@Test
public void dblPrecomputedTableContainsExpectedGroupElements() {
// Arrange:
GroupElement g = ed25519.getB();
GroupElement h = MathUtils.addGroupElements(g, g);
// Act + Assert:
for (int i = 0; i < 8; i++) {
Assert.assertThat(
MathUtils.toRepresentation(g, GroupElement.Representation.PRECOMP),
IsEqual.equalTo(ed25519.getB().dblPrecmp[i]));
g = MathUtils.addGroupElements(g, h);
}
}
@Test
public void precomputedTableContainsExpectedGroupElements() {
// Arrange:
GroupElement g = ed25519.getB();
// Act + Assert:
for (int i = 0; i < 32; i++) {
GroupElement h = g;
for (int j = 0; j < 8; j++) {
Assert.assertThat(
MathUtils.toRepresentation(h, GroupElement.Representation.PRECOMP),
IsEqual.equalTo(ed25519.getB().precmp[i][j]));
h = MathUtils.addGroupElements(h, g);
}
for (int k = 0; k < 8; k++) {
g = MathUtils.addGroupElements(g, g);
}
}
}
@Test
public void scalarMultiplyBasePointWithOneReturnsBasePoint() {
// Arrange:
final GroupElement basePoint = ed25519.getB();
// Act:
final GroupElement g = basePoint.scalarMultiply(curve.getField().ONE.toByteArray());
// Assert:
Assert.assertThat(basePoint, IsEqual.equalTo(g));
}
@Test
public void scalarMultiplyBasePointWithZeroReturnsNeutralElement() {
// Arrange:
final GroupElement basePoint = ed25519.getB();
// Act:
final GroupElement g = basePoint.scalarMultiply(curve.getField().ZERO.toByteArray());
// Assert:
Assert.assertThat(curve.getZero(GroupElement.Representation.P3), IsEqual.equalTo(g));
}
/**
* Test method for {@link GroupElement#scalarMultiply(byte[])}. Test values generated with Python
* Ed25519 implementation.
*/
@Test
public void testScalarMultiplyByteArray() {
// Little-endian
byte[] zero =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
byte[] one =
Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000");
byte[] two =
Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000");
byte[] a = Utils.hexToBytes("d072f8dd9c07fa7bc8d22a4b325d26301ee9202f6db89aa7c3731529e37e437c");
GroupElement A =
new GroupElement(
curve,
Utils.hexToBytes("d4cf8595571830644bd14af416954d09ab7159751ad9e0f7a6cbd92379e71a66"));
assertThat(
"scalarMultiply(0) failed",
ed25519.getB().scalarMultiply(zero),
is(equalTo(curve.getZero(GroupElement.Representation.P3))));
assertThat(
"scalarMultiply(1) failed",
ed25519.getB().scalarMultiply(one),
is(equalTo(ed25519.getB())));
assertThat(
"scalarMultiply(2) failed",
ed25519.getB().scalarMultiply(two),
is(equalTo(ed25519.getB().dbl())));
assertThat("scalarMultiply(a) failed", ed25519.getB().scalarMultiply(a), is(equalTo(A)));
}
// This test is slow (~6s) due to math utils using an inferior algorithm to calculate the result.
@Test
public void scalarMultiplyBasePointReturnsExpectedResult() {
for (int i = 0; i < 100; i++) {
// Arrange:
final GroupElement basePoint = ed25519.getB();
final FieldElement f = MathUtils.getRandomFieldElement();
// Act:
final GroupElement g = basePoint.scalarMultiply(f.toByteArray());
final GroupElement h = MathUtils.scalarMultiplyGroupElement(basePoint, f);
// Assert:
Assert.assertThat(g, IsEqual.equalTo(h));
}
}
/** Test method for {@link GroupElement#toP2()}. */
@Test
public void testToP2() {
GroupElement p3zero = curve.getZero(GroupElement.Representation.P3);
GroupElement t = p3zero.toP2();
assertThat(t.repr, is(GroupElement.Representation.P2));
assertThat(t.X, is(p3zero.X));
assertThat(t.Y, is(p3zero.Y));
assertThat(t.Z, is(p3zero.Z));
assertThat(t.T, is((FieldElement) null));
GroupElement B = ed25519.getB();
t = B.toP2();
assertThat(t.repr, is(GroupElement.Representation.P2));
assertThat(t.X, is(B.X));
assertThat(t.Y, is(B.Y));
assertThat(t.Z, is(B.Z));
assertThat(t.T, is((FieldElement) null));
}
// This test is slow (~6s) due to math utils using an inferior algorithm to calculate the result.
