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"""Provides Comb-like scalar multipliers, such as BGMW or Lim-Lee."""
import random
from copy import copy
from math import ceil
from typing import MutableMapping, Optional
from public import public
from pyecsca.ec.formula import AdditionFormula, DoublingFormula, ScalingFormula
from pyecsca.ec.mult import (
AccumulatorMultiplier,
ScalarMultiplier,
ProcessingDirection,
AccumulationOrder,
PrecomputationAction,
ScalarMultiplicationAction,
PrecompMultiplier,
)
from pyecsca.ec.params import DomainParameters
from pyecsca.ec.point import Point
from pyecsca.ec.scalar import convert_base
@public
class BGMWMultiplier(AccumulatorMultiplier, PrecompMultiplier, ScalarMultiplier):
"""
Brickell, Gordon, McCurley and Wilson (BGMW) scalar multiplier,
or rather, its one parametrization.
Algorithm 3.41 from [GECC]_
:param width: Window width.
:param direction: Whether it is LTR or RTL.
:param accumulation_order: The order of accumulation of points.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
direction: ProcessingDirection
"""Whether it is LTR or RTL."""
width: int
"""Window width."""
_points: MutableMapping[int, Point]
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
width: int,
scl: Optional[ScalingFormula] = None,
direction: ProcessingDirection = ProcessingDirection.LTR,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
accumulation_order=accumulation_order,
add=add,
dbl=dbl,
scl=scl,
)
self.direction = direction
self.width = width
def __hash__(self):
return hash(
(
BGMWMultiplier,
super().__hash__(),
self.width,
self.direction,
self.accumulation_order,
)
)
def __eq__(self, other):
if not isinstance(other, BGMWMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.width == other.width
and self.direction == other.direction
and self.accumulation_order == other.accumulation_order
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, width={self.width}, direction={self.direction.name}, accumulation_order={self.accumulation_order.name})"
def init(self, params: DomainParameters, point: Point, bits: Optional[int] = None):
with PrecomputationAction(params, point) as action:
super().init(params, point, bits)
d = ceil(self._bits / self.width)
self._points = {}
current_point = point
for i in range(d):
self._points[i] = current_point
if i != d - 1:
for _ in range(self.width):
current_point = self._dbl(current_point)
action.exit(self._points)
def multiply(self, scalar: int) -> Point:
if not self._initialized:
raise ValueError("ScalarMultiplier not initialized.")
with ScalarMultiplicationAction(self._point, self._params, scalar) as action:
if scalar == 0:
return action.exit(copy(self._params.curve.neutral))
a = copy(self._params.curve.neutral)
b = copy(self._params.curve.neutral)
recoded = convert_base(scalar, 2**self.width)
for j in range(2**self.width - 1, 0, -1):
if self.direction == ProcessingDirection.RTL:
for i, ki in enumerate(recoded):
if ki == j:
b = self._accumulate(b, self._points[i])
elif self.direction == ProcessingDirection.LTR:
for i, ki in reversed(list(enumerate(recoded))):
if ki == j:
b = self._accumulate(b, self._points[i])
if self.short_circuit and a == b:
# TODO: Double necessary here for incomplete formulas, maybe another param and not reuse short_cirtuit?
a = self._dbl(b)
else:
a = self._accumulate(a, b)
if "scl" in self.formulas:
a = self._scl(a)
return action.exit(a)
@public
class CombMultiplier(AccumulatorMultiplier, PrecompMultiplier, ScalarMultiplier):
"""
Comb multiplier.
Algorithm 3.44 from [GECC]_
:param width: Window width (number of comb teeth).
:param always: Whether the double and add always method is used.
:param accumulation_order: The order of accumulation of points.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
width: int
"""Window width."""
always: bool
"""Whether to always accumulate."""
_points: MutableMapping[int, Point]
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
width: int,
scl: Optional[ScalingFormula] = None,
always: bool = False,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
accumulation_order=accumulation_order,
add=add,
dbl=dbl,
scl=scl,
)
self.width = width
self.always = always
def __hash__(self):
return hash(
(CombMultiplier, super().__hash__(), self.width, self.accumulation_order, self.always)
)
def __eq__(self, other):
if not isinstance(other, CombMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.width == other.width
and self.accumulation_order == other.accumulation_order
and self.always == other.always
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, width={self.width}, accumulation_order={self.accumulation_order.name}, always={self.always})"
def init(self, params: DomainParameters, point: Point, bits: Optional[int] = None):
with PrecomputationAction(params, point) as action:
super().init(params, point, bits)
d = ceil(self._bits / self.width)
base_points = {}
current_point = point
for i in range(self.width):
base_points[i] = current_point
if i != d - 1:
for _ in range(d):
current_point = self._dbl(current_point)
self._points = {}
for j in range(1, 2**self.width):
points = []
for i in range(self.width):
if j & (1 << i):
points.append(base_points[i])
self._points[j] = points[0]
for other in points[1:]:
self._points[j] = self._accumulate(self._points[j], other)
action.exit(self._points)
def multiply(self, scalar: int) -> Point:
if not self._initialized:
raise ValueError("ScalarMultiplier not initialized.")
with ScalarMultiplicationAction(self._point, self._params, scalar) as action:
if scalar == 0:
return action.exit(copy(self._params.curve.neutral))
q = copy(self._params.curve.neutral)
d = ceil(self._bits / self.width)
recoded = convert_base(scalar, 2**d)
if len(recoded) != self.width:
recoded.extend([0] * (self.width - len(recoded)))
for i in range(d - 1, -1, -1):
q = self._dbl(q)
word = 0
for j in range(self.width):
# get i-th bit of recoded[j] and set it into the j-th bit of word
bit = (recoded[j] >> i) & 1
word |= bit << j
if word:
q = self._accumulate(q, self._points[word])
elif self.always:
j = random.randrange(0, 2 ** self.width)
# dummy
if j == 0:
self._accumulate(q, self._point)
else:
self._accumulate(q, self._points[j])
if "scl" in self.formulas:
q = self._scl(q)
return action.exit(q)
|
