@Test(expected = IllegalArgumentException.class)
public void toCachedThrowsIfGroupElementHasP1P1Representation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1);
// Assert:
g.toCached();
}
@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 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));
}
}
@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
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())));
}
}
@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 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()))));
}