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from unittest import TestCase
from pyecsca.ec.curve import EllipticCurve
from pyecsca.ec.mod import Mod
from pyecsca.ec.model import ShortWeierstrassModel, MontgomeryModel
from pyecsca.ec.mult import (LTRMultiplier, RTLMultiplier, LadderMultiplier, BinaryNAFMultiplier,
WindowNAFMultiplier, SimpleLadderMultiplier, CoronMultiplier)
from pyecsca.ec.point import Point
class ScalarMultiplierTests(TestCase):
def setUp(self):
self.p = 0xfffffffdffffffffffffffffffffffff
self.coords = ShortWeierstrassModel().coordinates["projective"]
self.base = Point(self.coords, X=Mod(0x161ff7528b899b2d0c28607ca52c5b86, self.p),
Y=Mod(0xcf5ac8395bafeb13c02da292dded7a83, self.p),
Z=Mod(1, self.p))
self.secp128r1 = EllipticCurve(ShortWeierstrassModel(), self.coords,
dict(a=0xfffffffdfffffffffffffffffffffffc,
b=0xe87579c11079f43dd824993c2cee5ed3),
Point(self.coords, X=Mod(0, self.p), Y=Mod(1, self.p),
Z=Mod(0, self.p)))
self.coords25519 = MontgomeryModel().coordinates["xz"]
self.p25519 = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed
self.base25519 = Point(self.coords25519, X=Mod(9, self.p25519),
Z=Mod(1, self.p25519))
self.curve25519 = EllipticCurve(MontgomeryModel(), self.coords25519,
dict(a=486662, b=1),
Point(self.coords25519,
X=Mod(0, self.p25519), Z=Mod(1, self.p25519)))
def test_rtl(self):
mult = RTLMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertEqual(res, other)
def test_ltr(self):
mult = LTRMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertEqual(res, other)
def test_coron(self):
mult = CoronMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertEqual(res, other)
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)
def test_simple_ladder(self):
mult = SimpleLadderMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["z"])
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertEqual(res, other)
def test_ladder_differential(self):
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(15, self.base25519)
res_differential = differential.multiply(15, self.base25519)
self.assertEqual(res_ladder, res_differential)
def test_binary_naf(self):
mult = BinaryNAFMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["neg"], self.coords.formulas["z"])
res = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertEqual(res, other)
def test_window_naf(self):
mult = 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 = mult.multiply(10, self.base)
other = mult.multiply(5, self.base)
other = mult.multiply(2, other)
self.assertEqual(res, other)
mult = WindowNAFMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"],
self.coords.formulas["neg"], 3, self.coords.formulas["z"],
precompute_negation=True)
res_precompute = mult.multiply(10, self.base)
self.assertEqual(res_precompute, res)
def test_basic_multipliers(self):
ltr = LTRMultiplier(self.secp128r1, self.coords.formulas["add-1998-cmo"],
self.coords.formulas["dbl-1998-cmo"], self.coords.formulas["z"])
res_ltr = ltr.multiply(10, 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(10, 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(10, self.base)
res_rtl_always = rtl_always.multiply(10, 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(10, 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(10, 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(10, 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(10, self.base)
self.assertEqual(res_coron, res_ltr)
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