path: root/core/src/test/java/org/spongycastle/math/ec/test/ECPointTest.java

package org.spongycastle.math.ec.test;

import java.math.BigInteger;
import java.security.SecureRandom;
import java.util.ArrayList;
import java.util.Enumeration;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Set;

import junit.framework.Test;
import junit.framework.TestCase;
import junit.framework.TestSuite;
import org.spongycastle.asn1.x9.ECNamedCurveTable;
import org.spongycastle.asn1.x9.X9ECParameters;
import org.spongycastle.crypto.ec.CustomNamedCurves;
import org.spongycastle.math.ec.ECAlgorithms;
import org.spongycastle.math.ec.ECConstants;
import org.spongycastle.math.ec.ECCurve;
import org.spongycastle.math.ec.ECFieldElement;
import org.spongycastle.math.ec.ECPoint;
import org.spongycastle.util.BigIntegers;

/**
 * Test class for {@link org.spongycastle.math.ec.ECPoint ECPoint}. All
 * literature values are taken from "Guide to elliptic curve cryptography",
 * Darrel Hankerson, Alfred J. Menezes, Scott Vanstone, 2004, Springer-Verlag
 * New York, Inc.
 */
public class ECPointTest extends TestCase
{
    /**
     * Random source used to generate random points
     */
    private SecureRandom secRand = new SecureRandom();

    private ECPointTest.Fp fp = null;

    private ECPointTest.F2m f2m = null;

    /**
     * Nested class containing sample literature values for <code>Fp</code>.
     */
    public static class Fp
    {
        private final BigInteger q = new BigInteger("29");

        private final BigInteger a = new BigInteger("4");

        private final BigInteger b = new BigInteger("20");

        private final BigInteger n = new BigInteger("38");

        private final BigInteger h = new BigInteger("1");

        private final ECCurve curve = new ECCurve.Fp(q, a, b, n, h);

        private final ECPoint infinity = curve.getInfinity();

        private final int[] pointSource = { 5, 22, 16, 27, 13, 6, 14, 6 };

        private ECPoint[] p = new ECPoint[pointSource.length / 2];

        /**
         * Creates the points on the curve with literature values.
         */
        private void createPoints()
        {
            for (int i = 0; i < pointSource.length / 2; i++)
            {
                p[i] = curve.createPoint(
                    new BigInteger(Integer.toString(pointSource[2 * i])),
                    new BigInteger(Integer.toString(pointSource[2 * i + 1])));
            }
        }
    }

    /**
     * Nested class containing sample literature values for <code>F2m</code>.
     */
    public static class F2m
    {
        // Irreducible polynomial for TPB z^4 + z + 1
        private final int m = 4;

        private final int k1 = 1;

        // a = z^3
        private final BigInteger aTpb = new BigInteger("1000", 2);

        // b = z^3 + 1
        private final BigInteger bTpb = new BigInteger("1001", 2);

        private final BigInteger n = new BigInteger("23");

        private final BigInteger h = new BigInteger("1");

        private final ECCurve.F2m curve = new ECCurve.F2m(m, k1, aTpb, bTpb, n, h);

        private final ECPoint.F2m infinity = (ECPoint.F2m) curve.getInfinity();

        private final String[] pointSource = { "0010", "1111", "1100", "1100",
                "0001", "0001", "1011", "0010" };

        private ECPoint[] p = new ECPoint[pointSource.length / 2];

        /**
         * Creates the points on the curve with literature values.
         */
        private void createPoints()
        {
            for (int i = 0; i < pointSource.length / 2; i++)
            {
                p[i] = curve.createPoint(
                    new BigInteger(pointSource[2 * i], 2),
                    new BigInteger(pointSource[2 * i + 1], 2));
            }
        }
    }

    public void setUp()
    {
        fp = new ECPointTest.Fp();
        fp.createPoints();

        f2m = new ECPointTest.F2m();
        f2m.createPoints();
    }

    /**
     * Tests, if inconsistent points can be created, i.e. points with exactly
     * one null coordinate (not permitted).
     */
    public void testPointCreationConsistency()
    {
        try
        {
            ECPoint bad = fp.curve.createPoint(new BigInteger("12"), null);
            fail();
        }
        catch (IllegalArgumentException expected)
        {
        }

