPolynomial448.MODULUS)) {
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return new IntegerPolynomial448();
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}
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throw new ProviderException("Unsupported prime: " + p.toString());
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}
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private int bitAt(byte[] arr, int index) {
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int byteIndex = index / 8;
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int bitIndex = index % 8;
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return (arr[byteIndex] & (1 << bitIndex)) >> bitIndex;
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}
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/*
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* Constant-time Montgomery ladder that computes k*u and returns the
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* result as a field element.
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*/
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private IntegerModuloP pointMultiply(byte[] k,
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ImmutableIntegerModuloP u) {
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ImmutableIntegerModuloP x_1 = u;
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MutableIntegerModuloP x_2 = this.one.mutable();
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MutableIntegerModuloP z_2 = this.zero.mutable();
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MutableIntegerModuloP x_3 = u.mutable();
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MutableIntegerModuloP z_3 = this.one.mutable();
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int swap = 0;
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// Variables below are reused to avoid unnecessary allocation
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// They will be assigned in the loop, so initial value doesn't matter
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MutableIntegerModuloP m1 = this.zero.mutable();
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MutableIntegerModuloP DA = this.zero.mutable();
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MutableIntegerModuloP E = this.zero.mutable();
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MutableIntegerModuloP a24_times_E = this.zero.mutable();
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// Comments describe the equivalent operations from RFC 7748
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// In comments, A(m1) means the variable m1 holds the value A
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for (int t = params.getBits() - 1; t >= 0; t--) {
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int k_t = bitAt(k, t);
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swap = swap ^ k_t;
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cswap(swap, x_2, x_3);
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cswap(swap, z_2, z_3);
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swap = k_t;
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// A(m1) = x_2 + z_2
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m1.setValue(x_2).setSum(z_2);
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// D = x_3 - z_3
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// DA = D * A(m1)
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DA.setValue(x_3).setDifference(z_3).setProduct(m1);
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// AA(m1) = A(m1)^2
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m1.setSquare();
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// B(x_2) = x_2 - z_2
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x_2.setDifference(z_2);
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// C = x_3 + z_3
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// CB(x_3) = C * B(x_2)
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x_3.setSum(z_3).setProduct(x_2);
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// BB(x_2) = B^2
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x_2.setSquare();
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// E = AA(m1) - BB(x_2)
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E.setValue(m1).setDifference(x_2);
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// compute a24 * E using SmallValue
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a24_times_E.setValue(E);
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a24_times_E.setProduct(this.a24);
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// assign results to x_3, z_3, x_2, z_2
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// x_2 = AA(m1) * BB
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x_2.setProduct(m1);
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// z_2 = E * (AA(m1) + a24 * E)
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z_2.setValue(m1).setSum(a24_times_E).setProduct(E);
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// z_3 = x_1*(DA - CB(x_3))^2
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z_3.setValue(DA).setDifference(x_3).setSquare().setProduct(x_1);
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// x_3 = (CB(x_3) + DA)^2
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x_3.setSum(DA).setSquare();
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}
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cswap(swap, x_2, x_3);
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cswap(swap, z_2, z_3);
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// return (x_2 * z_2^(p - 2))
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return x_2.setProduct(z_2.multiplicativeInverse());
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}
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}
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