def test_add(self): e = [] for i in range(100): seed = str(i).encode("ascii") s = password_to_scalar(seed) e.append(Base.scalarmult(s)) for i in range(100): x = random.choice(e) y = random.choice(e) sum1 = element_from_affine( slow_add_affine(xform_extended_to_affine(x.XYTZ), xform_extended_to_affine(y.XYTZ))) sum2 = x.add(y) self.assertElementsEqual(sum1, sum2) if x != y: sum3 = Element(_add_elements_nonunfied(x.XYTZ, y.XYTZ)) self.assertElementsEqual(sum1, sum3)
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))
def test_encodepoint(self): for i in range(200): P = basic.xform_extended_to_affine(basic.Base.scalarmult(i).XYTZ) self.assertEqual(self.orig_encodepoint(P), self.new_encodepoint(P))
def scalarmult_affine(pt, e): # affine->affine e = e % L return xform_extended_to_affine(scalarmult_element(xform_affine_to_extended(pt), e))
def scalarmult_affine(pt, e): # affine->affine e = e % L return xform_extended_to_affine( scalarmult_element( xform_affine_to_extended(pt), e))