@Test
public void doubleScalarMultiplyVariableTimeReturnsExpectedResult() {
for (int i = 0; i < 50; i++) {
// Arrange:
final GroupElement basePoint = ed25519.getB();
final GroupElement g = MathUtils.getRandomGroupElement();
g.precompute(false);
final FieldElement f1 = MathUtils.getRandomFieldElement();
final FieldElement f2 = MathUtils.getRandomFieldElement();
// Act:
final GroupElement h1 =
basePoint.doubleScalarMultiplyVariableTime(g, f2.toByteArray(), f1.toByteArray());
final GroupElement h2 = MathUtils.doubleScalarMultiplyGroupElements(basePoint, f1, g, f2);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
}
}
@Test
public void testDoubleScalarMultiplyVariableTime() {
// Little-endian
byte[] zero =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
byte[] one =
Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000");
byte[] two =
Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000");
byte[] a = Utils.hexToBytes("d072f8dd9c07fa7bc8d22a4b325d26301ee9202f6db89aa7c3731529e37e437c");
GroupElement A =
new GroupElement(
curve,
Utils.hexToBytes("d4cf8595571830644bd14af416954d09ab7159751ad9e0f7a6cbd92379e71a66"));
GroupElement B = ed25519.getB();
GroupElement geZero = curve.getZero(GroupElement.Representation.P3);
geZero.precompute(false);
// 0 * GE(0) + 0 * GE(0) = GE(0)
assertThat(geZero.doubleScalarMultiplyVariableTime(geZero, zero, zero), is(equalTo(geZero)));
// 0 * GE(0) + 0 * B = GE(0)
assertThat(B.doubleScalarMultiplyVariableTime(geZero, zero, zero), is(equalTo(geZero)));
// 1 * GE(0) + 0 * B = GE(0)
assertThat(B.doubleScalarMultiplyVariableTime(geZero, one, zero), is(equalTo(geZero)));
// 1 * GE(0) + 1 * B = B
assertThat(B.doubleScalarMultiplyVariableTime(geZero, one, one), is(equalTo(B)));
// 1 * B + 1 * B = 2 * B
assertThat(B.doubleScalarMultiplyVariableTime(B, one, one), is(equalTo(B.dbl())));
// 1 * B + 2 * B = 3 * B
assertThat(
B.doubleScalarMultiplyVariableTime(B, one, two),
is(equalTo(B.dbl().toP3().add(B.toCached()))));
// 2 * B + 2 * B = 4 * B
assertThat(B.doubleScalarMultiplyVariableTime(B, two, two), is(equalTo(B.dbl().toP3().dbl())));
// 0 * B + a * B = A
assertThat(B.doubleScalarMultiplyVariableTime(B, zero, a), is(equalTo(A)));
// a * B + 0 * B = A
assertThat(B.doubleScalarMultiplyVariableTime(B, a, zero), is(equalTo(A)));
// a * B + a * B = 2 * A
assertThat(B.doubleScalarMultiplyVariableTime(B, a, a), is(equalTo(A.dbl())));
}
/** Test method for {@link GroupElement#select(int, int)}. */
@Test
public void testSelect() {
GroupElement B = ed25519.getB();
for (int i = 0; i < 32; i++) {
// 16^i 0 B
assertThat(
i + ",0", B.select(i, 0), is(equalTo(GroupElement.precomp(curve, ONE, ONE, ZERO))));
for (int j = 1; j < 8; j++) {
// 16^i r_i B
GroupElement t = B.select(i, j);
assertThat(i + "," + j, t, is(equalTo(B.precmp[i][j - 1])));
// -16^i r_i B
t = B.select(i, -j);
GroupElement neg =
GroupElement.precomp(
curve, B.precmp[i][j - 1].Y, B.precmp[i][j - 1].X, B.precmp[i][j - 1].Z.negate());
assertThat(i + "," + -j, t, is(equalTo(neg)));
}
}
}
/** Test method for {@link GroupElement#dbl()}. */
@Test
public void testDbl() {
GroupElement B = ed25519.getB();
// 2 * B = B + B
assertThat(B.dbl(), is(equalTo(B.add(B.toCached()))));
}
/** Test method for {@link GroupElement#precompute(boolean)}. */
@Test
public void testPrecompute() {
GroupElement B = ed25519.getB();
assertThat(B.precmp, is(equalTo(PrecomputationTestVectors.testPrecmp)));
assertThat(B.dblPrecmp, is(equalTo(PrecomputationTestVectors.testDblPrecmp)));
}
/** @author str4d Additional tests by NEM project team. */
public class GroupElementTest {
static final byte[] BYTES_ZEROZERO =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
static final byte[] BYTES_ONEONE =
Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000080");
static final byte[] BYTES_TENZERO =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
static final byte[] BYTES_ONETEN =
Utils.hexToBytes("0a00000000000000000000000000000000000000000000000000000000000080");
static final EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName("ed25519-sha-512");
static final Curve curve = ed25519.getCurve();
static final FieldElement ZERO = curve.getField().ZERO;
static final FieldElement ONE = curve.getField().ONE;
static final FieldElement TWO = curve.getField().TWO;
static final FieldElement TEN =
curve
.getField()
.fromByteArray(
Utils.hexToBytes("0a00000000000000000000000000000000000000000000000000000000000000"));
static final GroupElement P2_ZERO = GroupElement.p2(curve, ZERO, ONE, ONE);
static final FieldElement[] PKR =
new FieldElement[] {
curve
.getField()
.fromByteArray(
Utils.hexToBytes(
"5849722e338aced7b50c7f0e9328f9a10c847b08e40af5c5b0577b0fd8984f15")),
curve
.getField()
.fromByteArray(
Utils.hexToBytes(
"3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29"))
};
static final byte[] BYTES_PKR =
Utils.hexToBytes("3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29");
@Rule public ExpectedException exception = ExpectedException.none();
/** Test method for {@link GroupElement#p2(Curve, FieldElement, FieldElement, FieldElement)}. */
@Test
public void testP2() {
final GroupElement t = GroupElement.p2(curve, ZERO, ONE, ONE);
assertThat(t.curve, is(equalTo(curve)));
assertThat(t.repr, is(GroupElement.Representation.P2));
assertThat(t.X, is(ZERO));
assertThat(t.Y, is(ONE));
assertThat(t.Z, is(ONE));
assertThat(t.T, is((FieldElement) null));
}
/**
* Test method for {@link GroupElement#p3(Curve, FieldElement, FieldElement, FieldElement,
* FieldElement)}.
