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from functools import partial
from math import isqrt
import pytest
from pyecsca.ec.context import local
from pyecsca.ec.curve import EllipticCurve
from pyecsca.ec.mod import mod
from pyecsca.ec.model import ShortWeierstrassModel
from pyecsca.ec.mult import (
LTRMultiplier,
RTLMultiplier,
BinaryNAFMultiplier,
WindowNAFMultiplier,
SimpleLadderMultiplier,
AccumulationOrder,
ProcessingDirection,
SlidingWindowMultiplier,
FixedWindowLTRMultiplier,
FullPrecompMultiplier,
BGMWMultiplier,
CombMultiplier,
WindowBoothMultiplier,
LadderMultiplier,
DifferentialLadderMultiplier,
)
from pyecsca.ec.params import DomainParameters
from pyecsca.ec.point import Point
from pyecsca.sca.re.rpa import (
MultipleContext,
rpa_point_0y,
rpa_point_x0,
rpa_distinguish,
multiples_computed,
)
@pytest.fixture()
def model():
return ShortWeierstrassModel()
@pytest.fixture()
def coords(model):
return model.coordinates["projective"]
@pytest.fixture()
def add(coords):
return coords.formulas["add-2007-bl"]
@pytest.fixture()
def dbl(coords):
return coords.formulas["dbl-2007-bl"]
@pytest.fixture()
def neg(coords):
return coords.formulas["neg"]
@pytest.fixture()
def rpa_params(model, coords):
p = 0x85D265945A4F5681
a = mod(0x7FC57B4110698BC0, p)
b = mod(0x37113EA591B04527, p)
gx = mod(0x80D2D78FDDB97597, p)
gy = mod(0x5586D818B7910930, p)
infty = Point(coords, X=mod(0, p), Y=mod(1, p), Z=mod(0, p))
g = Point(coords, X=gx, Y=gy, Z=mod(1, p))
curve = EllipticCurve(model, coords, p, infty, dict(a=a, b=b))
return DomainParameters(curve, g, 0x85D265932D90785C, 1)
def test_multiples(rpa_params):
multiples = multiples_computed(
17, rpa_params, LTRMultiplier, LTRMultiplier, True, True
)
assert 1 in multiples
assert 17 in multiples
assert 0 not in multiples
def test_multiples_kind(rpa_params):
multiples_all = multiples_computed(
17, rpa_params, RTLMultiplier, RTLMultiplier, True, True,
kind="all"
)
multiples_input = multiples_computed(
17, rpa_params, RTLMultiplier, RTLMultiplier, True, True,
kind="input"
)
multiples_necessary = multiples_computed(
17, rpa_params, RTLMultiplier, RTLMultiplier, True, True,
kind="necessary"
)
multiples_precomp = multiples_computed(
17, rpa_params, RTLMultiplier, RTLMultiplier, True, True,
kind="precomp+necessary"
)
assert multiples_all != multiples_input
assert multiples_all != multiples_necessary
assert multiples_input != multiples_necessary
assert multiples_precomp == multiples_necessary
wnaf = partial(WindowNAFMultiplier, width=4)
multiples_all = multiples_computed(
0xff, rpa_params, WindowNAFMultiplier, wnaf, True, True,
kind="all"
)
multiples_input = multiples_computed(
0xff, rpa_params, WindowNAFMultiplier, wnaf, True, True,
kind="input"
)
multiples_necessary = multiples_computed(
0xff, rpa_params, WindowNAFMultiplier, wnaf, True, True,
kind="necessary"
)
multiples_precomp = multiples_computed(
0xff, rpa_params, WindowNAFMultiplier, wnaf, True, True,
kind="precomp+necessary"
)
assert multiples_all != multiples_input
assert multiples_all != multiples_necessary
assert multiples_input != multiples_necessary
assert multiples_precomp != multiples_necessary
def test_x0_point(rpa_params):
res = rpa_point_x0(rpa_params)
assert res is not None
assert res.y == 0
def test_0y_point(rpa_params):
res = rpa_point_0y(rpa_params)
assert res is not None
assert res.x == 0
@pytest.fixture()
def distinguish_params_sw(model, coords):
p = 0xCB5E1D94A6168511
a = mod(0xB166CA7D2DFBF69F, p)
b = mod(0x855BB40CB6937C4B, p)
gx = mod(0x253B2638BD13D6F4, p)
gy = mod(0x1E91A1A182287E71, p)
infty = Point(coords, X=mod(0, p), Y=mod(1, p), Z=mod(0, p))
g = Point(coords, X=gx, Y=gy, Z=mod(1, p))
curve = EllipticCurve(model, coords, p, infty, dict(a=a, b=b))
return DomainParameters(curve, g, 0xCB5E1D94601A3AC5, 1)
def test_distinguish_basic(distinguish_params_sw, add, dbl, neg):
multipliers = [
LTRMultiplier(add, dbl, None, False, AccumulationOrder.PeqPR, True, True),
LTRMultiplier(add, dbl, None, True, AccumulationOrder.PeqPR, True, True),
RTLMultiplier(add, dbl, None, False, AccumulationOrder.PeqPR, True),
RTLMultiplier(add, dbl, None, True, AccumulationOrder.PeqPR, False),
SimpleLadderMultiplier(add, dbl, None, True, True),
