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from unittest import TestCase
from parameterized import parameterized
from pyecsca.ec.curves import get_curve
from pyecsca.ec.mult import (LTRMultiplier, RTLMultiplier, LadderMultiplier, BinaryNAFMultiplier,
WindowNAFMultiplier, SimpleLadderMultiplier, CoronMultiplier)
from pyecsca.ec.point import InfinityPoint
class ScalarMultiplierTests(TestCase):
def setUp(self):
self.secp128r1 = get_curve("secp128r1", "projective")
self.base = self.secp128r1.generator
self.coords = self.secp128r1.curve.coordinate_model
self.curve25519 = get_curve("curve25519", "xz")
self.base25519 = self.curve25519.generator
self.coords25519 = self.curve25519.curve.coordinate_model
def get_formulas(self, coords, *names):
return [coords.formulas[name] for name in names if name is not None]
def assertPointEquality(self, one, other, scale):
if scale:
self.assertEqual(one, other)
else:
assert one.equals(other)
@parameterized.expand([
("scaled", "add-1998-cmo", "dbl-1998-cmo", "z"),
("none", "add-1998-cmo", "dbl-1998-cmo", None)
])
def test_rtl(self, name, add, dbl, scale):
mult = RTLMultiplier(self.secp128r1, *self.get_formulas(self.coords, add, dbl, scale))
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertPointEquality(res, other, scale)
self.assertEqual(InfinityPoint(self.coords), mult.multiply(0, self.base))
@parameterized.expand([
("scaled", "add-1998-cmo", "dbl-1998-cmo", "z"),
("none", "add-1998-cmo", "dbl-1998-cmo", None)
])
def test_ltr(self, name, add, dbl, scale):
mult = LTRMultiplier(self.secp128r1, *self.get_formulas(self.coords, add, dbl, scale))
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertPointEquality(res, other, scale)
self.assertEqual(InfinityPoint(self.coords), mult.multiply(0, self.base))
@parameterized.expand([
("scaled", "add-1998-cmo", "dbl-1998-cmo", "z"),
("none", "add-1998-cmo", "dbl-1998-cmo", None)
])
def test_coron(self, name, add, dbl, scale):
mult = CoronMultiplier(self.secp128r1, *self.get_formulas(self.coords, add, dbl, scale))
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertPointEquality(res, other, scale)
self.assertEqual(InfinityPoint(self.coords), mult.multiply(0, self.base))
def test_ladder(self):
mult = LadderMultiplier(self.curve25519, self.coords25519.formulas["ladd-1987-m"],
self.coords25519.formulas["dbl-1987-m"],
self.coords25519.formulas["scale"])
res = mult.multiply(15, self.base25519)
other = mult.multiply(5, self.base25519)
other = mult.multiply(3, other)
self.assertEqual(res, other)
self.assertEqual(InfinityPoint(self.coords25519), mult.multiply(0, self.base25519))
@parameterized.expand([
("scaled", "add-1998-cmo", "dbl-1998-cmo", "z"),
("none", "add-1998-cmo", "dbl-1998-cmo", None)
])
def test_simple_ladder(self, name, add, dbl, scale):
mult = SimpleLadderMultiplier(self.secp128r1,
*self.get_formulas(self.coords, add, dbl, scale))
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertPointEquality(res, other, scale)
self.assertEqual(InfinityPoint(self.coords), mult.multiply(0, self.base))
@parameterized.expand([
("10", 15),
("2355498743", 2355498743,)
])
def test_ladder_differential(self, name, num):
ladder = LadderMultiplier(self.curve25519, self.coords25519.formulas["ladd-1987-m"],
self.coords25519.formulas["dbl-1987-m"],
self.coords25519.formulas["scale"])
differential = SimpleLadderMultiplier(self.curve25519,
self.coords25519.formulas["dadd-1987-m"],
self.coords25519.formulas["dbl-1987-m"],
self.coords25519.formulas["scale"])
res_ladder = ladder.multiply(num, self.base25519)
res_differential = differential.multiply(num, self.base25519)
self.assertEqual(res_ladder, res_differential)
self.assertEqual(InfinityPoint(self.coords25519), differential.multiply(0, self.base25519))
@parameterized.expand([
("scaled", "add-1998-cmo", "dbl-1998-cmo", "neg", "z"),
("none", "add-1998-cmo", "dbl-1998-cmo", "neg", None)
])
def test_binary_naf(self, name, add, dbl, neg, scale):
mult = BinaryNAFMultiplier(self.secp128r1,
*self.get_formulas(self.coords, add, dbl, neg, scale))
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertPointEquality(res, other, scale)
self.assertEqual(InfinityPoint(self.coords), mult.multiply(0, self.base))
@parameterized.expand([
("scaled3", "add-1998-cmo", "dbl-1998-cmo", "neg", 3, "z"),
("none3", "add-1998-cmo", "dbl-1998-cmo", "neg", 3, None)
])
def test_window_naf(self, name, add, dbl, neg, width, scale):
formulas = self.get_formulas(self.coords, add, dbl, neg, scale)
mult = WindowNAFMultiplier(self.secp128r1, *formulas[:3], width, *formulas[3:])
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertPointEquality(res, other, scale)
self.assertEqual(InfinityPoint(self.coords), mult.multiply(0, self.base))
mult = WindowNAFMultiplier(self.secp128r1, *formulas[:3], width, *formulas[3:],
precompute_negation=True)
res_precompute = mult.multiply(10, self.base)
self.assertPointEquality(res_precompute, res, scale)
@parameterized.expand([
("10", 10),
("2355498743", 2355498743,)
])
def test_basic_multipliers(self, name, num):
ltr = LTRMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
res_ltr = ltr.multiply(num, self.base)
rtl = RTLMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
res_rtl = rtl.multiply(num, self.base)
self.assertEqual(res_ltr, res_rtl)
ltr_always = LTRMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"],
always=True)
rtl_always = RTLMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"],
always=True)
res_ltr_always = ltr_always.multiply(num, self.base)
res_rtl_always = rtl_always.multiply(num, self.base)
self.assertEqual(res_ltr, res_ltr_always)
self.assertEqual(res_rtl, res_rtl_always)
bnaf = BinaryNAFMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["neg"], self.coords.formulas["z"])
res_bnaf = bnaf.multiply(num, self.base)
self.assertEqual(res_bnaf, res_ltr)
wnaf = WindowNAFMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["neg"], 3, self.coords.formulas["z"])
res_wnaf = wnaf.multiply(num, self.base)
self.assertEqual(res_wnaf, res_ltr)
ladder = SimpleLadderMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["z"])
res_ladder = ladder.multiply(num, self.base)
self.assertEqual(res_ladder, res_ltr)
coron = CoronMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["z"])
res_coron = coron.multiply(num, self.base)
self.assertEqual(res_coron, res_ltr)
def test_init_fail(self):
with self.assertRaises(ValueError):
SimpleLadderMultiplier(self.secp128r1,
self.coords25519.formulas["dadd-1987-m"],
self.coords25519.formulas["dbl-1987-m"],
self.coords25519.formulas["scale"])
def test_mult_fail(self):
mult = LTRMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
with self.assertRaises(ValueError):
mult.multiply(15)
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