*/
@Test
public void testP3() {
final GroupElement t = GroupElement.p3(curve, ZERO, ONE, ONE, ZERO);
assertThat(t.curve, is(equalTo(curve)));
assertThat(t.repr, is(GroupElement.Representation.P3));
assertThat(t.X, is(ZERO));
assertThat(t.Y, is(ONE));
assertThat(t.Z, is(ONE));
assertThat(t.T, is(ZERO));
}
/**
* Test method for {@link GroupElement#p1p1(Curve, FieldElement, FieldElement, FieldElement,
* FieldElement)}.
*/
@Test
public void testP1p1() {
final GroupElement t = GroupElement.p1p1(curve, ZERO, ONE, ONE, ONE);
assertThat(t.curve, is(equalTo(curve)));
assertThat(t.repr, is(GroupElement.Representation.P1P1));
assertThat(t.X, is(ZERO));
assertThat(t.Y, is(ONE));
assertThat(t.Z, is(ONE));
assertThat(t.T, is(ONE));
}
/**
* Test method for {@link GroupElement#precomp(Curve, FieldElement, FieldElement, FieldElement)}.
*/
@Test
public void testPrecomp() {
final GroupElement t = GroupElement.precomp(curve, ONE, ONE, ZERO);
assertThat(t.curve, is(equalTo(curve)));
assertThat(t.repr, is(GroupElement.Representation.PRECOMP));
assertThat(t.X, is(ONE));
assertThat(t.Y, is(ONE));
assertThat(t.Z, is(ZERO));
assertThat(t.T, is((FieldElement) null));
}
/**
* Test method for {@link GroupElement#cached(Curve, FieldElement, FieldElement, FieldElement,
* FieldElement)}.
*/
@Test
public void testCached() {
final GroupElement t = GroupElement.cached(curve, ONE, ONE, ONE, ZERO);
assertThat(t.curve, is(equalTo(curve)));
assertThat(t.repr, is(GroupElement.Representation.CACHED));
assertThat(t.X, is(ONE));
assertThat(t.Y, is(ONE));
assertThat(t.Z, is(ONE));
assertThat(t.T, is(ZERO));
}
/**
* Test method for {@link GroupElement#GroupElement(Curve, GroupElement.Representation,
* FieldElement, FieldElement, FieldElement, FieldElement)}.
*/
@Test
public void
testGroupElementCurveRepresentationFieldElementFieldElementFieldElementFieldElement() {
final GroupElement t =
new GroupElement(curve, GroupElement.Representation.P3, ZERO, ONE, ONE, ZERO);
assertThat(t.curve, is(equalTo(curve)));
assertThat(t.repr, is(GroupElement.Representation.P3));
assertThat(t.X, is(ZERO));
assertThat(t.Y, is(ONE));
assertThat(t.Z, is(ONE));
assertThat(t.T, is(ZERO));
}
/**
* Tests {@link GroupElement#GroupElement(Curve, byte[])} and {@link GroupElement#toByteArray()}
* against valid public keys.
