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import pytest
from sympy import symbols, Poly, sympify, FF
from pyecsca.ec.context import local, DefaultContext
from pyecsca.ec.coordinates import AffineCoordinateModel
from pyecsca.ec.formula.unroll import unroll_formula
from pyecsca.ec.mod import mod
from pyecsca.ec.mult import LTRMultiplier, AccumulationOrder
from pyecsca.ec.point import Point
from pyecsca.sca.re.zvp import (
map_to_affine,
subs_curve_equation,
remove_z,
eliminate_y,
subs_dlog,
subs_curve_params,
zvp_points,
compute_factor_set,
addition_chain,
solve_easy_dcp,
solve_hard_dcp,
)
@pytest.fixture(params=["add-2007-bl", "add-2015-rcb", "dbl-2007-bl"])
def formula(secp128r1, request):
return secp128r1.curve.coordinate_model.formulas[request.param]
def test_unroll(formula):
results = unroll_formula(formula)
assert results is not None
for name, res in results:
assert isinstance(res, Poly)
def test_map_to_affine(formula):
results = unroll_formula(formula)
mapped = map_to_affine(formula, results)
assert mapped is not None
for name, res in mapped:
assert isinstance(res, Poly)
def test_factor_set(formula):
factor_set = compute_factor_set(formula, affine=True)
assert factor_set is not None
assert isinstance(factor_set, set)
expr_set = set(map(lambda poly: poly.as_expr(), factor_set))
expected_factors = {
"add-2007-bl": {
# "y2", RPA
# "y1", RPA
# "y1 + y2", RPA
# "x2", RPA
# "x1", RPA
"x1 + x2",
# "y1^2 + 2*y1*y2 + y2^2 + x1 + x2", Non-homogenous
# "y1^2 + 2*y1*y2 + y2^2 + 2*x1 + 2*x2", Non-homogenous
"x1^2 + x1*x2 + x2^2",
"a + x1^2 + x1*x2 + x2^2",
# "a^2 + x1^4 + 2*x1^3*x2 + 3*x1^2*x2^2 + 2*x1*x2^3 + x2^4 - x1*y1^2 - x2*y1^2 - 2*x1*y1*y2 - 2*x2*y1*y2 - x1*y2^2 - x2*y2^2 + 2*x1^2*a + 2*x1*x2*a + 2*x2^2*a", RPA
"2*a^2 + 2*x1^4 + 4*x1^3*x2 + 6*x1^2*x2^2 + 4*x1*x2^3 + 2*x2^4 - 3*x1*y1^2 - 3*x2*y1^2 - 6*x1*y1*y2 - 6*x2*y1*y2 - 3*x1*y2^2 - 3*x2*y2^2 + 4*x1^2*a + 4*x1*x2*a + 4*x2^2*a",
# "2*a^3 + 2*x1^6 + 6*x1^5*x2 + 12*x1^4*x2^2 + 14*x1^3*x2^3 + 12*x1^2*x2^4 + 6*x1*x2^5 + 2*x2^6 - 3*x1^3*y1^2 - 6*x1^2*x2*y1^2 - 6*x1*x2^2*y1^2 - 3*x2^3*y1^2 - 6*x1^3*y1*y2 - 12*x1^2*x2*y1*y2 - 12*x1*x2^2*y1*y2 - 6*x2^3*y1*y2 - 3*x1^3*y2^2 - 6*x1^2*x2*y2^2 - 6*x1*x2^2*y2^2 - 3*x2^3*y2^2 + 6*x1^4*a + 12*x1^3*x2*a + 18*x1^2*x2^2*a + 12*x1*x2^3*a + 6*x2^4*a + y1^4 + 4*y1^3*y2 + 6*y1^2*y2^2 + 4*y1*y2^3 + y2^4 - 3*x1*y1^2*a - 3*x2*y1^2*a - 6*x1*y1*y2*a - 6*x2*y1*y2*a - 3*x1*y2^2*a - 3*x2*y2^2*a + 6*x1^2*a^2 + 6*x1*x2*a^2 + 6*x2^2*a^2" RPA
},
"add-2015-rcb": {
# "y2", RPA
"y2 + 1",
# "y1", RPA
"y1 + 1",
"y1 + y2",
# "x2", RPA
"x2 + 1",
"x2 + y2",
# "x1", RPA
"x1 + 1",
"x1 + y1",
"x1 + x2",
"x1*a + x2*a + 3*b",
"-y1*y2 + x1*a + x2*a + 3*b",
"y1*y2 + 1",
"y1*y2 + x1*a + x2*a + 3*b",
"x2*y1 + x1*y2",
"-x1*x2 + a",
"x1*x2 + 1",
"x1*x2 + y1*y2",
"3*x1*x2 + a",
"a^2 - x1*x2*a - 3*x1*b - 3*x2*b",
