768 lines
24 KiB
Java
768 lines
24 KiB
Java
/*
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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.util.math.intpoly;
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import sun.security.util.math.*;
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import java.math.BigInteger;
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import java.nio.ByteBuffer;
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import java.nio.ByteOrder;
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import java.util.Arrays;
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/**
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* A large number polynomial representation using sparse limbs of signed
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* long (64-bit) values. Limb values will always fit within a long, so inputs
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* to multiplication must be less than 32 bits. All IntegerPolynomial
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* implementations allow at most one addition before multiplication. Additions
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* after that will result in an ArithmeticException.
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*
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* The following element operations are branch-free for all subclasses:
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*
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* fixed
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* mutable
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* add
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* additiveInverse
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* multiply
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* square
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* subtract
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* conditionalSwapWith
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* setValue (may branch on high-order byte parameter only)
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* setSum
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* setDifference
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* setProduct
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* setSquare
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* addModPowerTwo
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* asByteArray
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*
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* All other operations may branch in some subclasses.
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*
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*/
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public abstract class IntegerPolynomial implements IntegerFieldModuloP {
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protected static final BigInteger TWO = BigInteger.valueOf(2);
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protected final int numLimbs;
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private final BigInteger modulus;
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protected final int bitsPerLimb;
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private final long[] posModLimbs;
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private final int maxAdds;
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/**
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* Reduce an IntegerPolynomial representation (a) and store the result
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* in a. Requires that a.length == numLimbs.
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*/
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protected abstract void reduce(long[] a);
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/**
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* Multiply an IntegerPolynomial representation (a) with a long (b) and
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* store the result in an IntegerPolynomial representation in a. Requires
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* that a.length == numLimbs.
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*/
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protected void multByInt(long[] a, long b) {
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for (int i = 0; i < a.length; i++) {
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a[i] *= b;
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}
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reduce(a);
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}
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/**
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* Multiply two IntegerPolynomial representations (a and b) and store the
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* result in an IntegerPolynomial representation (r). Requires that
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* a.length == b.length == r.length == numLimbs. It is allowed for a and r
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* to be the same array.
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*/
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protected abstract void mult(long[] a, long[] b, long[] r);
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/**
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* Multiply an IntegerPolynomial representation (a) with itself and store
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* the result in an IntegerPolynomialRepresentation (r). Requires that
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* a.length == r.length == numLimbs. It is allowed for a and r
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* to be the same array.
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*/
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protected abstract void square(long[] a, long[] r);
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IntegerPolynomial(int bitsPerLimb,
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int numLimbs,
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int maxAdds,
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BigInteger modulus) {
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this.numLimbs = numLimbs;
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this.modulus = modulus;
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this.bitsPerLimb = bitsPerLimb;
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this.maxAdds = maxAdds;
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posModLimbs = setPosModLimbs();
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}
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private long[] setPosModLimbs() {
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long[] result = new long[numLimbs];
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setLimbsValuePositive(modulus, result);
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return result;
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}
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protected int getNumLimbs() {
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return numLimbs;
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}
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public int getMaxAdds() {
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return maxAdds;
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}
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@Override
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public BigInteger getSize() {
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return modulus;
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}
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@Override
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public ImmutableElement get0() {
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return new ImmutableElement(false);
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}
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@Override
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public ImmutableElement get1() {
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return new ImmutableElement(true);
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}
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@Override
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public ImmutableElement getElement(BigInteger v) {
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return new ImmutableElement(v);
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}
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@Override
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public SmallValue getSmallValue(int value) {
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int maxMag = 1 << (bitsPerLimb - 1);
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if (Math.abs(value) >= maxMag) {
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throw new IllegalArgumentException(
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"max magnitude is " + maxMag);
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}
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return new Limb(value);
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}
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/**
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* This version of encode takes a ByteBuffer that is properly ordered, and
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* may extract larger values (e.g. long) from the ByteBuffer for better
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* performance. The implementation below only extracts bytes from the
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* buffer, but this method may be overridden in field-specific
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* implementations.