*/
@Test
public void testToAndFromByteArray() {
GroupElement t;
for (Ed25519TestVectors.TestTuple testCase : Ed25519TestVectors.testCases) {
t = new GroupElement(curve, testCase.pk);
assertThat(
"Test case " + testCase.caseNum + " failed", t.toByteArray(), is(equalTo(testCase.pk)));
}
}
/** Test method for {@link GroupElement#GroupElement(Curve, byte[])}. */
@Test
public void testGroupElementByteArray() {
final GroupElement t = new GroupElement(curve, BYTES_PKR);
final GroupElement s = GroupElement.p3(curve, PKR[0], PKR[1], ONE, PKR[0].multiply(PKR[1]));
assertThat(t, is(equalTo(s)));
}
@Test
public void constructorUsingByteArrayReturnsExpectedResult() {
for (int i = 0; i < 100; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
final byte[] bytes = g.toByteArray();
// Act:
final GroupElement h1 = new GroupElement(curve, bytes);
final GroupElement h2 = MathUtils.toGroupElement(bytes);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
}
}
/**
* Test method for {@link GroupElement#toByteArray()}. TODO 20141001 BR: why test with points
* which are not on the curve?
*/
@Test
public void testToByteArray() {
byte[] zerozero = GroupElement.p2(curve, ZERO, ZERO, ONE).toByteArray();
assertThat(zerozero.length, is(equalTo(BYTES_ZEROZERO.length)));
assertThat(zerozero, is(equalTo(BYTES_ZEROZERO)));
byte[] oneone = GroupElement.p2(curve, ONE, ONE, ONE).toByteArray();
assertThat(oneone.length, is(equalTo(BYTES_ONEONE.length)));
assertThat(oneone, is(equalTo(BYTES_ONEONE)));
byte[] tenzero = GroupElement.p2(curve, TEN, ZERO, ONE).toByteArray();
assertThat(tenzero.length, is(equalTo(BYTES_TENZERO.length)));
assertThat(tenzero, is(equalTo(BYTES_TENZERO)));
byte[] oneten = GroupElement.p2(curve, ONE, TEN, ONE).toByteArray();
assertThat(oneten.length, is(equalTo(BYTES_ONETEN.length)));
assertThat(oneten, is(equalTo(BYTES_ONETEN)));
byte[] pkr = GroupElement.p2(curve, PKR[0], PKR[1], ONE).toByteArray();
assertThat(pkr.length, is(equalTo(BYTES_PKR.length)));
assertThat(pkr, is(equalTo(BYTES_PKR)));
}
@Test
public void toByteArrayReturnsExpectedResult() {
for (int i = 0; i < 100; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Act:
final byte[] gBytes = g.toByteArray();
final byte[] bytes = MathUtils.toByteArray(MathUtils.toBigInteger(g.getY()));
if (MathUtils.toBigInteger(g.getX()).mod(new BigInteger("2")).equals(BigInteger.ONE)) {
bytes[31] |= 0x80;
}
// Assert:
Assert.assertThat(Arrays.equals(gBytes, bytes), IsEqual.equalTo(true));
}
}
// region toX where X is the representation
/** Test method for {@link GroupElement#toP2()}. */
@Test
public void testToP2() {
GroupElement p3zero = curve.getZero(GroupElement.Representation.P3);
GroupElement t = p3zero.toP2();
assertThat(t.repr, is(GroupElement.Representation.P2));
assertThat(t.X, is(p3zero.X));
assertThat(t.Y, is(p3zero.Y));
assertThat(t.Z, is(p3zero.Z));
assertThat(t.T, is((FieldElement) null));
GroupElement B = ed25519.getB();
t = B.toP2();
assertThat(t.repr, is(GroupElement.Representation.P2));
assertThat(t.X, is(B.X));
assertThat(t.Y, is(B.Y));
assertThat(t.Z, is(B.Z));
assertThat(t.T, is((FieldElement) null));
}
@Test(expected = IllegalArgumentException.class)
public void toP2ThrowsIfGroupElementHasPrecompRepresentation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP);
// Assert:
g.toP2();
}
@Test(expected = IllegalArgumentException.class)
public void toP2ThrowsIfGroupElementHasCachedRepresentation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.CACHED);
// Assert:
g.toP2();
}
@Test
public void toP2ReturnsExpectedResultIfGroupElementHasP2Representation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P2);
// Act:
final GroupElement h = g.toP2();
// Assert:
Assert.assertThat(h, IsEqual.equalTo(g));
Assert.assertThat(h.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P2));
Assert.assertThat(h.getX(), IsEqual.equalTo(g.getX()));
Assert.assertThat(h.getY(), IsEqual.equalTo(g.getY()));
Assert.assertThat(h.getZ(), IsEqual.equalTo(g.getZ()));
Assert.assertThat(h.getT(), IsEqual.equalTo(null));
}
}
@Test
public void toP2ReturnsExpectedResultIfGroupElementHasP3Representation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h1 = g.toP2();
final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P2);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P2));
Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX()));
Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY()));
Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ()));