# "x2*y1^2*y2 + x1*y1*y2^2 - 2*x1*x2*y1*a - x2^2*y1*a - x1^2*y2*a - 2*x1*x2*y2*a + y1*a^2 + y2*a^2 - 3*x1*y1*b - 6*x2*y1*b - 6*x1*y2*b - 3*x2*y2*b", RPA
# "3*x1*x2^2*y1 + 3*x1^2*x2*y2 + y1^2*y2 + y1*y2^2 + x1*y1*a + 2*x2*y1*a + 2*x1*y2*a + x2*y2*a + 3*y1*b + 3*y2*b", RPA
# "-3*x1^2*x2^2*a - y1^2*y2^2 + x1^2*a^2 + 4*x1*x2*a^2 + x2^2*a^2 - 9*x1^2*x2*b - 9*x1*x2^2*b + a^3 + 3*x1*a*b + 3*x2*a*b + 9*b^2" RPA
},
"dbl-2007-bl": {"a + 3*x1^2", "a^2 + 6*x1^2*a + 9*x1^4 - 12*x1*y1^2"},
}
if formula.name in expected_factors:
expected_set = set(
map(lambda s: Poly(s).as_expr(), expected_factors[formula.name])
)
assert expr_set == expected_set
def test_curve_elimination(secp128r1, formula):
unrolled = unroll_formula(formula)
unrolled = map_to_affine(formula, unrolled)
subbed = subs_curve_equation(unrolled[-1][1], secp128r1.curve)
assert subbed is not None
Y1, Y2 = symbols("Y1,Y2")
# The resulting polynomial should not have Y1 and Y2 in higher powers than 1.
for term in subbed.terms():
powers = dict(zip(subbed.gens, term[0]))
assert powers.get(Y1, 0) in (0, 1)
assert powers.get(Y2, 0) in (0, 1)
def test_remove_z(secp128r1, formula):
unrolled = unroll_formula(formula)
unrolled = map_to_affine(formula, unrolled)
removed = remove_z(unrolled[-1][1])
for gen in removed.gens:
assert not str(gen).startswith("Z")
def test_eliminate_y(secp128r1, formula):
unrolled = unroll_formula(formula)
unrolled = map_to_affine(formula, unrolled)
subbed = subs_curve_equation(unrolled[-1][1], secp128r1.curve)
eliminated = eliminate_y(subbed, secp128r1.curve.model)
assert eliminated is not None
assert isinstance(eliminated, Poly)
y1, y2 = symbols("y1,y2")
assert y1 not in eliminated.gens
assert y2 not in eliminated.gens
eliminated_second = eliminate_y(eliminated, secp128r1.curve.model)
assert eliminated_second == eliminated
def test_full(secp128r1, formula):
unrolled = unroll_formula(formula)
unrolled = map_to_affine(formula, unrolled)
subbed = subs_curve_equation(unrolled[-1][1], secp128r1.curve)
removed = remove_z(subbed)
eliminated = eliminate_y(removed, secp128r1.curve.model)
dlog = subs_dlog(eliminated, 3, secp128r1.curve)
assert dlog is not None
assert isinstance(dlog, Poly)
x1, x2 = symbols("x1,x2")
assert x2 not in dlog.gens
final = subs_curve_params(dlog, secp128r1.curve)
assert final is not None
assert isinstance(final, Poly)
assert final.gens == (x1,)
@pytest.mark.slow
def test_zvp(secp128r1, formula):
unrolled = unroll_formula(formula)
unrolled = map_to_affine(formula, unrolled)
# Try all intermediates, zvp_point should return empty set if ZVP points do not exist
# Try with a few scalars to actually test more resulting ZVP points
for name, poly in unrolled:
for k in (2, 3, 5):
points = zvp_points(poly, secp128r1.curve, k, secp128r1.order)
if points:
break
assert isinstance(points, set)