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*/
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protected void encode(ByteBuffer buf, int length, byte highByte,
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long[] result) {
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int numHighBits = 32 - Integer.numberOfLeadingZeros(highByte);
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int numBits = 8 * length + numHighBits;
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int requiredLimbs = (numBits + bitsPerLimb - 1) / bitsPerLimb;
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if (requiredLimbs > numLimbs) {
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long[] temp = new long[requiredLimbs];
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encodeSmall(buf, length, highByte, temp);
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// encode does a full carry/reduce
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System.arraycopy(temp, 0, result, 0, result.length);
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} else {
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encodeSmall(buf, length, highByte, result);
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}
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}
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protected void encodeSmall(ByteBuffer buf, int length, byte highByte,
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long[] result) {
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int limbIndex = 0;
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long curLimbValue = 0;
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int bitPos = 0;
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for (int i = 0; i < length; i++) {
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long curV = buf.get() & 0xFF;
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if (bitPos + 8 >= bitsPerLimb) {
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int bitsThisLimb = bitsPerLimb - bitPos;
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curLimbValue += (curV & (0xFF >> (8 - bitsThisLimb))) << bitPos;
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result[limbIndex++] = curLimbValue;
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curLimbValue = curV >> bitsThisLimb;
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bitPos = 8 - bitsThisLimb;
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}
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else {
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curLimbValue += curV << bitPos;
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bitPos += 8;
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}
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}
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// one more for the high byte
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if (highByte != 0) {
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long curV = highByte & 0xFF;
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if (bitPos + 8 >= bitsPerLimb) {
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int bitsThisLimb = bitsPerLimb - bitPos;
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curLimbValue += (curV & (0xFF >> (8 - bitsThisLimb))) << bitPos;
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result[limbIndex++] = curLimbValue;
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curLimbValue = curV >> bitsThisLimb;
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}
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else {
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curLimbValue += curV << bitPos;
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}
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}
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if (limbIndex < result.length) {
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result[limbIndex++] = curLimbValue;
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}
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Arrays.fill(result, limbIndex, result.length, 0);
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postEncodeCarry(result);
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}
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protected void encode(byte[] v, int offset, int length, byte highByte,
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long[] result) {
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ByteBuffer buf = ByteBuffer.wrap(v, offset, length);
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buf.order(ByteOrder.LITTLE_ENDIAN);
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encode(buf, length, highByte, result);
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}
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// Encode does not produce compressed limbs. A simplified carry/reduce
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// operation can be used to compress the limbs.
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protected void postEncodeCarry(long[] v) {
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reduce(v);
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}
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public ImmutableElement getElement(byte[] v, int offset, int length,
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byte highByte) {
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long[] result = new long[numLimbs];
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encode(v, offset, length, highByte, result);
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return new ImmutableElement(result, 0);
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}
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protected BigInteger evaluate(long[] limbs) {
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BigInteger result = BigInteger.ZERO;
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for (int i = limbs.length - 1; i >= 0; i--) {
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result = result.shiftLeft(bitsPerLimb)
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.add(BigInteger.valueOf(limbs[i]));
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}
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return result.mod(modulus);
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}
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protected long carryValue(long x) {
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// compressing carry operation
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// if large positive number, carry one more to make it negative
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// if large negative number (closer to zero), carry one fewer
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return (x + (1 << (bitsPerLimb - 1))) >> bitsPerLimb;
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}
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protected void carry(long[] limbs, int start, int end) {
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for (int i = start; i < end; i++) {
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long carry = carryOut(limbs, i);
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limbs[i + 1] += carry;
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}
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}
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protected void carry(long[] limbs) {
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carry(limbs, 0, limbs.length - 1);
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}
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/**
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* Carry out of the specified position and return the carry value.
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*/
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protected long carryOut(long[] limbs, int index) {
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long carry = carryValue(limbs[index]);
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limbs[index] -= (carry << bitsPerLimb);
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return carry;
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}
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private void setLimbsValue(BigInteger v, long[] limbs) {
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// set all limbs positive, and then carry
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setLimbsValuePositive(v, limbs);
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carry(limbs);
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}
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protected void setLimbsValuePositive(BigInteger v, long[] limbs) {
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BigInteger mod = BigInteger.valueOf(1 << bitsPerLimb);
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for (int i = 0; i < limbs.length; i++) {
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limbs[i] = v.mod(mod).longValue();
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v = v.shiftRight(bitsPerLimb);
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}
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}
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/**
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* Carry out of the last limb and reduce back in. This method will be
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* called as part of the "finalReduce" operation that puts the
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* representation into a fully-reduced form. It is representation-
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* specific, because representations have different amounts of empty
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* space in the high-order limb. Requires that limbs.length=numLimbs.
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*/
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protected abstract void finalCarryReduceLast(long[] limbs);
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/**
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* Convert reduced limbs into a number between 0 and MODULUS-1.
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* Requires that limbs.length == numLimbs. This method only works if the
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* modulus has at most three terms.
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*/
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protected void finalReduce(long[] limbs) {
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// This method works by doing several full carry/reduce operations.