Assert.assertThat(h1.getT(), IsEqual.equalTo(null));
}
}
@Test
public void toP2ReturnsExpectedResultIfGroupElementHasP1P1Representation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1);
// Act:
final GroupElement h1 = g.toP2();
final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P2);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P2));
Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX().multiply(g.getT())));
Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().multiply(g.getZ())));
Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ().multiply(g.getT())));
Assert.assertThat(h1.getT(), IsEqual.equalTo(null));
}
}
@Test(expected = IllegalArgumentException.class)
public void toP3ThrowsIfGroupElementHasP2Representation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P2);
// Assert:
g.toP3();
}
@Test(expected = IllegalArgumentException.class)
public void toP3ThrowsIfGroupElementHasPrecompRepresentation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP);
// Assert:
g.toP3();
}
@Test(expected = IllegalArgumentException.class)
public void toP3ThrowsIfGroupElementHasCachedRepresentation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.CACHED);
// Assert:
g.toP3();
}
@Test
public void toP3ReturnsExpectedResultIfGroupElementHasP1P1Representation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1);
// Act:
final GroupElement h1 = g.toP3();
final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P3);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P3));
Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX().multiply(g.getT())));
Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().multiply(g.getZ())));
Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ().multiply(g.getT())));
Assert.assertThat(h1.getT(), IsEqual.equalTo(g.getX().multiply(g.getY())));
}
}
@Test
public void toP3ReturnsExpectedResultIfGroupElementHasP3Representation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h = g.toP3();
// Assert:
Assert.assertThat(h, IsEqual.equalTo(g));
Assert.assertThat(h.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P3));
Assert.assertThat(h, IsEqual.equalTo(g));
Assert.assertThat(h.getX(), IsEqual.equalTo(g.getX()));
Assert.assertThat(h.getY(), IsEqual.equalTo(g.getY()));
Assert.assertThat(h.getZ(), IsEqual.equalTo(g.getZ()));
Assert.assertThat(h.getT(), IsEqual.equalTo(g.getT()));
}
}
@Test(expected = IllegalArgumentException.class)
public void toCachedThrowsIfGroupElementHasP2Representation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P2);
// Assert:
g.toCached();
}
@Test(expected = IllegalArgumentException.class)
public void toCachedThrowsIfGroupElementHasPrecompRepresentation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP);
// Assert:
g.toCached();
}
@Test(expected = IllegalArgumentException.class)
public void toCachedThrowsIfGroupElementHasP1P1Representation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1);
// Assert:
g.toCached();
}
@Test
public void toCachedReturnsExpectedResultIfGroupElementHasCachedRepresentation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.CACHED);
// Act:
final GroupElement h = g.toCached();
// Assert:
Assert.assertThat(h, IsEqual.equalTo(g));
Assert.assertThat(h.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.CACHED));
Assert.assertThat(h, IsEqual.equalTo(g));
Assert.assertThat(h.getX(), IsEqual.equalTo(g.getX()));
Assert.assertThat(h.getY(), IsEqual.equalTo(g.getY()));
Assert.assertThat(h.getZ(), IsEqual.equalTo(g.getZ()));
Assert.assertThat(h.getT(), IsEqual.equalTo(g.getT()));
}
}
@Test
public void toCachedReturnsExpectedResultIfGroupElementHasP3Representation() {
for (int i = 0; i < 10; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h1 = g.toCached();
final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.CACHED);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
Assert.assertThat(
h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.CACHED));
Assert.assertThat(h1, IsEqual.equalTo(g));
Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getY().add(g.getX())));
Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().subtract(g.getX())));
Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ()));
Assert.assertThat(h1.getT(), IsEqual.equalTo(g.getT().multiply(curve.get2D())));
}
}
// endregion
/** Test method for {@link GroupElement#precompute(boolean)}. */
@Test
public void testPrecompute() {
GroupElement B = ed25519.getB();
