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from copy import copy
from typing import Mapping, Tuple, Optional, List
from pyecsca.ec.naf import naf, wnaf
from .context import Context
from .curve import EllipticCurve
from .formula import Formula, AdditionFormula, DoublingFormula, ScalingFormula, LadderFormula
from .point import Point
class ScalarMultiplier(object):
curve: EllipticCurve
formulas: Mapping[str, Formula]
context: Context
_point: Point = None
def __init__(self, curve: EllipticCurve, ctx: Context = None, **formulas: Optional[Formula]):
for formula in formulas.values():
if formula is not None and formula.coordinate_model is not curve.coordinate_model:
raise ValueError
self.curve = curve
if ctx:
self.context = ctx
else:
self.context = Context()
self.formulas = dict(filter(lambda pair: pair[1] is not None, formulas.items()))
def _add(self, one: Point, other: Point) -> Point:
if "add" not in self.formulas:
raise NotImplementedError
if one == self.curve.neutral:
return copy(other)
if other == self.curve.neutral:
return copy(one)
return self.context.execute(self.formulas["add"], one, other, **self.curve.parameters)[0]
def _dbl(self, point: Point) -> Point:
if "dbl" not in self.formulas:
raise NotImplementedError
if point == self.curve.neutral:
return copy(point)
return self.context.execute(self.formulas["dbl"], point, **self.curve.parameters)[0]
def _scl(self, point: Point) -> Point:
if "scl" not in self.formulas:
raise NotImplementedError
return self.context.execute(self.formulas["scl"], point, **self.curve.parameters)[0]
def _ladd(self, start: Point, to_dbl: Point, to_add: Point) -> Tuple[Point, ...]:
if "ladd" not in self.formulas:
raise NotImplementedError
return self.context.execute(self.formulas["ladd"], start, to_dbl, to_add,
**self.curve.parameters)
def _neg(self, point: Point) -> Point:
# TODO
raise NotImplementedError
def init(self, point: Point):
self._point = point
def _init_multiply(self, point: Optional[Point]) -> Point:
if point is None:
if self._point is None:
raise ValueError
else:
if self._point != point:
self.init(point)
return self._point
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
raise NotImplementedError
class LTRMultiplier(ScalarMultiplier):
always: bool
def __init__(self, curve: EllipticCurve, add: AdditionFormula, dbl: DoublingFormula,
scl: ScalingFormula = None,
ctx: Context = None, always: bool = False):
super().__init__(curve, ctx, add=add, dbl=dbl, scl=scl)
self.always = always
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
q = self._init_multiply(point)
r = copy(self.curve.neutral)
for i in range(scalar.bit_length(), -1, -1):
r = self._dbl(r)
if scalar & (1 << i) != 0:
r = self._add(r, q)
elif self.always:
self._add(r, q)
if "scl" in self.formulas:
r = self._scl(r)
return r
class RTLMultiplier(ScalarMultiplier):
always: bool
def __init__(self, curve: EllipticCurve, add: AdditionFormula, dbl: DoublingFormula,
scl: ScalingFormula = None,
ctx: Context = None, always: bool = False):
super().__init__(curve, ctx, add=add, dbl=dbl, scl=scl)
self.always = always
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
q = self._init_multiply(point)
r = copy(self.curve.neutral)
while scalar > 0:
if scalar & 1 != 0:
r = self._add(r, q)
elif self.always:
self._add(r, q)
q = self._dbl(q)
scalar >>= 1
if "scl" in self.formulas:
r = self._scl(r)
return r
class LadderMultiplier(ScalarMultiplier):
def __init__(self, curve: EllipticCurve, ladd: LadderFormula, scl: ScalingFormula = None,
ctx: Context = None):
super().__init__(curve, ctx, ladd=ladd, scl=scl)
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
q = self._init_multiply(point)
p0 = copy(q)
p1 = self._ladd(self.curve.neutral, q, q)[1]
for i in range(scalar.bit_length(), -1, -1):
if scalar & i != 0:
p0, p1 = self._ladd(q, p1, p0)
else:
p0, p1 = self._ladd(q, p0, p1)
if "scl" in self.formulas:
p0 = self._scl(p0)
return p0
class BinaryNAFMultiplier(ScalarMultiplier):
_point_neg: Point
def __init__(self, curve: EllipticCurve, add: AdditionFormula, dbl: DoublingFormula,
scl: ScalingFormula = None,
ctx: Context = None):
super().__init__(curve, ctx, add=add, dbl=dbl, scl=scl)
def init(self, point: Point):
super().init(point)
self._point_neg = self._neg(point)
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
self._init_multiply(point)
bnaf = naf(scalar)
q = copy(self.curve.neutral)
for val in bnaf:
q = self._dbl(q)
if val == 1:
q = self._add(q, self._point)
if val == -1:
q = self._add(q, self._point_neg)
return q
class WindowNAFMultiplier(ScalarMultiplier):
_points: List[Point]
_width: int
def __init__(self, curve: EllipticCurve, add: AdditionFormula, dbl: DoublingFormula, width: int,
scl: ScalingFormula = None,
ctx: Context = None):
super().__init__(curve, ctx, add=add, dbl=dbl, scl=scl)
self._width = width
def init(self, point: Point):
self._point = point
# TODO: precompute {1, 3, 5, upto 2^(w-1)-1}
def multiply(self, scalar: int, point: Optional[Point] = None):
self._init_multiply(point)
naf = wnaf(scalar, self._width)
q = copy(self.curve.neutral)
for val in naf:
q = self._dbl(q)
if val > 0:
q = self._add(q, self._points[val])
elif val < 0:
neg = self._neg(self._points[-val])
q = self._add(q, neg)
return q
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