def test_orders(self):
# the point (0,1) is the identity, and has order 1
p0 = xform_affine_to_extended((0,1))
# p0+p0=p0
# p0+anything=anything
# The point (0,-1) has order 2
p2 = xform_affine_to_extended((0,-1))
p3 = add_elements(p2, p2) # p3=p2+p2=p0
p4 = add_elements(p3, p2) # p4=p3+p2=p2
p5 = add_elements(p4, p2) # p5=p4+p2=p0
self.assertBytesEqual(encodepoint(xform_extended_to_affine(p3)),
encodepoint(xform_extended_to_affine(p0)))
self.assertBytesEqual(encodepoint(xform_extended_to_affine(p4)),
encodepoint(xform_extended_to_affine(p2)))
self.assertBytesEqual(encodepoint(xform_extended_to_affine(p5)),
encodepoint(xform_extended_to_affine(p0)))
# now same thing, but with Element
p0 = ElementOfUnknownGroup(xform_affine_to_extended((0,1)))
self.assertElementsEqual(p0, Zero)
p2 = ElementOfUnknownGroup(xform_affine_to_extended((0,-1)))
p3 = p2.add(p2)
p4 = p3.add(p2)
p5 = p4.add(p2)
self.assertElementsEqual(p3, p0)
self.assertElementsEqual(p4, p2)
self.assertElementsEqual(p5, p0)
self.assertFalse(isinstance(p3, Element))
self.assertFalse(isinstance(p4, Element))
self.assertFalse(isinstance(p5, Element))
# and again, with .scalarmult instead of .add
p3 = p2.scalarmult(2) # p3=2*p2=p0
p4 = p2.scalarmult(3) # p4=3*p2=p2
p5 = p2.scalarmult(4) # p5=4*p2=p0
self.assertElementsEqual(p3, p0) # TODO: failing
self.assertElementsEqual(p4, p2)
self.assertElementsEqual(p5, p0)
self.assertFalse(isinstance(p3, Element))
self.assertFalse(isinstance(p4, Element))
self.assertFalse(isinstance(p5, Element))
def test_orders(self):
# all points should have an order that's listed in ORDERS. Test some
# specific points. For low-order points, actually find the complete
# subgroup and measure its size.
p = Zero
values = self.collect(p)
self.assertEqual(len(values), 1)
self.assertEqual(values, set([Zero.to_bytes()]))
self.assertEqual(get_order(p), 1)
# (0,-1) should be order 2
p = ElementOfUnknownGroup(xform_affine_to_extended((0,-1)))
values = self.collect(p)
self.assertEqual(len(values), 2)
self.assertEqual(values, set([Zero.to_bytes(), p.to_bytes()]))
self.assertEqual(get_order(p), 2)
# (..,26) is in the right group (order L)
b = b"\x1a" + b"\x00"*31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), L)
# (..,35) is maybe order 2*L
b = b"\x23" + b"\x00"*31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), 2*L)
# (..,48) is maybe order 4*L
b = b"\x30" + b"\x00"*31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), 4*L)
# (..,55) is maybe order 8*L
b = b"\x37" + b"\x00"*31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), 8*L)
def test_orders(self):
# all points should have an order that's listed in ORDERS. Test some
# specific points. For low-order points, actually find the complete
# subgroup and measure its size.
p = Zero
values = self.collect(p)
self.assertEqual(len(values), 1)
self.assertEqual(values, set([Zero.to_bytes()]))
self.assertEqual(get_order(p), 1)
# (0,-1) should be order 2
p = ElementOfUnknownGroup(xform_affine_to_extended((0, -1)))
values = self.collect(p)
self.assertEqual(len(values), 2)
self.assertEqual(values, set([Zero.to_bytes(), p.to_bytes()]))
self.assertEqual(get_order(p), 2)
# (..,26) is in the right group (order L)
b = b"\x1a" + b"\x00" * 31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), L)
# (..,35) is maybe order 2*L
b = b"\x23" + b"\x00" * 31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), 2 * L)
# (..,48) is maybe order 4*L
b = b"\x30" + b"\x00" * 31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), 4 * L)
# (..,55) is maybe order 8*L
b = b"\x37" + b"\x00" * 31
p = bytes_to_unknown_group_element(b)
self.assertEqual(get_order(p), 8 * L)
def test_orders(self):
# the point (0,1) is the identity, and has order 1
p0 = xform_affine_to_extended((0, 1))
# p0+p0=p0
# p0+anything=anything
# The point (0,-1) has order 2
p2 = xform_affine_to_extended((0, -1))
p3 = add_elements(p2, p2) # p3=p2+p2=p0
p4 = add_elements(p3, p2) # p4=p3+p2=p2
p5 = add_elements(p4, p2) # p5=p4+p2=p0
self.assertBytesEqual(
encodepoint(xform_extended_to_affine(p3)),
encodepoint(xform_extended_to_affine(p0)),
)
self.assertBytesEqual(
encodepoint(xform_extended_to_affine(p4)),
encodepoint(xform_extended_to_affine(p2)),
)
self.assertBytesEqual(
encodepoint(xform_extended_to_affine(p5)),
encodepoint(xform_extended_to_affine(p0)),
)
# now same thing, but with Element
p0 = ElementOfUnknownGroup(xform_affine_to_extended((0, 1)))
self.assertElementsEqual(p0, Zero)
p2 = ElementOfUnknownGroup(xform_affine_to_extended((0, -1)))
p3 = p2.add(p2)
p4 = p3.add(p2)
p5 = p4.add(p2)
self.assertElementsEqual(p3, p0)
self.assertElementsEqual(p4, p2)
self.assertElementsEqual(p5, p0)
self.assertFalse(isinstance(p3, Element))
self.assertFalse(isinstance(p4, Element))
self.assertFalse(isinstance(p5, Element))
# and again, with .scalarmult instead of .add
p3 = p2.scalarmult(2) # p3=2*p2=p0
p4 = p2.scalarmult(3) # p4=3*p2=p2
p5 = p2.scalarmult(4) # p5=4*p2=p0
self.assertElementsEqual(p3, p0) # TODO: failing
self.assertElementsEqual(p4, p2)
self.assertElementsEqual(p5, p0)
self.assertFalse(isinstance(p3, Element))
self.assertFalse(isinstance(p4, Element))
self.assertFalse(isinstance(p5, Element))