assertThat(B.precmp, is(equalTo(PrecomputationTestVectors.testPrecmp)));
assertThat(B.dblPrecmp, is(equalTo(PrecomputationTestVectors.testDblPrecmp)));
}
@Test
public void precomputedTableContainsExpectedGroupElements() {
// Arrange:
GroupElement g = ed25519.getB();
// Act + Assert:
for (int i = 0; i < 32; i++) {
GroupElement h = g;
for (int j = 0; j < 8; j++) {
Assert.assertThat(
MathUtils.toRepresentation(h, GroupElement.Representation.PRECOMP),
IsEqual.equalTo(ed25519.getB().precmp[i][j]));
h = MathUtils.addGroupElements(h, g);
}
for (int k = 0; k < 8; k++) {
g = MathUtils.addGroupElements(g, g);
}
}
}
@Test
public void dblPrecomputedTableContainsExpectedGroupElements() {
// Arrange:
GroupElement g = ed25519.getB();
GroupElement h = MathUtils.addGroupElements(g, g);
// Act + Assert:
for (int i = 0; i < 8; i++) {
Assert.assertThat(
MathUtils.toRepresentation(g, GroupElement.Representation.PRECOMP),
IsEqual.equalTo(ed25519.getB().dblPrecmp[i]));
g = MathUtils.addGroupElements(g, h);
}
}
/** Test method for {@link GroupElement#dbl()}. */
@Test
public void testDbl() {
GroupElement B = ed25519.getB();
// 2 * B = B + B
assertThat(B.dbl(), is(equalTo(B.add(B.toCached()))));
}
@Test
public void dblReturnsExpectedResult() {
for (int i = 0; i < 1000; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h1 = g.dbl();
final GroupElement h2 = MathUtils.doubleGroupElement(g);
// Assert:
Assert.assertThat(h2, IsEqual.equalTo(h1));
}
}
@Test
public void addingNeutralGroupElementDoesNotChangeGroupElement() {
final GroupElement neutral =
GroupElement.p3(
curve,
curve.getField().ZERO,
curve.getField().ONE,
curve.getField().ONE,
curve.getField().ZERO);
for (int i = 0; i < 1000; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h1 = g.add(neutral.toCached());
final GroupElement h2 = neutral.add(g.toCached());
// Assert:
Assert.assertThat(g, IsEqual.equalTo(h1));
Assert.assertThat(g, IsEqual.equalTo(h2));
}
}
@Test
public void addReturnsExpectedResult() {
for (int i = 0; i < 1000; i++) {
// Arrange:
final GroupElement g1 = MathUtils.getRandomGroupElement();
final GroupElement g2 = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h1 = g1.add(g2.toCached());
final GroupElement h2 = MathUtils.addGroupElements(g1, g2);
// Assert:
Assert.assertThat(h2, IsEqual.equalTo(h1));
}
}
@Test
public void subReturnsExpectedResult() {
for (int i = 0; i < 1000; i++) {
// Arrange:
final GroupElement g1 = MathUtils.getRandomGroupElement();
final GroupElement g2 = MathUtils.getRandomGroupElement();
// Act:
final GroupElement h1 = g1.sub(g2.toCached());
final GroupElement h2 = MathUtils.addGroupElements(g1, MathUtils.negateGroupElement(g2));
// Assert:
Assert.assertThat(h2, IsEqual.equalTo(h1));
}
}
// region hashCode / equals
/** Test method for {@link GroupElement#equals(java.lang.Object)}. */
@Test
public void testEqualsObject() {
assertThat(GroupElement.p2(curve, ZERO, ONE, ONE), is(equalTo(P2_ZERO)));
}
@Test
public void equalsOnlyReturnsTrueForEquivalentObjects() {
// Arrange:
final GroupElement g1 = MathUtils.getRandomGroupElement();
final GroupElement g2 = MathUtils.toRepresentation(g1, GroupElement.Representation.P2);
final GroupElement g3 = MathUtils.toRepresentation(g1, GroupElement.Representation.CACHED);
final GroupElement g4 = MathUtils.toRepresentation(g1, GroupElement.Representation.P1P1);
final GroupElement g5 = MathUtils.getRandomGroupElement();
// Assert
Assert.assertThat(g2, IsEqual.equalTo(g1));
Assert.assertThat(g3, IsEqual.equalTo(g1));
Assert.assertThat(g1, IsEqual.equalTo(g4));
Assert.assertThat(g1, IsNot.not(IsEqual.equalTo(g5)));
Assert.assertThat(g2, IsNot.not(IsEqual.equalTo(g5)));
Assert.assertThat(g3, IsNot.not(IsEqual.equalTo(g5)));
Assert.assertThat(g5, IsNot.not(IsEqual.equalTo(g4)));
}
@Test
public void hashCodesAreEqualForEquivalentObjects() {
// Arrange:
final GroupElement g1 = MathUtils.getRandomGroupElement();
final GroupElement g2 = MathUtils.toRepresentation(g1, GroupElement.Representation.P2);
final GroupElement g3 = MathUtils.toRepresentation(g1, GroupElement.Representation.P1P1);
final GroupElement g4 = MathUtils.getRandomGroupElement();
// Assert
Assert.assertThat(g2.hashCode(), IsEqual.equalTo(g1.hashCode()));
Assert.assertThat(g3.hashCode(), IsEqual.equalTo(g1.hashCode()));
Assert.assertThat(g1.hashCode(), IsNot.not(IsEqual.equalTo(g4.hashCode())));
Assert.assertThat(g2.hashCode(), IsNot.not(IsEqual.equalTo(g4.hashCode())));
