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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
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_ladder(self):
mult = LadderMultiplier(self.curve25519, self.coords25519.formulas["ladd-1987-m"],
self.coords25519.formulas["scale"])
res = mult.multiply(15, self.base25519)
other = mult.multiply(3, self.base25519)
other = mult.multiply(5, 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_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)
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)
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