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// Some representations have extra high bits, so the carry/reduce out
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// of the high position is implementation-specific. The "unsigned"
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// carry operation always carries some (negative) value out of a
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// position occupied by a negative value. So after a number of
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// passes, all negative values are removed.
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// The first pass may leave a negative value in the high position, but
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// this only happens if something was carried out of the previous
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// position. So the previous position must have a "small" value. The
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// next full carry is guaranteed not to carry out of that position.
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for (int pass = 0; pass < 2; pass++) {
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// unsigned carry out of last position and reduce in to
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// first position
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finalCarryReduceLast(limbs);
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// unsigned carry on all positions
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long carry = 0;
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for (int i = 0; i < numLimbs - 1; i++) {
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limbs[i] += carry;
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carry = limbs[i] >> bitsPerLimb;
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limbs[i] -= carry << bitsPerLimb;
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}
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limbs[numLimbs - 1] += carry;
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}
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// Limbs are positive and all less than 2^bitsPerLimb, and the
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// high-order limb may be even smaller due to the representation-
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// specific carry/reduce out of the high position.
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// The value may still be greater than the modulus.
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// Subtract the max limb values only if all limbs end up non-negative
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// This only works if there is at most one position where posModLimbs
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// is less than 2^bitsPerLimb - 1 (not counting the high-order limb,
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// if it has extra bits that are cleared by finalCarryReduceLast).
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int smallerNonNegative = 1;
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long[] smaller = new long[numLimbs];
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for (int i = numLimbs - 1; i >= 0; i--) {
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smaller[i] = limbs[i] - posModLimbs[i];
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// expression on right is 1 if smaller[i] is nonnegative,
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// 0 otherwise
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smallerNonNegative *= (int) (smaller[i] >> 63) + 1;
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}
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conditionalSwap(smallerNonNegative, limbs, smaller);
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}
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/**
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* Decode the value in v and store it in dst. Requires that v is final
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* reduced. I.e. all limbs in [0, 2^bitsPerLimb) and value in [0, modulus).
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*/
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protected void decode(long[] v, byte[] dst, int offset, int length) {
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int nextLimbIndex = 0;
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long curLimbValue = v[nextLimbIndex++];
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int bitPos = 0;
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for (int i = 0; i < length; i++) {
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int dstIndex = i + offset;
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if (bitPos + 8 >= bitsPerLimb) {
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dst[dstIndex] = (byte) curLimbValue;
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curLimbValue = 0;
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if (nextLimbIndex < v.length) {
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curLimbValue = v[nextLimbIndex++];
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}
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int bitsAdded = bitsPerLimb - bitPos;
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int bitsLeft = 8 - bitsAdded;
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dst[dstIndex] += (curLimbValue & (0xFF >> bitsAdded))
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<< bitsAdded;
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curLimbValue >>= bitsLeft;
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bitPos = bitsLeft;
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} else {
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dst[dstIndex] = (byte) curLimbValue;
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curLimbValue >>= 8;
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bitPos += 8;
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}
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}
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}
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/**
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* Add two IntegerPolynomial representations (a and b) and store the result
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* in an IntegerPolynomialRepresentation (dst). Requires that
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* a.length == b.length == dst.length. It is allowed for a and
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* dst to be the same array.
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*/
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protected void addLimbs(long[] a, long[] b, long[] dst) {
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for (int i = 0; i < dst.length; i++) {
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dst[i] = a[i] + b[i];
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}
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}
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/**
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* Branch-free conditional assignment of b to a. Requires that set is 0 or
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* 1, and that a.length == b.length. If set==0, then the values of a and b
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* will be unchanged. If set==1, then the values of b will be assigned to a.
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* The behavior is undefined if swap has any value other than 0 or 1.
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*/
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protected static void conditionalAssign(int set, long[] a, long[] b) {
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int maskValue = 0 - set;
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for (int i = 0; i < a.length; i++) {
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long dummyLimbs = maskValue & (a[i] ^ b[i]);
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a[i] = dummyLimbs ^ a[i];
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}
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}
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/**
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* Branch-free conditional swap of a and b. Requires that swap is 0 or 1,
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* and that a.length == b.length. If swap==0, then the values of a and b
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* will be unchanged. If swap==1, then the values of a and b will be
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* swapped. The behavior is undefined if swap has any value other than
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* 0 or 1.
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*/
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protected static void conditionalSwap(int swap, long[] a, long[] b) {
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int maskValue = 0 - swap;
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for (int i = 0; i < a.length; i++) {
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long dummyLimbs = maskValue & (a[i] ^ b[i]);
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a[i] = dummyLimbs ^ a[i];
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b[i] = dummyLimbs ^ b[i];
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}
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}
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/**
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* Stores the reduced, little-endian value of limbs in result.
