@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)));
}