jdk.crypto.ec/share/classes/sun/security/ec/XECOperations.java - SunEC - Git at Google

 /*
  * 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
  * or visit www.oracle.com if you need additional information or have any
  * questions.
  */

 package sun.security.ec;

 import sun.security.util.math.IntegerFieldModuloP;
 import sun.security.util.math.ImmutableIntegerModuloP;
 import sun.security.util.math.IntegerModuloP;
 import sun.security.util.math.MutableIntegerModuloP;
 import sun.security.util.math.SmallValue;
 import sun.security.util.math.intpoly.IntegerPolynomial25519;
 import sun.security.util.math.intpoly.IntegerPolynomial448;

 import java.math.BigInteger;
 import java.security.ProviderException;
 import java.security.SecureRandom;

 public class XECOperations {

     private final XECParameters params;
     private final IntegerFieldModuloP field;
     private final ImmutableIntegerModuloP zero;
     private final ImmutableIntegerModuloP one;
     private final SmallValue a24;
     private final ImmutableIntegerModuloP basePoint;

     public XECOperations(XECParameters c) {
         this.params = c;

         BigInteger p = params.getP();
         this.field = getIntegerFieldModulo(p);
         this.zero = field.getElement(BigInteger.ZERO).fixed();
         this.one = field.get1().fixed();
         this.a24 = field.getSmallValue(params.getA24());
         this.basePoint = field.getElement(
             BigInteger.valueOf(c.getBasePoint()));
     }

     public XECParameters getParameters() {
         return params;
     }

     public byte[] generatePrivate(SecureRandom random) {
         byte[] result = new byte[this.params.getBytes()];
         random.nextBytes(result);
         return result;
     }

     /**
      * Compute a public key from an encoded private key. This method will
      * modify the supplied array in order to prune it.
      */
     public BigInteger computePublic(byte[] k) {
         pruneK(k);
         return pointMultiply(k, this.basePoint).asBigInteger();
     }

     /**
      *
      * Multiply an encoded scalar with a point as a BigInteger and return an
      * encoded point. The array k holding the scalar will be pruned by
      * modifying it in place.
      *
      * @param k an encoded scalar
      * @param u the u-coordinate of a point as a BigInteger
      * @return the encoded product
      */
     public byte[] encodedPointMultiply(byte[] k, BigInteger u) {
         pruneK(k);
         ImmutableIntegerModuloP elemU = field.getElement(u);
         return pointMultiply(k, elemU).asByteArray(params.getBytes());
     }

     /**
      *
      * Multiply an encoded scalar with an encoded point and return an encoded
      * point. The array k holding the scalar will be pruned by
      * modifying it in place.
      *
      * @param k an encoded scalar
      * @param u an encoded point
      * @return the encoded product
      */
     public byte[] encodedPointMultiply(byte[] k, byte[] u) {
         pruneK(k);
         ImmutableIntegerModuloP elemU = decodeU(u);
         return pointMultiply(k, elemU).asByteArray(params.getBytes());
     }

     /**
      * Return the field element corresponding to an encoded u-coordinate.
      * This method prunes u by modifying it in place.
      *
      * @param u
      * @param bits
      * @return
      */
     private ImmutableIntegerModuloP decodeU(byte[] u, int bits) {

         maskHighOrder(u, bits);

         return field.getElement(u);
     }

     /**
      * Mask off the high order bits of an encoded integer in an array. The
      * array is modified in place.
      *
      * @param arr an array containing an encoded integer
      * @param bits the number of bits to keep
      * @return the number, in range [1,8], of bits kept in the highest byte
      */
     private static byte maskHighOrder(byte[] arr, int bits) {

         int lastByteIndex = arr.length - 1;
         byte bitsMod8 = (byte) (bits % 8);
         byte highBits = bitsMod8 == 0 ? 8 : bitsMod8;
         byte msbMaskOff = (byte) ((1 << highBits) - 1);
         arr[lastByteIndex] &= msbMaskOff;

         return highBits;
     }

     /**
      * Prune an encoded scalar value by modifying it in place. The extra
      * high-order bits are masked off, the highest valid bit it set, and the
      * number is rounded down to a multiple of the cofactor.
      *
      * @param k an encoded scalar value
      * @param bits the number of bits in the scalar
      * @param logCofactor the base-2 logarithm of the cofactor
      */
     private static void pruneK(byte[] k, int bits, int logCofactor) {

         int lastByteIndex = k.length - 1;