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*/
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protected void limbsToByteArray(long[] limbs, byte[] result) {
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long[] reducedLimbs = limbs.clone();
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finalReduce(reducedLimbs);
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decode(reducedLimbs, result, 0, result.length);
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}
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/**
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* Add the reduced number corresponding to limbs and other, and store
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* the low-order bytes of the sum in result. Requires that
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* limbs.length==other.length. The result array may have any length.
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*/
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protected void addLimbsModPowerTwo(long[] limbs, long[] other,
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byte[] result) {
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long[] reducedOther = other.clone();
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long[] reducedLimbs = limbs.clone();
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finalReduce(reducedOther);
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finalReduce(reducedLimbs);
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addLimbs(reducedLimbs, reducedOther, reducedLimbs);
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// may carry out a value which can be ignored
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long carry = 0;
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for (int i = 0; i < numLimbs; i++) {
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reducedLimbs[i] += carry;
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carry = reducedLimbs[i] >> bitsPerLimb;
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reducedLimbs[i] -= carry << bitsPerLimb;
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}
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decode(reducedLimbs, result, 0, result.length);
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}
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private abstract class Element implements IntegerModuloP {
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protected long[] limbs;
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protected int numAdds;
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public Element(BigInteger v) {
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limbs = new long[numLimbs];
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setValue(v);
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}
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public Element(boolean v) {
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this.limbs = new long[numLimbs];
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this.limbs[0] = v ? 1l : 0l;
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this.numAdds = 0;
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}
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private Element(long[] limbs, int numAdds) {
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this.limbs = limbs;
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this.numAdds = numAdds;
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}
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private void setValue(BigInteger v) {
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setLimbsValue(v, limbs);
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this.numAdds = 0;
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}
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@Override
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public IntegerFieldModuloP getField() {
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return IntegerPolynomial.this;
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}
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@Override
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public BigInteger asBigInteger() {
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return evaluate(limbs);
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}
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@Override
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public MutableElement mutable() {
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return new MutableElement(limbs.clone(), numAdds);
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}
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protected boolean isSummand() {
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return numAdds < maxAdds;
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}
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@Override
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public ImmutableElement add(IntegerModuloP genB) {
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Element b = (Element) genB;
|
|
if (!(isSummand() && b.isSummand())) {
|
|
