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"""Provides binary scalar multipliers (LTR and RTL), that process the scalar as-is, bit-by-bit."""
from abc import ABC
from copy import copy
from typing import Optional
from public import public
from pyecsca.ec.mult.base import (
ScalarMultiplier,
ProcessingDirection,
AccumulationOrder,
ScalarMultiplicationAction,
AccumulatorMultiplier,
)
from pyecsca.ec.formula import AdditionFormula, DoublingFormula, ScalingFormula
from pyecsca.ec.point import Point
@public
class DoubleAndAddMultiplier(AccumulatorMultiplier, ScalarMultiplier, ABC):
"""
Classic double and add scalar multiplication algorithm.
.. note::
This is an ABC, you should use the `LTRMultiplier` and `RTLMultiplier` classes.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param always: Whether the double and add always method is used.
:param direction: Whether it is LTR or RTL.
:param accumulation_order: The order of accumulation of points.
:param complete: Whether it starts processing at full order-bit-length.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
always: bool
"""Whether the double and add always method is used."""
direction: ProcessingDirection
"""Whether it is LTR or RTL."""
complete: bool
"""Whether it starts processing at full order-bit-length."""
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
scl: Optional[ScalingFormula] = None,
always: bool = False,
direction: ProcessingDirection = ProcessingDirection.LTR,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
complete: bool = True,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
accumulation_order=accumulation_order,
add=add,
dbl=dbl,
scl=scl,
)
self.always = always
self.direction = direction
self.complete = complete
def __hash__(self):
return hash(
(
DoubleAndAddMultiplier,
super().__hash__(),
self.direction,
self.accumulation_order,
self.always,
self.complete,
)
)
def __eq__(self, other):
if not isinstance(other, DoubleAndAddMultiplier):
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
and self.always == other.always
and self.complete == other.complete
)
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}, always={self.always}, complete={self.complete})"
def _ltr(self, scalar: int) -> Point:
if self.complete:
q = self._point
r = copy(self._params.curve.neutral)
top = self._bits - 1
else:
q = copy(self._point)
r = copy(self._point)
top = scalar.bit_length() - 2
for i in range(top, -1, -1):
r = self._dbl(r)
if scalar & (1 << i) != 0:
r = self._accumulate(r, q)
elif self.always:
# dummy add
self._accumulate(r, q)
return r
def _rtl(self, scalar: int) -> Point:
q = self._point
r = copy(self._params.curve.neutral)
if self.complete:
top = self._bits
else:
top = scalar.bit_length()
for _ in range(top):
if scalar & 1 != 0:
r = self._accumulate(r, q)
elif self.always:
# dummy add
self._accumulate(r, q)
# TODO: This double is unnecessary in the last iteration.
q = self._dbl(q)
scalar >>= 1
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))
if self.direction is ProcessingDirection.LTR:
r = self._ltr(scalar)
elif self.direction is ProcessingDirection.RTL:
r = self._rtl(scalar)
if "scl" in self.formulas:
r = self._scl(r)
return action.exit(r)
@public
class LTRMultiplier(DoubleAndAddMultiplier):
"""
Classic double and add scalar multiplication algorithm, that scans the scalar left-to-right (msb to lsb).
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param always: Whether the double and add always method is used.
:param accumulation_order: The order of accumulation of points.
:param complete: Whether it starts processing at full order-bit-length.
"""
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
scl: Optional[ScalingFormula] = None,
always: bool = False,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
complete: bool = True,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
direction=ProcessingDirection.LTR,
accumulation_order=accumulation_order,
always=always,
complete=complete,
add=add,
dbl=dbl,
scl=scl,
)
@public
class RTLMultiplier(DoubleAndAddMultiplier):
"""
Classic double and add scalar multiplication algorithm, that scans the scalar right-to-left (lsb to msb).
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param always: Whether the double and add always method is used.
:param accumulation_order: The order of accumulation of points.
:param complete: Whether it starts processing at full order-bit-length.
"""
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
scl: Optional[ScalingFormula] = None,
always: bool = False,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
complete: bool = True,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
direction=ProcessingDirection.RTL,
accumulation_order=accumulation_order,
always=always,
add=add,
dbl=dbl,
scl=scl,
complete=complete,
)
@public
class CoronMultiplier(ScalarMultiplier):
"""
Coron's double and add resistant against SPA.
From [CO2002]_.
: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}
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
scl: Optional[ScalingFormula] = None,
short_circuit: bool = True,
):
super().__init__(short_circuit=short_circuit, add=add, dbl=dbl, scl=scl)
def __hash__(self):
return hash((CoronMultiplier, super().__hash__()))
def __eq__(self, other):
if not isinstance(other, CoronMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
)
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 = self._point
p0 = copy(q)
for i in range(scalar.bit_length() - 2, -1, -1):
p0 = self._dbl(p0)
p1 = self._add(p0, q)
if scalar & (1 << i) != 0:
p0 = p1
if "scl" in self.formulas:
p0 = self._scl(p0)
return action.exit(p0)
|