Assert.assertThat(g3.hashCode(), IsNot.not(IsEqual.equalTo(g4.hashCode())));
}
// endregion
static final byte[] BYTES_ZERO =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
static final byte[] BYTES_ONE =
Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000");
static final byte[] BYTES_42 =
Utils.hexToBytes("2A00000000000000000000000000000000000000000000000000000000000000");
static final byte[] BYTES_1234567890 =
Utils.hexToBytes("D202964900000000000000000000000000000000000000000000000000000000");
static final byte[] RADIX16_ZERO =
Utils.hexToBytes(
"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
static final byte[] RADIX16_ONE =
Utils.hexToBytes(
"01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
static final byte[] RADIX16_42 =
Utils.hexToBytes(
"FA030000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
/** Test method for {@link GroupElement#toRadix16(byte[])}. */
@Test
public void testToRadix16() {
assertThat(GroupElement.toRadix16(BYTES_ZERO), is(RADIX16_ZERO));
assertThat(GroupElement.toRadix16(BYTES_ONE), is(RADIX16_ONE));
assertThat(GroupElement.toRadix16(BYTES_42), is(RADIX16_42));
byte[] from1234567890 = GroupElement.toRadix16(BYTES_1234567890);
int total = 0;
for (int i = 0; i < from1234567890.length; i++) {
assertThat(from1234567890[i], is(greaterThanOrEqualTo((byte) -8)));
assertThat(from1234567890[i], is(lessThanOrEqualTo((byte) 8)));
total += from1234567890[i] * Math.pow(16, i);
}
assertThat(total, is(1234567890));
byte[] pkrR16 = GroupElement.toRadix16(BYTES_PKR);
for (int i = 0; i < pkrR16.length; i++) {
assertThat(pkrR16[i], is(greaterThanOrEqualTo((byte) -8)));
assertThat(pkrR16[i], is(lessThanOrEqualTo((byte) 8)));
}
}
/** Test method for {@link GroupElement#cmov(GroupElement, int)}. */
@Test
public void testCmov() {
GroupElement a = curve.getZero(GroupElement.Representation.PRECOMP);
GroupElement b = GroupElement.precomp(curve, TWO, ZERO, TEN);
assertThat(a.cmov(b, 0), is(equalTo(a)));
assertThat(a.cmov(b, 1), is(equalTo(b)));
}
/** Test method for {@link GroupElement#select(int, int)}. */
@Test
public void testSelect() {
GroupElement B = ed25519.getB();
for (int i = 0; i < 32; i++) {
// 16^i 0 B
assertThat(
i + ",0", B.select(i, 0), is(equalTo(GroupElement.precomp(curve, ONE, ONE, ZERO))));
for (int j = 1; j < 8; j++) {
// 16^i r_i B
GroupElement t = B.select(i, j);
assertThat(i + "," + j, t, is(equalTo(B.precmp[i][j - 1])));
// -16^i r_i B
t = B.select(i, -j);
GroupElement neg =
GroupElement.precomp(
curve, B.precmp[i][j - 1].Y, B.precmp[i][j - 1].X, B.precmp[i][j - 1].Z.negate());
assertThat(i + "," + -j, t, is(equalTo(neg)));
}
}
}
// region scalar multiplication
/**
* Test method for {@link GroupElement#scalarMultiply(byte[])}. Test values generated with Python
* Ed25519 implementation.
*/
@Test
public void testScalarMultiplyByteArray() {
// Little-endian
byte[] zero =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
byte[] one =
Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000");
byte[] two =
Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000");
byte[] a = Utils.hexToBytes("d072f8dd9c07fa7bc8d22a4b325d26301ee9202f6db89aa7c3731529e37e437c");
GroupElement A =
new GroupElement(
curve,
Utils.hexToBytes("d4cf8595571830644bd14af416954d09ab7159751ad9e0f7a6cbd92379e71a66"));
assertThat(
"scalarMultiply(0) failed",
ed25519.getB().scalarMultiply(zero),
is(equalTo(curve.getZero(GroupElement.Representation.P3))));
assertThat(
"scalarMultiply(1) failed",
ed25519.getB().scalarMultiply(one),
is(equalTo(ed25519.getB())));
assertThat(
"scalarMultiply(2) failed",
ed25519.getB().scalarMultiply(two),
is(equalTo(ed25519.getB().dbl())));
assertThat("scalarMultiply(a) failed", ed25519.getB().scalarMultiply(a), is(equalTo(A)));
}
@Test
public void scalarMultiplyBasePointWithZeroReturnsNeutralElement() {
// Arrange:
final GroupElement basePoint = ed25519.getB();
// Act:
final GroupElement g = basePoint.scalarMultiply(curve.getField().ZERO.toByteArray());
// Assert:
Assert.assertThat(curve.getZero(GroupElement.Representation.P3), IsEqual.equalTo(g));
}
@Test
public void scalarMultiplyBasePointWithOneReturnsBasePoint() {
// Arrange:
final GroupElement basePoint = ed25519.getB();
// Act:
final GroupElement g = basePoint.scalarMultiply(curve.getField().ONE.toByteArray());
// Assert:
Assert.assertThat(basePoint, IsEqual.equalTo(g));
}
// This test is slow (~6s) due to math utils using an inferior algorithm to calculate the result.