        try
        {
            ECPoint bad = fp.curve.createPoint(null, new BigInteger("12"));
            fail();
        }
        catch (IllegalArgumentException expected)
        {
        }

        try
        {
            ECPoint bad = f2m.curve.createPoint(new BigInteger("1011"), null);
            fail();
        }
        catch (IllegalArgumentException expected)
        {
        }

        try
        {
            ECPoint bad = f2m.curve.createPoint(null, new BigInteger("1011"));
            fail();
        }
        catch (IllegalArgumentException expected)
        {
        }
    }

    /**
     * Tests <code>ECPoint.add()</code> against literature values.
     * 
     * @param p
     *            The array of literature values.
     * @param infinity
     *            The point at infinity on the respective curve.
     */
    private void implTestAdd(ECPoint[] p, ECPoint infinity)
    {
        assertPointsEqual("p0 plus p1 does not equal p2", p[2], p[0].add(p[1]));
        assertPointsEqual("p1 plus p0 does not equal p2", p[2], p[1].add(p[0]));
        for (int i = 0; i < p.length; i++)
        {
            assertPointsEqual("Adding infinity failed", p[i], p[i].add(infinity));
            assertPointsEqual("Adding to infinity failed", p[i], infinity.add(p[i]));
        }
    }

    /**
     * Calls <code>implTestAdd()</code> for <code>Fp</code> and
     * <code>F2m</code>.
     */
    public void testAdd()
    {
        implTestAdd(fp.p, fp.infinity);
        implTestAdd(f2m.p, f2m.infinity);
    }

    /**
     * Tests <code>ECPoint.twice()</code> against literature values.
     * 
     * @param p
     *            The array of literature values.
     */
    private void implTestTwice(ECPoint[] p)
    {
        assertPointsEqual("Twice incorrect", p[3], p[0].twice());
        assertPointsEqual("Add same point incorrect", p[3], p[0].add(p[0]));
    }

    /**
     * Calls <code>implTestTwice()</code> for <code>Fp</code> and
     * <code>F2m</code>.
     */
    public void testTwice()
    {
        implTestTwice(fp.p);
        implTestTwice(f2m.p);
    }

    private void implTestThreeTimes(ECPoint[] p)
    {
        ECPoint P = p[0];
        ECPoint _3P = P.add(P).add(P);
        assertPointsEqual("ThreeTimes incorrect", _3P, P.threeTimes());
        assertPointsEqual("TwicePlus incorrect", _3P, P.twicePlus(P));
    }

    /**
     * Calls <code>implTestThreeTimes()</code> for <code>Fp</code> and
     * <code>F2m</code>.
     */
    public void testThreeTimes()
    {
        implTestThreeTimes(fp.p);
        implTestThreeTimes(f2m.p);
    }

    /**
     * Goes through all points on an elliptic curve and checks, if adding a
     * point <code>k</code>-times is the same as multiplying the point by
     * <code>k</code>, for all <code>k</code>. Should be called for points
     * on very small elliptic curves only.
     * 
     * @param p
     *            The base point on the elliptic curve.
     * @param infinity
     *            The point at infinity on the elliptic curve.
     */
    private void implTestAllPoints(ECPoint p, ECPoint infinity)
    {
        ECPoint adder = infinity;
        ECPoint multiplier = infinity;

        BigInteger i = BigInteger.valueOf(1);
        do
        {
            adder = adder.add(p);
            multiplier = p.multiply(i);
            assertPointsEqual("Results of add() and multiply() are inconsistent "
                    + i, adder, multiplier);
            i = i.add(BigInteger.ONE);
        }
        while (!(adder.equals(infinity)));
    }

    /**
     * Calls <code>implTestAllPoints()</code> for the small literature curves,
     * both for <code>Fp</code> and <code>F2m</code>.
     */
    public void testAllPoints()
    {
        for (int i = 0; i < fp.p.length; i++)
        {
            implTestAllPoints(fp.p[0], fp.infinity);
        }

        for (int i = 0; i < f2m.p.length; i++)
        {
            implTestAllPoints(f2m.p[0], f2m.infinity);
        }
    }

