8171277: Elliptic Curves for Security in Crypto

Implementations of X25519 and X448 key agreement in SunEC

Reviewed-by: mullan

src/jdk.crypto.ec/share/classes/sun/security/ec/XECOperations.java

@@ -0,0 +1,271 @@
+/*
+ * 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());
+    }
+}