@Test
public void scalarMultiplyBasePointReturnsExpectedResult() {
for (int i = 0; i < 100; i++) {
// Arrange:
final GroupElement basePoint = ed25519.getB();
final FieldElement f = MathUtils.getRandomFieldElement();
// Act:
final GroupElement g = basePoint.scalarMultiply(f.toByteArray());
final GroupElement h = MathUtils.scalarMultiplyGroupElement(basePoint, f);
// Assert:
Assert.assertThat(g, IsEqual.equalTo(h));
}
}
@Test
public void testDoubleScalarMultiplyVariableTime() {
// Little-endian
byte[] zero =
Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000");
byte[] one =
Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000");
byte[] two =
Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000");
byte[] a = Utils.hexToBytes("d072f8dd9c07fa7bc8d22a4b325d26301ee9202f6db89aa7c3731529e37e437c");
GroupElement A =
new GroupElement(
curve,
Utils.hexToBytes("d4cf8595571830644bd14af416954d09ab7159751ad9e0f7a6cbd92379e71a66"));
GroupElement B = ed25519.getB();
GroupElement geZero = curve.getZero(GroupElement.Representation.P3);
geZero.precompute(false);
// 0 * GE(0) + 0 * GE(0) = GE(0)
assertThat(geZero.doubleScalarMultiplyVariableTime(geZero, zero, zero), is(equalTo(geZero)));
// 0 * GE(0) + 0 * B = GE(0)
assertThat(B.doubleScalarMultiplyVariableTime(geZero, zero, zero), is(equalTo(geZero)));
// 1 * GE(0) + 0 * B = GE(0)
assertThat(B.doubleScalarMultiplyVariableTime(geZero, one, zero), is(equalTo(geZero)));
// 1 * GE(0) + 1 * B = B
assertThat(B.doubleScalarMultiplyVariableTime(geZero, one, one), is(equalTo(B)));
// 1 * B + 1 * B = 2 * B
assertThat(B.doubleScalarMultiplyVariableTime(B, one, one), is(equalTo(B.dbl())));
// 1 * B + 2 * B = 3 * B
assertThat(
B.doubleScalarMultiplyVariableTime(B, one, two),
is(equalTo(B.dbl().toP3().add(B.toCached()))));
// 2 * B + 2 * B = 4 * B
assertThat(B.doubleScalarMultiplyVariableTime(B, two, two), is(equalTo(B.dbl().toP3().dbl())));
// 0 * B + a * B = A
assertThat(B.doubleScalarMultiplyVariableTime(B, zero, a), is(equalTo(A)));
// a * B + 0 * B = A
assertThat(B.doubleScalarMultiplyVariableTime(B, a, zero), is(equalTo(A)));
// a * B + a * B = 2 * A
assertThat(B.doubleScalarMultiplyVariableTime(B, a, a), is(equalTo(A.dbl())));
}
// This test is slow (~6s) due to math utils using an inferior algorithm to calculate the result.
@Test
public void doubleScalarMultiplyVariableTimeReturnsExpectedResult() {
for (int i = 0; i < 50; i++) {
// Arrange:
final GroupElement basePoint = ed25519.getB();
final GroupElement g = MathUtils.getRandomGroupElement();
g.precompute(false);
final FieldElement f1 = MathUtils.getRandomFieldElement();
final FieldElement f2 = MathUtils.getRandomFieldElement();
// Act:
final GroupElement h1 =
basePoint.doubleScalarMultiplyVariableTime(g, f2.toByteArray(), f1.toByteArray());
final GroupElement h2 = MathUtils.doubleScalarMultiplyGroupElements(basePoint, f1, g, f2);
// Assert:
Assert.assertThat(h1, IsEqual.equalTo(h2));
}
}
// endregion
/** Test method for {@link GroupElement#isOnCurve(Curve)}. */
@Test
public void testIsOnCurve() {
assertThat(P2_ZERO.isOnCurve(curve), is(true));
assertThat(GroupElement.p2(curve, ZERO, ZERO, ONE).isOnCurve(curve), is(false));
assertThat(GroupElement.p2(curve, ONE, ONE, ONE).isOnCurve(curve), is(false));
assertThat(GroupElement.p2(curve, TEN, ZERO, ONE).isOnCurve(curve), is(false));
assertThat(GroupElement.p2(curve, ONE, TEN, ONE).isOnCurve(curve), is(false));
assertThat(GroupElement.p2(curve, PKR[0], PKR[1], ONE).isOnCurve(curve), is(true));
}
@Test
public void isOnCurveReturnsTrueForPointsOnTheCurve() {
for (int i = 0; i < 100; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
// Assert:
Assert.assertThat(g.isOnCurve(), IsEqual.equalTo(true));
}
}
@Test
public void isOnCurveReturnsFalseForPointsNotOnTheCurve() {
for (int i = 0; i < 100; i++) {
// Arrange:
final GroupElement g = MathUtils.getRandomGroupElement();
final GroupElement h =
GroupElement.p2(curve, g.getX(), g.getY(), g.getZ().multiply(curve.getField().TWO));
// Assert (can only fail for 5*Z^2=1):
Assert.assertThat(h.isOnCurve(), IsEqual.equalTo(false));
}
}
}