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):
# 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))