# If points are produced, try them all.
for point in points:
inputs = [point.to_model(formula.coordinate_model, secp128r1.curve)]
if formula.num_inputs > 1:
second_point = secp128r1.curve.affine_multiply(point, k)
inputs.append(
second_point.to_model(formula.coordinate_model, secp128r1.curve)
)
with local(DefaultContext()) as ctx:
formula(secp128r1.curve.prime, *inputs, **secp128r1.curve.parameters)
action = ctx.actions[0].action
results = list(map(lambda o: int(o.value), action.op_results))
assert 0 in results
@pytest.mark.parametrize(
"poly_str,point,k",
[
(
"y1 + y2",
(
54027047743185503031379008986257148598,
42633567686060343012155773792291852040,
),
4,
),
(
"x1 + x2",
(
285130337309757533508049972949147801522,
55463852278545391044040942536845640298,
),
3,
),
(
"x1*x2 + y1*y2",
(
155681799415564546404955983367992137717,
227436010604106449719780498844151836756,
),
5,
),
(
"y1*y2 - x1*a - x2*a - 3*b",
(
169722400242675158455680894146658513260,
33263376472545436059176357032150610796,
),
4,
),
("x1", (0, 594107526960909229279178399525926007), 3),
(
"x2",
(
234937379492809870217296988280059595814,
101935882302108071650074851009662355573,
),
4,
),
],
)
def test_points(secp128r1, poly_str, point, k):
pt = Point(
AffineCoordinateModel(secp128r1.curve.model),
x=mod(point[0], secp128r1.curve.prime),
y=mod(point[1], secp128r1.curve.prime),
)
poly_expr = sympify(poly_str)
poly = Poly(poly_expr, domain=FF(secp128r1.curve.prime))
res = zvp_points(poly, secp128r1.curve, k, secp128r1.order)
assert pt in res
def test_addition_chain(secp128r1):
res = addition_chain(
78699,
secp128r1,
LTRMultiplier,
lambda add, dbl, *args, **kwargs: LTRMultiplier(
add, dbl, None, False, AccumulationOrder.PeqPR, True, False
),
)
assert res is not None
# Plenty of operations on infty point, due to complete=True and no short_circuit
assert len(res) == 138
@pytest.mark.parametrize("k", [7, 25, 31])
def test_big_boy(secp128r1, k):
poly_expr = sympify("x1*x2 + y1*y2")
poly = Poly(poly_expr, domain=FF(secp128r1.curve.prime))
res = zvp_points(poly, secp128r1.curve, k, secp128r1.order)
assert res is not None
@pytest.mark.parametrize("numero", [5, 1, 0])
def test_small_boy(secp128r1, numero):
x = symbols("x1")
poly = Poly(numero, x, domain=FF(secp128r1.curve.prime))
res = solve_easy_dcp(poly, secp128r1.curve)
assert res is not None
if numero == 0:
assert len(res) >= 1
# secp128r1 has a = -3 so the first poly is zero as well
@pytest.mark.parametrize("poly_expr", ["a+3", "0"])
def test_zero_boy(secp128r1, poly_expr):
x, a = symbols("x1 a")
poly = Poly(sympify(poly_expr), x, a, domain=FF(secp128r1.curve.prime))
res = solve_hard_dcp(poly, secp128r1.curve, 5)
assert res is not None
assert len(res) >= 1
|