BinaryNAFMultiplier(
add, dbl, neg, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
BinaryNAFMultiplier(
add, dbl, neg, None, ProcessingDirection.RTL, AccumulationOrder.PeqPR, True
),
WindowNAFMultiplier(
add, dbl, neg, 3, None, AccumulationOrder.PeqPR, True, True
),
WindowNAFMultiplier(
add, dbl, neg, 4, None, AccumulationOrder.PeqPR, True, True
),
WindowNAFMultiplier(
add, dbl, neg, 5, None, AccumulationOrder.PeqPR, True, True
),
WindowBoothMultiplier(
add, dbl, neg, 3, None, AccumulationOrder.PeqPR, True, True
),
WindowBoothMultiplier(
add, dbl, neg, 4, None, AccumulationOrder.PeqPR, True, True
),
WindowBoothMultiplier(
add, dbl, neg, 5, None, AccumulationOrder.PeqPR, True, True
),
SlidingWindowMultiplier(
add, dbl, 3, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
SlidingWindowMultiplier(
add, dbl, 4, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
SlidingWindowMultiplier(
add, dbl, 5, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
SlidingWindowMultiplier(
add, dbl, 3, None, ProcessingDirection.RTL, AccumulationOrder.PeqPR, True
),
SlidingWindowMultiplier(
add, dbl, 4, None, ProcessingDirection.RTL, AccumulationOrder.PeqPR, True
),
SlidingWindowMultiplier(
add, dbl, 5, None, ProcessingDirection.RTL, AccumulationOrder.PeqPR, True
),
FixedWindowLTRMultiplier(add, dbl, 3, None, AccumulationOrder.PeqPR, True),
FixedWindowLTRMultiplier(add, dbl, 4, None, AccumulationOrder.PeqPR, True),
FixedWindowLTRMultiplier(add, dbl, 5, None, AccumulationOrder.PeqPR, True),
FixedWindowLTRMultiplier(add, dbl, 8, None, AccumulationOrder.PeqPR, True),
FixedWindowLTRMultiplier(add, dbl, 16, None, AccumulationOrder.PeqPR, True),
FullPrecompMultiplier(
add,
dbl,
None,
True,
ProcessingDirection.LTR,
AccumulationOrder.PeqPR,
True,
True,
),
FullPrecompMultiplier(
add,
dbl,
None,
False,
ProcessingDirection.LTR,
AccumulationOrder.PeqPR,
True,
True,
),
BGMWMultiplier(
add, dbl, 2, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
BGMWMultiplier(
add, dbl, 3, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
BGMWMultiplier(
add, dbl, 4, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
BGMWMultiplier(
add, dbl, 5, None, ProcessingDirection.LTR, AccumulationOrder.PeqPR, True
),
CombMultiplier(add, dbl, 2, None, AccumulationOrder.PeqPR, True),
CombMultiplier(add, dbl, 3, None, AccumulationOrder.PeqPR, True),
CombMultiplier(add, dbl, 4, None, AccumulationOrder.PeqPR, True),
CombMultiplier(add, dbl, 5, None, AccumulationOrder.PeqPR, True),
]
for real_mult in multipliers:
def simulated_oracle(scalar, affine_point):
point = affine_point.to_model(
distinguish_params_sw.curve.coordinate_model,
distinguish_params_sw.curve,
)
with local(MultipleContext()) as ctx:
real_mult.init(distinguish_params_sw, point)
real_mult.multiply(scalar)
return any(
map(lambda P: P.X == 0 or P.Y == 0, sum(ctx.parents.values(), []))
)
result = rpa_distinguish(distinguish_params_sw, multipliers, simulated_oracle)
assert real_mult in result
assert 1 == len(result)
def test_distinguish_ladders(curve25519):
ladd = curve25519.curve.coordinate_model.formulas["ladd-1987-m"]
dbl = curve25519.curve.coordinate_model.formulas["dbl-1987-m"]
dadd = curve25519.curve.coordinate_model.formulas["dadd-1987-m"]
multipliers = [
LadderMultiplier(ladd, None, None, True, False, False),
LadderMultiplier(ladd, dbl, None, False, False, False),
LadderMultiplier(ladd, None, None, False, False, True),
DifferentialLadderMultiplier(dadd, dbl, None, True, False, False),
DifferentialLadderMultiplier(dadd, dbl, None, False, False, True),
DifferentialLadderMultiplier(dadd, dbl, None, False, False, False),
]
for real_mult in multipliers:
def simulated_oracle(scalar, affine_point):
point = affine_point.to_model(
curve25519.curve.coordinate_model, curve25519.curve
)
with local(MultipleContext()) as ctx:
real_mult.init(curve25519, point)
real_mult.multiply(scalar)
return any(map(lambda P: P.X == 0, sum(ctx.parents.values(), [])))
result = rpa_distinguish(
curve25519, multipliers, simulated_oracle, bound=isqrt(curve25519.order)
)
assert real_mult in result
# These multipliers are not distinguishable by a binary RPA oracle.
# assert 1 == len(result)
|