         // mask off unused high-order bits
         byte highBits = maskHighOrder(k, bits);

         // set the highest bit
         byte msbMaskOn = (byte) (1 << (highBits - 1));
         k[lastByteIndex] |= msbMaskOn;

         // round down to a multiple of the cofactor
         byte lsbMaskOff = (byte) (0xFF << logCofactor);
         k[0] &= lsbMaskOff;
     }

     private void pruneK(byte[] k) {
         pruneK(k, params.getBits(), params.getLogCofactor());
     }

     private ImmutableIntegerModuloP decodeU(byte [] u) {
         return decodeU(u, params.getBits());
     }

     // Constant-time conditional swap
     private static void cswap(int swap, MutableIntegerModuloP x1,
         MutableIntegerModuloP x2) {

         x1.conditionalSwapWith(x2, swap);
     }

     private static IntegerFieldModuloP getIntegerFieldModulo(BigInteger p) {

         if (p.equals(IntegerPolynomial25519.MODULUS)) {
             return new IntegerPolynomial25519();
         }
         else if (p.equals(IntegerPolynomial448.MODULUS)) {
             return new IntegerPolynomial448();
         }

         throw new ProviderException("Unsupported prime: " + p.toString());
     }

     private int bitAt(byte[] arr, int index) {
         int byteIndex = index / 8;
         int bitIndex = index % 8;
         return (arr[byteIndex] & (1 << bitIndex)) >> bitIndex;
     }

     /*
      * Constant-time Montgomery ladder that computes k*u and returns the
      * result as a field element.
      */
     private IntegerModuloP pointMultiply(byte[] k,
                                          ImmutableIntegerModuloP u) {

         ImmutableIntegerModuloP x_1 = u;
         MutableIntegerModuloP x_2 = this.one.mutable();
         MutableIntegerModuloP z_2 = this.zero.mutable();
         MutableIntegerModuloP x_3 = u.mutable();
         MutableIntegerModuloP z_3 = this.one.mutable();
         int swap = 0;

         // Variables below are reused to avoid unnecessary allocation
         // They will be assigned in the loop, so initial value doesn't matter
         MutableIntegerModuloP m1 = this.zero.mutable();
         MutableIntegerModuloP DA = this.zero.mutable();
         MutableIntegerModuloP E = this.zero.mutable();
         MutableIntegerModuloP a24_times_E = this.zero.mutable();

         // Comments describe the equivalent operations from RFC 7748
         // In comments, A(m1) means the variable m1 holds the value A
         for (int t = params.getBits() - 1; t >= 0; t--) {
             int k_t = bitAt(k, t);
             swap = swap ^ k_t;
             cswap(swap, x_2, x_3);
             cswap(swap, z_2, z_3);
             swap = k_t;

             // A(m1) = x_2 + z_2
             m1.setValue(x_2).setSum(z_2);
             // D = x_3 - z_3
             // DA = D * A(m1)
             DA.setValue(x_3).setDifference(z_3).setProduct(m1);
             // AA(m1) = A(m1)^2
             m1.setSquare();
             // B(x_2) = x_2 - z_2
             x_2.setDifference(z_2);
             // C = x_3 + z_3
             // CB(x_3) = C * B(x_2)
             x_3.setSum(z_3).setProduct(x_2);
             // BB(x_2) = B^2
             x_2.setSquare();
             // E = AA(m1) - BB(x_2)
             E.setValue(m1).setDifference(x_2);
             // compute a24 * E using SmallValue
             a24_times_E.setValue(E);
             a24_times_E.setProduct(this.a24);

             // assign results to x_3, z_3, x_2, z_2
             // x_2 = AA(m1) * BB
             x_2.setProduct(m1);
             // z_2 = E * (AA(m1) + a24 * E)
             z_2.setValue(m1).setSum(a24_times_E).setProduct(E);
             // z_3 = x_1*(DA - CB(x_3))^2
             z_3.setValue(DA).setDifference(x_3).setSquare().setProduct(x_1);
             // x_3 = (CB(x_3) + DA)^2
             x_3.setSum(DA).setSquare();
         }

         cswap(swap, x_2, x_3);
         cswap(swap, z_2, z_3);