    /**
     * Checks, if the point multiplication algorithm of the given point yields
     * the same result as point multiplication done by the reference
     * implementation given in <code>multiply()</code>. This method chooses a
     * random number by which the given point <code>p</code> is multiplied.
     * 
     * @param p
     *            The point to be multiplied.
     * @param numBits
     *            The bitlength of the random number by which <code>p</code>
     *            is multiplied.
     */
    private void implTestMultiply(ECPoint p, int numBits)
    {
        BigInteger k = new BigInteger(numBits, secRand);
        ECPoint ref = ECAlgorithms.referenceMultiply(p, k);
        ECPoint q = p.multiply(k);
        assertPointsEqual("ECPoint.multiply is incorrect", ref, q);
    }

    /**
     * Checks, if the point multiplication algorithm of the given point yields
     * the same result as point multiplication done by the reference
     * implementation given in <code>multiply()</code>. This method tests
     * multiplication of <code>p</code> by every number of bitlength
     * <code>numBits</code> or less.
     * 
     * @param p
     *            The point to be multiplied.
     * @param numBits
     *            Try every multiplier up to this bitlength
     */
    private void implTestMultiplyAll(ECPoint p, int numBits)
    {
        BigInteger bound = BigInteger.ONE.shiftLeft(numBits);
        BigInteger k = BigInteger.ZERO;

        do
        {
            ECPoint ref = ECAlgorithms.referenceMultiply(p, k);
            ECPoint q = p.multiply(k);
            assertPointsEqual("ECPoint.multiply is incorrect", ref, q);
            k = k.add(BigInteger.ONE);
        }
        while (k.compareTo(bound) < 0);
    }

    /**
     * Tests <code>ECPoint.add()</code> and <code>ECPoint.subtract()</code>
     * for the given point and the given point at infinity.
     * 
     * @param p
     *            The point on which the tests are performed.
     * @param infinity
     *            The point at infinity on the same curve as <code>p</code>.
     */
    private void implTestAddSubtract(ECPoint p, ECPoint infinity)
    {
        assertPointsEqual("Twice and Add inconsistent", p.twice(), p.add(p));
        assertPointsEqual("Twice p - p is not p", p, p.twice().subtract(p));
        assertPointsEqual("TwicePlus(p, -p) is not p", p, p.twicePlus(p.negate()));
        assertPointsEqual("p - p is not infinity", infinity, p.subtract(p));
        assertPointsEqual("p plus infinity is not p", p, p.add(infinity));
        assertPointsEqual("infinity plus p is not p", p, infinity.add(p));
        assertPointsEqual("infinity plus infinity is not infinity ", infinity, infinity.add(infinity));
        assertPointsEqual("Twice infinity is not infinity ", infinity, infinity.twice());
    }

    /**
     * Calls <code>implTestAddSubtract()</code> for literature values, both
     * for <code>Fp</code> and <code>F2m</code>.
     */
    public void testAddSubtractMultiplySimple()
    {
        int fpBits = fp.curve.getOrder().bitLength();
        for (int iFp = 0; iFp < fp.pointSource.length / 2; iFp++)
        {
            implTestAddSubtract(fp.p[iFp], fp.infinity);

            implTestMultiplyAll(fp.p[iFp], fpBits);
            implTestMultiplyAll(fp.infinity, fpBits);
        }

        int f2mBits = f2m.curve.getOrder().bitLength();
        for (int iF2m = 0; iF2m < f2m.pointSource.length / 2; iF2m++)
        {
            implTestAddSubtract(f2m.p[iF2m], f2m.infinity);

            implTestMultiplyAll(f2m.p[iF2m], f2mBits);
            implTestMultiplyAll(f2m.infinity, f2mBits);
        }
    }

    /**
     * Test encoding with and without point compression.
     * 
     * @param p
     *            The point to be encoded and decoded.
     */
    private void implTestEncoding(ECPoint p)
    {
        // Not Point Compression
        byte[] unCompBarr = p.getEncoded(false);
        ECPoint decUnComp = p.getCurve().decodePoint(unCompBarr);
        assertPointsEqual("Error decoding uncompressed point", p, decUnComp);

