def test_mult_w_NAF() -> None:
for w in range(1, 6):
for ec in low_card_curves.values():
assert ec._jac_equality(_mult_w_NAF(0, ec.GJ, ec, w), INFJ)
assert ec._jac_equality(_mult_w_NAF(0, INFJ, ec, w), INFJ)
assert ec._jac_equality(_mult_w_NAF(1, INFJ, ec, w), INFJ)
assert ec._jac_equality(_mult_w_NAF(1, ec.GJ, ec, w), ec.GJ)
PJ = _mult_w_NAF(2, ec.GJ, ec, w)
assert ec._jac_equality(PJ, ec._add_jac(ec.GJ, ec.GJ))
PJ = _mult_w_NAF(ec.n - 1, ec.GJ, ec, w)
assert ec._jac_equality(ec.negate_jac(ec.GJ), PJ)
assert ec._jac_equality(_mult_w_NAF(ec.n - 1, INFJ, ec, w), INFJ)
assert ec._jac_equality(ec._add_jac(PJ, ec.GJ), INFJ)
assert ec._jac_equality(_mult_w_NAF(ec.n, ec.GJ, ec, w), INFJ)
with pytest.raises(BTClibValueError, match="negative m: "):
_mult_w_NAF(-1, ec.GJ, ec, w)
with pytest.raises(BTClibValueError, match="non positive w: "):
_mult_w_NAF(1, ec.GJ, ec, -w)
ec = ec23_31
for w in range(1, 10):
for k1 in range(ec.n):
K1 = _mult_w_NAF(k1, ec.GJ, ec, w)
assert ec._jac_equality(K1, _mult(k1, ec.GJ, ec))
def test_mult_recursive_aff() -> None:
for ec in all_curves.values():
assert _mult_recursive_aff(0, ec.G, ec) == INF
assert _mult_recursive_aff(0, INF, ec) == INF
assert _mult_recursive_aff(1, INF, ec) == INF
assert _mult_aff(1, ec.G, ec) == ec.G
Q = ec._add_aff(ec.G, ec.G)
assert Q == _mult_recursive_aff(2, ec.G, ec)
Q = _mult_recursive_aff(ec.n - 1, ec.G, ec)
assert ec.negate(ec.G) == Q
assert _mult_recursive_aff(ec.n - 1, INF, ec) == INF
assert ec._add_aff(Q, ec.G) == INF
assert _mult_recursive_aff(ec.n, ec.G, ec) == INF
assert _mult_recursive_aff(ec.n, INF, ec) == INF
with pytest.raises(BTClibValueError, match="negative m: "):
_mult_recursive_aff(-1, ec.G, ec)
for ec in low_card_curves.values():
for q in range(ec.n):
Q = _mult_recursive_aff(q, ec.G, ec)
assert ec.is_on_curve(Q), f"{q}, {ec}"
QJ = _mult(q, ec.GJ, ec)
assert ec.is_on_curve(ec._aff_from_jac(QJ)), f"{q}, {ec}"
assert Q == ec._aff_from_jac(QJ), f"{q}, {ec}"
assert INF == _mult_recursive_aff(q, INF, ec), f"{q}, {ec}"
assert ec._jac_equality(INFJ, _mult(q, INFJ, ec)), f"{q}, {ec}"
def test_mult_fixed_window() -> None:
for w in range(1, _MAX_W):
for ec in low_card_curves.values():
assert ec._jac_equality(_mult_fixed_window(0, ec.GJ, ec, w), INFJ)
assert ec._jac_equality(_mult_fixed_window(0, INFJ, ec, w), INFJ)
assert ec._jac_equality(_mult_fixed_window(1, INFJ, ec, w), INFJ)
assert ec._jac_equality(_mult_fixed_window(1, ec.GJ, ec, w), ec.GJ)
PJ = _mult_fixed_window(2, ec.GJ, ec, w)
assert ec._jac_equality(PJ, ec._add_jac(ec.GJ, ec.GJ))
PJ = _mult_fixed_window(ec.n - 1, ec.GJ, ec, w)
assert ec._jac_equality(ec.negate_jac(ec.GJ), PJ)
assert ec._jac_equality(_mult_fixed_window(ec.n - 1, INFJ, ec, w),
INFJ)
assert ec._jac_equality(ec._add_jac(PJ, ec.GJ), INFJ)
assert ec._jac_equality(_mult_fixed_window(ec.n, ec.GJ, ec, w),
INFJ)
assert ec._jac_equality(_mult_mont_ladder(ec.n, INFJ, ec), INFJ)
with pytest.raises(ValueError, match="negative m: "):
_mult_fixed_window(-1, ec.GJ, ec, w)
with pytest.raises(ValueError, match="non positive w: "):
_mult_fixed_window(1, ec.GJ, ec, -w)
ec = ec23_31
for w in range(1, 10):
for k1 in range(ec.n):
K1 = _mult_fixed_window(k1, ec.GJ, ec, w)
assert ec._jac_equality(K1, _mult_jac(k1, ec.GJ, ec))
def test_mult_base_3() -> None:
for ec in low_card_curves.values():
assert ec._jac_equality(_mult_base_3(0, ec.GJ, ec), INFJ)
assert ec._jac_equality(_mult_base_3(0, INFJ, ec), INFJ)
assert ec._jac_equality(_mult_base_3(1, INFJ, ec), INFJ)
assert ec._jac_equality(_mult_base_3(1, ec.GJ, ec), ec.GJ)
PJ = _mult_base_3(2, ec.GJ, ec)
assert ec._jac_equality(PJ, ec._add_jac(ec.GJ, ec.GJ))
PJ = _mult_base_3(ec.n - 1, ec.GJ, ec)
assert ec._jac_equality(ec.negate_jac(ec.GJ), PJ)
assert ec._jac_equality(_mult_base_3(ec.n - 1, INFJ, ec), INFJ)
assert ec._jac_equality(ec._add_jac(PJ, ec.GJ), INFJ)
assert ec._jac_equality(_mult_base_3(ec.n, ec.GJ, ec), INFJ)
assert ec._jac_equality(_mult_mont_ladder(ec.n, INFJ, ec), INFJ)
with pytest.raises(BTClibValueError, match="negative m: "):
_mult_base_3(-1, ec.GJ, ec)
ec = ec23_31
for k1 in range(ec.n):
K1 = _mult_base_3(k1, ec.GJ, ec)
assert ec._jac_equality(K1, _mult(k1, ec.GJ, ec))
def test_mult() -> None:
for ec in low_card_curves.values():
for q in range(ec.n):
Q = _mult_aff(q, ec.G, ec)
assert ec.is_on_curve(Q), f"{q}, {ec}"
QJ = _mult(q, ec.GJ, ec)
assert ec.is_on_curve(ec._aff_from_jac(QJ)), f"{q}, {ec}"
assert Q == ec._aff_from_jac(QJ), f"{q}, {ec}"
assert INF == _mult_aff(q, INF, ec), f"{q}, {ec}"
assert ec._jac_equality(INFJ, _mult(q, INFJ, ec)), f"{q}, {ec}"
