@Test(expected = IllegalArgumentException.class)
public void toCachedThrowsIfGroupElementHasP1P1Representation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1);
// Assert:
g.toCached();
}
@Test(expected = IllegalArgumentException.class)
public void toP3ThrowsIfGroupElementHasPrecompRepresentation() {
// Arrange:
final GroupElement g =
MathUtils.toRepresentation(
MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP);
// Assert:
g.toP3();
}
@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 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 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 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())));
}
// 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 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
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));
}
}
@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 dIsAsExpected() {
// Arrange:
final BigInteger D =
new BigInteger(
"37095705934669439343138083508754565189542113879843219016388785533085940283555");
// Assert:
Assert.assertThat(D, IsEqual.equalTo(MathUtils.toBigInteger(Ed25519Field.D)));
}
@Test
public void dTimesTwoIsAsExpected() {
// Arrange:
final BigInteger DTimesTwo =
new BigInteger(
"16295367250680780974490674513165176452449235426866156013048779062215315747161");
// Assert:
Assert.assertThat(DTimesTwo, IsEqual.equalTo(MathUtils.toBigInteger(Ed25519Field.D_Times_TWO)));
}
// 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 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 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 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 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));
}
}
@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())));
}
}
@Test
public void iIsAsExpected() {
// Arrange:
final BigInteger I =
new BigInteger(
"19681161376707505956807079304988542015446066515923890162744021073123829784752");
// Assert (i^2 == -1):
Assert.assertThat(I, IsEqual.equalTo(MathUtils.toBigInteger(Ed25519Field.I)));
Assert.assertThat(
I.multiply(I).mod(Ed25519Field.P),
IsEqual.equalTo(BigInteger.ONE.shiftLeft(255).subtract(new BigInteger("20"))));
}
@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 twoIsAsExpected() {
// Assert:
Assert.assertThat(
new BigInteger("2"), IsEqual.equalTo(MathUtils.toBigInteger(Ed25519Field.TWO)));
}
@Test
public void oneIsAsExpected() {
// Assert:
Assert.assertThat(BigInteger.ONE, IsEqual.equalTo(MathUtils.toBigInteger(Ed25519Field.ONE)));
}
@Test
public void zeroIsAsExpected() {
// Assert:
Assert.assertThat(BigInteger.ZERO, IsEqual.equalTo(MathUtils.toBigInteger(Ed25519Field.ZERO)));
}