        // Point compression
        byte[] compBarr = p.getEncoded(true);
        ECPoint decComp = p.getCurve().decodePoint(compBarr);
        assertPointsEqual("Error decoding compressed point", p, decComp);
    }

    private void implAddSubtractMultiplyTwiceEncodingTest(ECCurve curve, ECPoint q, BigInteger n)
    {
        // Get point at infinity on the curve
        ECPoint infinity = curve.getInfinity();

        implTestAddSubtract(q, infinity);
        implTestMultiply(q, n.bitLength());
        implTestMultiply(infinity, n.bitLength());

        ECPoint p = q;
        for (int i = 0; i < 10; ++i)
        {
            implTestEncoding(p);
            p = p.twice();
        }
    }

    private void implSqrtTest(ECCurve c)
    {
        if (ECAlgorithms.isFpCurve(c))
        {
            BigInteger p = c.getField().getCharacteristic();
            BigInteger pMinusOne = p.subtract(ECConstants.ONE);
            BigInteger legendreExponent = p.shiftRight(1);

            int count = 0;
            while (count < 10)
            {
                BigInteger nonSquare = BigIntegers.createRandomInRange(ECConstants.TWO, pMinusOne, secRand);
                if (!nonSquare.modPow(legendreExponent, p).equals(ECConstants.ONE))
                {
                    ECFieldElement root = c.fromBigInteger(nonSquare).sqrt();
                    assertNull(root);
                    ++count;
                }
            }
        }
    }

    private void implAddSubtractMultiplyTwiceEncodingTestAllCoords(X9ECParameters x9ECParameters)
    {
        BigInteger n = x9ECParameters.getN();
        ECPoint G = x9ECParameters.getG();
        ECCurve C = x9ECParameters.getCurve();

        int[] coords = ECCurve.getAllCoordinateSystems();
        for (int i = 0; i < coords.length; ++i)
        {
            int coord = coords[i];
            if (C.supportsCoordinateSystem(coord))
            {
                ECCurve c = C;
                ECPoint g = G;

                if (c.getCoordinateSystem() != coord)
                {
                    c = C.configure().setCoordinateSystem(coord).create();
                    g = c.importPoint(G);
                }

                // The generator is multiplied by random b to get random q
                BigInteger b = new BigInteger(n.bitLength(), secRand);
                ECPoint q = g.multiply(b).normalize();

                implAddSubtractMultiplyTwiceEncodingTest(c, q, n);

                implSqrtTest(c);
            }
        }
    }

    /**
     * Calls <code>implTestAddSubtract()</code>,
     * <code>implTestMultiply</code> and <code>implTestEncoding</code> for
     * the standard elliptic curves as given in <code>SECNamedCurves</code>.
     */
    public void testAddSubtractMultiplyTwiceEncoding()
    {
        Set names = new HashSet(enumToList(ECNamedCurveTable.getNames()));
        names.addAll(enumToList(CustomNamedCurves.getNames()));

        Iterator it = names.iterator();
        while (it.hasNext())
        {
            String name = (String)it.next();

            X9ECParameters x9ECParameters = ECNamedCurveTable.getByName(name);
            if (x9ECParameters != null)
            {
                implAddSubtractMultiplyTwiceEncodingTestAllCoords(x9ECParameters);
            }

            x9ECParameters = CustomNamedCurves.getByName(name);
            if (x9ECParameters != null)
            {
                implAddSubtractMultiplyTwiceEncodingTestAllCoords(x9ECParameters);
            }
        }
    }

    private List enumToList(Enumeration en)
    {
        List rv = new ArrayList();

        while (en.hasMoreElements())
        {
            rv.add(en.nextElement());
        }

        return rv;
    }

    private void assertPointsEqual(String message, ECPoint a, ECPoint b)
    {
        assertEquals(message, a, b);
    }

    public static Test suite()
    {
        return new TestSuite(ECPointTest.class);
    }
}