         // return (x_2 * z_2^(p - 2))
         return x_2.setProduct(z_2.multiplicativeInverse());
     }
 }
	/*
	* 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
	* or visit www.oracle.com if you need additional information or have any
	* questions.
	*/

	package sun.security.ec;

	import sun.security.util.math.IntegerFieldModuloP;
	import sun.security.util.math.ImmutableIntegerModuloP;
	import sun.security.util.math.IntegerModuloP;
	import sun.security.util.math.MutableIntegerModuloP;
	import sun.security.util.math.SmallValue;
	import sun.security.util.math.intpoly.IntegerPolynomial25519;
	import sun.security.util.math.intpoly.IntegerPolynomial448;

	import java.math.BigInteger;
	import java.security.ProviderException;
	import java.security.SecureRandom;

	public class XECOperations {

	private final XECParameters params;
	private final IntegerFieldModuloP field;
	private final ImmutableIntegerModuloP zero;
	private final ImmutableIntegerModuloP one;
	private final SmallValue a24;
	private final ImmutableIntegerModuloP basePoint;

	public XECOperations(XECParameters c) {
	this.params = c;

	BigInteger p = params.getP();
	this.field = getIntegerFieldModulo(p);
	this.zero = field.getElement(BigInteger.ZERO).fixed();
	this.one = field.get1().fixed();
	this.a24 = field.getSmallValue(params.getA24());
	this.basePoint = field.getElement(
	BigInteger.valueOf(c.getBasePoint()));
	}

	public XECParameters getParameters() {
	return params;
	}

	public byte[] generatePrivate(SecureRandom random) {
	byte[] result = new byte[this.params.getBytes()];
	random.nextBytes(result);
	return result;
	}

	/**
	* Compute a public key from an encoded private key. This method will
	* modify the supplied array in order to prune it.
	*/
	public BigInteger computePublic(byte[] k) {
	pruneK(k);
	return pointMultiply(k, this.basePoint).asBigInteger();
	}

	/**
	*
	* Multiply an encoded scalar with a point as a BigInteger and return an
	* encoded point. The array k holding the scalar will be pruned by
	* modifying it in place.
	*
	* @param k an encoded scalar
	* @param u the u-coordinate of a point as a BigInteger
	* @return the encoded product
	*/
	public byte[] encodedPointMultiply(byte[] k, BigInteger u) {
	pruneK(k);
	ImmutableIntegerModuloP elemU = field.getElement(u);
	return pointMultiply(k, elemU).asByteArray(params.getBytes());
	}

	/**
	*
	* Multiply an encoded scalar with an encoded point and return an encoded
	* point. The array k holding the scalar will be pruned by
	* modifying it in place.
	*
	* @param k an encoded scalar
	* @param u an encoded point
	* @return the encoded product
	*/
	public byte[] encodedPointMultiply(byte[] k, byte[] u) {
	pruneK(k);
	ImmutableIntegerModuloP elemU = decodeU(u);
	return pointMultiply(k, elemU).asByteArray(params.getBytes());
	}

	/**
	* Return the field element corresponding to an encoded u-coordinate.
	* This method prunes u by modifying it in place.
	*
	* @param u
	* @param bits
	* @return
	*/
	private ImmutableIntegerModuloP decodeU(byte[] u, int bits) {

	maskHighOrder(u, bits);

	return field.getElement(u);
	}

	/**
	* Mask off the high order bits of an encoded integer in an array. The
	* array is modified in place.
	*
	* @param arr an array containing an encoded integer
	* @param bits the number of bits to keep
	* @return the number, in range [1,8], of bits kept in the highest byte
	*/
	private static byte maskHighOrder(byte[] arr, int bits) {

	int lastByteIndex = arr.length - 1;
	byte bitsMod8 = (byte) (bits % 8);
	byte highBits = bitsMod8 == 0 ? 8 : bitsMod8;
	byte msbMaskOff = (byte) ((1 << highBits) - 1);
	arr[lastByteIndex] &= msbMaskOff;

	return highBits;
	}

	/**
	* Prune an encoded scalar value by modifying it in place. The extra
	* high-order bits are masked off, the highest valid bit it set, and the
	* number is rounded down to a multiple of the cofactor.
	*
	* @param k an encoded scalar value
	* @param bits the number of bits in the scalar
	* @param logCofactor the base-2 logarithm of the cofactor
	*/
	private static void pruneK(byte[] k, int bits, int logCofactor) {

	int lastByteIndex = k.length - 1;

