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(BTClibValueError, match="negative m: "):
_mult_fixed_window(-1, ec.GJ, ec, w)
with pytest.raises(BTClibValueError, 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_jac() -> None:
for ec in all_curves.values():
assert ec._jac_equality(_mult_jac(0, ec.GJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(0, INFJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(1, INFJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(1, ec.GJ, ec), ec.GJ)
PJ = ec._add_jac(ec.GJ, ec.GJ)
assert ec._jac_equality(PJ, _mult_jac(2, ec.GJ, ec))
PJ = _mult_jac(ec.n - 1, ec.GJ, ec)
assert ec._jac_equality(ec.negate_jac(ec.GJ), PJ)
assert ec._jac_equality(_mult_jac(ec.n - 1, INFJ, ec), INFJ)
assert ec._jac_equality(ec._add_jac(PJ, ec.GJ), INFJ)
assert ec._jac_equality(_mult_jac(ec.n, ec.GJ, ec), INFJ)
with pytest.raises(ValueError, match="negative m: "):
_mult_jac(-1, ec.GJ, ec)
from btclib.curve import secp256k1 as ec
from btclib.curvegroup import (
_mult_aff,
_mult_jac,
_mult_recursive_aff,
_mult_recursive_jac,
)
# setup
random.seed(42)
qs = [random.getrandbits(ec.nlen) % ec.n for _ in range(100)]
start = time.time()
for q in qs:
# starts from affine coordinates, ends with affine coordinates
ec._aff_from_jac(_mult_jac(q, ec.GJ, ec))
benchmark = time.time() - start
print("Benchmark completed")
start = time.time()
for q in qs:
_mult_recursive_aff(q, ec.G, ec)
recursive_aff = time.time() - start
print(f"Recursive aff : {recursive_aff / benchmark:.0%}")
start = time.time()
for q in qs:
ec._aff_from_jac(_mult_recursive_jac(q, ec.GJ, ec))
recursive_jac = time.time() - start
print(f"Recursive jac : {recursive_jac / benchmark:.0%}")
gen_only = True
print("generator only") if gen_only else print("random points")
cached_multiples.cache_clear()
cached_multiples(ec.GJ, ec)
T = ec.GJ
start = time.time()
for q in qs:
T = _mult(q, ec.GJ, ec) if gen_only else _mult(q, T, ec)
benchmark = time.time() - start
print("Benchmark completed", cached_multiples.cache_info())
T = ec.GJ
start = time.time()
for q in qs:
T = _mult_jac(q, ec.GJ, ec) if gen_only else _mult_jac(q, T, ec)
double_and_add = time.time() - start
print(f"Double & add : {double_and_add / benchmark:.0%}")
T = ec.GJ
start = time.time()
for q in qs:
T = _mult_mont_ladder(q, ec.GJ, ec) if gen_only else _mult_mont_ladder(
q, T, ec)
montgomery = time.time() - start
print(f"Montgomery ladder: {montgomery / benchmark:.0%}")
cached_multiples.cache_clear()
cached_multiples(ec.GJ, ec)
T = ec.GJ
start = time.time()
def test_mult_jac() -> None:
for ec in all_curves.values():
assert ec._jac_equality(_mult_jac(0, ec.GJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(0, INFJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(1, INFJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(1, ec.GJ, ec), ec.GJ)
PJ = ec._add_jac(ec.GJ, ec.GJ)
assert ec._jac_equality(PJ, _mult_jac(2, ec.GJ, ec))
PJ = _mult_jac(ec.n - 1, ec.GJ, ec)
assert ec._jac_equality(ec.negate_jac(ec.GJ), PJ)
assert ec._jac_equality(_mult_jac(ec.n - 1, INFJ, ec), INFJ)
assert ec._jac_equality(ec._add_jac(PJ, ec.GJ), INFJ)
assert ec._jac_equality(_mult_jac(ec.n, ec.GJ, ec), INFJ)
assert ec._jac_equality(_mult_jac(ec.n, INFJ, ec), INFJ)
with pytest.raises(BTClibValueError, match="negative m: "):
_mult_jac(-1, ec.GJ, ec)
ec = ec23_31
for k1 in range(ec.n):
K1 = _mult_jac(k1, ec.GJ, ec)
assert ec._jac_equality(K1, _mult(k1, ec.GJ, ec))
from btclib.curve import secp256k1 as ec
from btclib.curvegroup import (
_mult_base_3,
_mult_fixed_window,
_mult_jac,
_mult_mont_ladder,
)
# setup
random.seed(42)
qs = [random.getrandbits(ec.nlen) % ec.n for _ in range(300)]
T = ec.GJ
start = time.time()
for q in qs:
T = _mult_jac(q, T, ec)
benchmark = time.time() - start
print("Benchmark completed")
T = ec.GJ
start = time.time()
for q in qs:
T = _mult_jac(q, T, ec)
double_and_add = time.time() - start
print(f"Double & add : {double_and_add / benchmark:.0%}")
T = ec.GJ
start = time.time()
for q in qs:
T = _mult_mont_ladder(q, T, ec)
montgomery = time.time() - start