throw new ArithmeticException("Not a valid summand");
|
|
}
|
|
|
|
long[] newLimbs = new long[limbs.length];
|
|
for (int i = 0; i < limbs.length; i++) {
|
|
newLimbs[i] = limbs[i] + b.limbs[i];
|
|
}
|
|
|
|
int newNumAdds = Math.max(numAdds, b.numAdds) + 1;
|
|
return new ImmutableElement(newLimbs, newNumAdds);
|
|
}
|
|
|
|
@Override
|
|
public ImmutableElement additiveInverse() {
|
|
|
|
long[] newLimbs = new long[limbs.length];
|
|
for (int i = 0; i < limbs.length; i++) {
|
|
newLimbs[i] = -limbs[i];
|
|
}
|
|
|
|
ImmutableElement result = new ImmutableElement(newLimbs, numAdds);
|
|
return result;
|
|
}
|
|
|
|
protected long[] cloneLow(long[] limbs) {
|
|
long[] newLimbs = new long[numLimbs];
|
|
copyLow(limbs, newLimbs);
|
|
return newLimbs;
|
|
}
|
|
protected void copyLow(long[] limbs, long[] out) {
|
|
System.arraycopy(limbs, 0, out, 0, out.length);
|
|
}
|
|
|
|
@Override
|
|
public ImmutableElement multiply(IntegerModuloP genB) {
|
|
|
|
Element b = (Element) genB;
|
|
|
|
long[] newLimbs = new long[limbs.length];
|
|
mult(limbs, b.limbs, newLimbs);
|
|
return new ImmutableElement(newLimbs, 0);
|
|
}
|
|
|
|
@Override
|
|
public ImmutableElement square() {
|
|
long[] newLimbs = new long[limbs.length];
|
|
IntegerPolynomial.this.square(limbs, newLimbs);
|
|
return new ImmutableElement(newLimbs, 0);
|
|
}
|
|
|
|
public void addModPowerTwo(IntegerModuloP arg, byte[] result) {
|
|
|
|
Element other = (Element) arg;
|
|
if (!(isSummand() && other.isSummand())) {
|
|
throw new ArithmeticException("Not a valid summand");
|
|
}
|
|
addLimbsModPowerTwo(limbs, other.limbs, result);
|
|
}
|
|
|
|
public void asByteArray(byte[] result) {
|
|
if (!isSummand()) {
|
|
throw new ArithmeticException("Not a valid summand");
|
|
}
|
|
limbsToByteArray(limbs, result);
|
|
}
|
|
}
|
|
|
|
protected class MutableElement extends Element
|
|
implements MutableIntegerModuloP {
|
|
|
|
protected MutableElement(long[] limbs, int numAdds) {
|
|
super(limbs, numAdds);
|
|
}
|
|
|
|
@Override
|
|
public ImmutableElement fixed() {
|
|
return new ImmutableElement(limbs.clone(), numAdds);
|
|
}
|
|
|
|
@Override
|
|
public void conditionalSet(IntegerModuloP b, int set) {
|
|
|
|
Element other = (Element) b;
|
|
|
|
conditionalAssign(set, limbs, other.limbs);
|
|
numAdds = other.numAdds;
|
|
}
|
|
|
|
@Override
|
|
public void conditionalSwapWith(MutableIntegerModuloP b, int swap) {
|
|
|
|
MutableElement other = (MutableElement) b;
|
|
|
|
conditionalSwap(swap, limbs, other.limbs);
|
|
int numAddsTemp = numAdds;
|
|
numAdds = other.numAdds;
|
|
other.numAdds = numAddsTemp;
|
|
}
|
|
|
|
|
|
@Override
|
|
public MutableElement setValue(IntegerModuloP v) {
|
|
Element other = (Element) v;
|
|
|
|
System.arraycopy(other.limbs, 0, limbs, 0, other.limbs.length);
|
|
numAdds = other.numAdds;
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setValue(byte[] arr, int offset,
|
|
int length, byte highByte) {
|
|
|
|
encode(arr, offset, length, highByte, limbs);
|
|
this.numAdds = 0;
|
|
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setValue(ByteBuffer buf, int length,
|
|
byte highByte) {
|
|
|
|
encode(buf, length, highByte, limbs);
|
|
numAdds = 0;
|
|
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setProduct(IntegerModuloP genB) {
|
|
Element b = (Element) genB;
|
|
mult(limbs, b.limbs, limbs);
|
|
numAdds = 0;
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setProduct(SmallValue v) {
|
|
int value = ((Limb) v).value;
|
|
multByInt(limbs, value);
|
|
numAdds = 0;
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setSum(IntegerModuloP genB) {
|
|
|
|
Element b = (Element) genB;
|
|
if (!(isSummand() && b.isSummand())) {
|
|
throw new ArithmeticException("Not a valid summand");
|
|
}
|
|
|
|
for (int i = 0; i < limbs.length; i++) {
|
|
limbs[i] = limbs[i] + b.limbs[i];
|
|
}
|
|
|
|
numAdds = Math.max(numAdds, b.numAdds) + 1;
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setDifference(IntegerModuloP genB) {
|
|
|
|
Element b = (Element) genB;
|
|
if (!(isSummand() && b.isSummand())) {
|
|
throw new ArithmeticException("Not a valid summand");
|
|
}
|
|
|
|
for (int i = 0; i < limbs.length; i++) {
|
|
limbs[i] = limbs[i] - b.limbs[i];
|
|
}
|
|
|
|
numAdds = Math.max(numAdds, b.numAdds) + 1;
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setSquare() {
|
|
IntegerPolynomial.this.square(limbs, limbs);
|
|
numAdds = 0;
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setAdditiveInverse() {
|
|
|
|
for (int i = 0; i < limbs.length; i++) {
|
|
limbs[i] = -limbs[i];
|
|
}
|
|
return this;
|
|
}
|
|
|
|
@Override
|
|
public MutableElement setReduced() {
|
|
|
|
reduce(limbs);
|
|
numAdds = 0;
|
|
return this;
|
|
}
|
|
}
|
|
|
|
class ImmutableElement extends Element implements ImmutableIntegerModuloP {
|
|
|
|
protected ImmutableElement(BigInteger v) {
|
|
super(v);
|
|
}
|
|
|
|
protected ImmutableElement(boolean v) {
|
|
super(v);
|
|
}
|
|
|
|
protected ImmutableElement(long[] limbs, int numAdds) {
|
|
super(limbs, numAdds);
|
|
}
|
|
|
|
@Override
|
|
public ImmutableElement fixed() {
|
|
return this;
|
|
}
|
|
|
|
}
|
|
|
|
class Limb implements SmallValue {
|
|
int value;
|
|
|
|
Limb(int value) {
|
|
this.value = value;
|
|
}
|
|
}
|
|
|
|
|
|
}
|