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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
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