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from abc import ABC
from copy import copy
from typing import Optional
from public import public
from .base import ScalarMultiplier, ProcessingDirection, AccumulationOrder, ScalarMultiplicationAction, \
AccumulatorMultiplier
from ..formula import (
AdditionFormula,
DoublingFormula,
ScalingFormula,
)
from ..point import Point
@public
class DoubleAndAddMultiplier(AccumulatorMultiplier, ScalarMultiplier, ABC):
"""
Classic double and add scalar multiplication algorithm.
: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: (Only for LTR, always false for RTL) Whether it starts processing at full order-bit-length.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
always: bool
direction: ProcessingDirection
complete: bool
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 id(self)
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__}({tuple(self.formulas.values())}, short_circuit={self.short_circuit}, accumulation_order={self.accumulation_order}, 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._params.order.bit_length() - 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._params.order.bit_length()
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, 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).
"""
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).
"""
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:
**Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems**
https://link.springer.com/content/pdf/10.1007/3-540-48059-5_25.pdf
"""
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 id(self)
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, 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)
|