	// mask off unused high-order bits
	byte highBits = maskHighOrder(k, bits);

	// set the highest bit
	byte msbMaskOn = (byte) (1 << (highBits - 1));
	k[lastByteIndex] \|= msbMaskOn;

	// round down to a multiple of the cofactor
	byte lsbMaskOff = (byte) (0xFF << logCofactor);
	k[0] &= lsbMaskOff;
	}

	private void pruneK(byte[] k) {
	pruneK(k, params.getBits(), params.getLogCofactor());
	}

	private ImmutableIntegerModuloP decodeU(byte [] u) {
	return decodeU(u, params.getBits());
	}

	// Constant-time conditional swap
	private static void cswap(int swap, MutableIntegerModuloP x1,
	MutableIntegerModuloP x2) {

	x1.conditionalSwapWith(x2, swap);
	}

	private static IntegerFieldModuloP getIntegerFieldModulo(BigInteger p) {

	if (p.equals(IntegerPolynomial25519.MODULUS)) {
	return new IntegerPolynomial25519();
	}
	else if (p.equals(IntegerPolynomial448.MODULUS)) {
	return new IntegerPolynomial448();
	}

	throw new ProviderException("Unsupported prime: " + p.toString());
	}

	private int bitAt(byte[] arr, int index) {
	int byteIndex = index / 8;
	int bitIndex = index % 8;
	return (arr[byteIndex] & (1 << bitIndex)) >> bitIndex;
	}

	/*
	* Constant-time Montgomery ladder that computes k*u and returns the
	* result as a field element.
	*/
	private IntegerModuloP pointMultiply(byte[] k,
	ImmutableIntegerModuloP u) {

	ImmutableIntegerModuloP x_1 = u;
	MutableIntegerModuloP x_2 = this.one.mutable();
	MutableIntegerModuloP z_2 = this.zero.mutable();
	MutableIntegerModuloP x_3 = u.mutable();
	MutableIntegerModuloP z_3 = this.one.mutable();
	int swap = 0;

	// Variables below are reused to avoid unnecessary allocation
	// They will be assigned in the loop, so initial value doesn't matter
	MutableIntegerModuloP m1 = this.zero.mutable();
	MutableIntegerModuloP DA = this.zero.mutable();
	MutableIntegerModuloP E = this.zero.mutable();
	MutableIntegerModuloP a24_times_E = this.zero.mutable();

	// Comments describe the equivalent operations from RFC 7748
	// In comments, A(m1) means the variable m1 holds the value A
	for (int t = params.getBits() - 1; t >= 0; t--) {
	int k_t = bitAt(k, t);
	swap = swap ^ k_t;
	cswap(swap, x_2, x_3);
	cswap(swap, z_2, z_3);
	swap = k_t;

	// A(m1) = x_2 + z_2
	m1.setValue(x_2).setSum(z_2);
	// D = x_3 - z_3
	// DA = D * A(m1)
	DA.setValue(x_3).setDifference(z_3).setProduct(m1);
	// AA(m1) = A(m1)^2
	m1.setSquare();
	// B(x_2) = x_2 - z_2
	x_2.setDifference(z_2);
	// C = x_3 + z_3
	// CB(x_3) = C * B(x_2)
	x_3.setSum(z_3).setProduct(x_2);
	// BB(x_2) = B^2
	x_2.setSquare();
	// E = AA(m1) - BB(x_2)
	E.setValue(m1).setDifference(x_2);
	// compute a24 * E using SmallValue
	a24_times_E.setValue(E);
	a24_times_E.setProduct(this.a24);

	// assign results to x_3, z_3, x_2, z_2
	// x_2 = AA(m1) * BB
	x_2.setProduct(m1);
	// z_2 = E * (AA(m1) + a24 * E)
	z_2.setValue(m1).setSum(a24_times_E).setProduct(E);
	// z_3 = x_1*(DA - CB(x_3))^2
	z_3.setValue(DA).setDifference(x_3).setSquare().setProduct(x_1);
	// x_3 = (CB(x_3) + DA)^2
	x_3.setSum(DA).setSquare();
	}

	cswap(swap, x_2, x_3);
	cswap(swap, z_2, z_3);

	// return (x_2 * z_2^(p - 2))
	return x_2.setProduct(z_2.multiplicativeInverse());
	}
	}