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"""Provides scalar multipliers based on the Non Adjacent Form (NAF) recoding."""
from copy import copy
from typing import Optional, List, MutableMapping
from public import public
from pyecsca.ec.mult.base import (
ScalarMultiplier,
ScalarMultiplicationAction,
ProcessingDirection,
AccumulationOrder,
PrecomputationAction,
AccumulatorMultiplier,
)
from pyecsca.ec.formula import (
AdditionFormula,
DoublingFormula,
ScalingFormula,
NegationFormula,
)
from pyecsca.ec.params import DomainParameters
from pyecsca.ec.point import Point
from pyecsca.ec.scalar import naf, wnaf
@public
class BinaryNAFMultiplier(AccumulatorMultiplier, ScalarMultiplier):
"""
Binary NAF (Non Adjacent Form) multiplier.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param direction: Whether it is LTR or RTL.
:param accumulation_order: The order of accumulation of points.
"""
requires = {AdditionFormula, DoublingFormula, NegationFormula}
optionals = {ScalingFormula}
direction: ProcessingDirection
_point_neg: Point
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
neg: NegationFormula,
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,
neg=neg,
scl=scl,
)
self.direction = direction
def __hash__(self):
return hash(
(
BinaryNAFMultiplier,
super().__hash__(),
self.direction,
self.accumulation_order,
)
)
def __eq__(self, other):
if not isinstance(other, BinaryNAFMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
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}, direction={self.direction.name}, accumulation_order={self.accumulation_order.name})"
def init(self, params: DomainParameters, point: Point):
with PrecomputationAction(params, point):
super().init(params, point)
self._point_neg = self._neg(point)
def _ltr(self, scalar_naf: List[int]) -> Point:
q = copy(self._params.curve.neutral)
for val in scalar_naf:
q = self._dbl(q)
if val == 1:
q = self._accumulate(q, self._point)
if val == -1:
# TODO: Whether this negation is precomputed can be a parameter
q = self._accumulate(q, self._point_neg)
return q
def _rtl(self, scalar_naf: List[int]) -> Point:
q = self._point
r = copy(self._params.curve.neutral)
for val in reversed(scalar_naf):
if val == 1:
r = self._accumulate(r, q)
if val == -1:
neg = self._neg(q)
r = self._accumulate(r, neg)
q = self._dbl(q)
return r
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))
scalar_naf = naf(scalar)
if self.direction is ProcessingDirection.LTR:
q = self._ltr(scalar_naf)
elif self.direction is ProcessingDirection.RTL:
q = self._rtl(scalar_naf)
if "scl" in self.formulas:
q = self._scl(q)
return action.exit(q)
@public
class WindowNAFMultiplier(AccumulatorMultiplier, ScalarMultiplier):
"""
Window NAF (Non Adjacent Form) multiplier, left-to-right.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param width: The width of the window.
:param accumulation_order: The order of accumulation of points.
:param precompute_negation: Whether to precompute the negation of the precomputed points as well.
It is computed on the fly otherwise.
"""
requires = {AdditionFormula, DoublingFormula, NegationFormula}
optionals = {ScalingFormula}
_points: MutableMapping[int, Point]
_points_neg: MutableMapping[int, Point]
precompute_negation: bool = False
"""Whether to precompute the negation of the precomputed points as well."""
width: int
"""The width of the window."""
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
neg: NegationFormula,
width: int,
scl: Optional[ScalingFormula] = None,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
precompute_negation: bool = False,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
accumulation_order=accumulation_order,
add=add,
dbl=dbl,
neg=neg,
scl=scl,
)
self.width = width
self.precompute_negation = precompute_negation
def __hash__(self):
return hash(
(
WindowNAFMultiplier,
super().__hash__(),
self.width,
self.precompute_negation,
self.accumulation_order,
)
)
def __eq__(self, other):
if not isinstance(other, WindowNAFMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.width == other.width
and self.precompute_negation == other.precompute_negation
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}, precompute_negation={self.precompute_negation}, accumulation_order={self.accumulation_order.name})"
def init(self, params: DomainParameters, point: Point):
with PrecomputationAction(params, point):
super().init(params, point)
self._points = {}
self._points_neg = {}
current_point = point
double_point = self._dbl(point)
for i in range(0, 2 ** (self.width - 2)):
self._points[2 * i + 1] = current_point
if self.precompute_negation:
self._points_neg[2 * i + 1] = self._neg(current_point)
current_point = self._add(current_point, double_point)
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))
scalar_naf = wnaf(scalar, self.width)
q = copy(self._params.curve.neutral)
for val in scalar_naf:
q = self._dbl(q)
if val > 0:
q = self._accumulate(q, self._points[val])
elif val < 0:
if self.precompute_negation:
neg = self._points_neg[-val]
else:
neg = self._neg(self._points[-val])
q = self._accumulate(q, neg)
if "scl" in self.formulas:
q = self._scl(q)
return action.exit(q)
|
