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from copy import copy
from typing import Mapping, Tuple, Optional, MutableMapping, Union
from public import public
from .context import getcontext
from .formula import (Formula, AdditionFormula, DoublingFormula, DifferentialAdditionFormula,
ScalingFormula, LadderFormula, NegationFormula)
from .group import AbelianGroup
from .naf import naf, wnaf
from .point import Point
class ScalarMultiplier(object):
group: AbelianGroup
formulas: Mapping[str, Formula]
_point: Point = None
def __init__(self, group: AbelianGroup, **formulas: Optional[Formula]):
for formula in formulas.values():
if formula is not None and formula.coordinate_model is not group.curve.coordinate_model:
raise ValueError
self.group = group
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.group.neutral:
return copy(other)
if other == self.group.neutral:
return copy(one)
return \
getcontext().execute(self.formulas["add"], one, other, **self.group.curve.parameters)[0]
def _dbl(self, point: Point) -> Point:
if "dbl" not in self.formulas:
raise NotImplementedError
if point == self.group.neutral:
return copy(point)
return getcontext().execute(self.formulas["dbl"], point, **self.group.curve.parameters)[0]
def _scl(self, point: Point) -> Point:
if "scl" not in self.formulas:
raise NotImplementedError
return getcontext().execute(self.formulas["scl"], point, **self.group.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 getcontext().execute(self.formulas["ladd"], start, to_dbl, to_add,
**self.group.curve.parameters)
def _dadd(self, start: Point, one: Point, other: Point) -> Point:
if "dadd" not in self.formulas:
raise NotImplementedError
if one == self.group.neutral:
return copy(other)
if other == self.group.neutral:
return copy(one)
return getcontext().execute(self.formulas["dadd"], start, one, other,
**self.group.curve.parameters)[0]
def _neg(self, point: Point) -> Point:
if "neg" not in self.formulas:
raise NotImplementedError
return getcontext().execute(self.formulas["neg"], point, **self.group.curve.parameters)[0]
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
@public
class LTRMultiplier(ScalarMultiplier):
"""
Classic double and add scalar multiplication algorithm, that scans the scalar left-to-right (msb to lsb)
The `always` parameter determines whether the double and add always method is used.
"""
always: bool
def __init__(self, group: AbelianGroup, add: AdditionFormula, dbl: DoublingFormula,
scl: ScalingFormula = None, always: bool = False):
super().__init__(group, add=add, dbl=dbl, scl=scl)
self.always = always
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
if scalar == 0:
return copy(self.group.neutral)
q = self._init_multiply(point)
r = copy(self.group.neutral)
for i in range(scalar.bit_length() - 1, -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
@public
class RTLMultiplier(ScalarMultiplier):
"""
Classic double and add scalar multiplication algorithm, that scans the scalar right-to-left (lsb to msb)
The `always` parameter determines whether the double and add always method is used.
"""
always: bool
def __init__(self, group: AbelianGroup, add: AdditionFormula, dbl: DoublingFormula,
scl: ScalingFormula = None, always: bool = False):
super().__init__(group, add=add, dbl=dbl, scl=scl)
self.always = always
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
if scalar == 0:
return copy(self.group.neutral)
q = self._init_multiply(point)
r = copy(self.group.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 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
"""
def __init__(self, group: AbelianGroup, add: AdditionFormula, dbl: DoublingFormula,
scl: ScalingFormula = None):
super().__init__(group, add=add, dbl=dbl, scl=scl)
def multiply(self, scalar: int, point: Optional[Point] = None):
if scalar == 0:
return copy(self.group.neutral)
q = self._init_multiply(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 p0
@public
class LadderMultiplier(ScalarMultiplier):
"""
Montgomery ladder multiplier, using a three input, two output ladder formula.
"""
def __init__(self, group: AbelianGroup, ladd: LadderFormula, dbl: DoublingFormula,
scl: ScalingFormula = None):
super().__init__(group, ladd=ladd, dbl=dbl, scl=scl)
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
if scalar == 0:
return copy(self.group.neutral)
q = self._init_multiply(point)
p0 = copy(q)
p1 = self._dbl(q)
for i in range(scalar.bit_length() - 2, -1, -1):
if scalar & (1 << i) == 0:
p0, p1 = self._ladd(q, p0, p1)
else:
p1, p0 = self._ladd(q, p1, p0)
if "scl" in self.formulas:
p0 = self._scl(p0)
return p0
@public
class SimpleLadderMultiplier(ScalarMultiplier):
"""
Montgomery ladder multiplier, using addition and doubling formulas.
"""
_differential: bool = False
def __init__(self, group: AbelianGroup,
add: Union[AdditionFormula, DifferentialAdditionFormula], dbl: DoublingFormula,
scl: ScalingFormula = None):
if isinstance(add, AdditionFormula):
super().__init__(group, add=add, dbl=dbl, scl=scl)
elif isinstance(add, DifferentialAdditionFormula):
super().__init__(group, dadd=add, dbl=dbl, scl=scl)
self._differential = True
else:
raise ValueError
def multiply(self, scalar: int, point: Optional[Point] = None) -> Point:
if scalar == 0:
return copy(self.group.neutral)
q = self._init_multiply(point)
p0 = copy(self.group.neutral)
p1 = copy(q)
for i in range(scalar.bit_length() - 1, -1, -1):
if scalar & (1 << i) == 0:
if self._differential:
p1 = self._dadd(q, p0, p1)
else:
p1 = self._add(p0, p1)
p0 = self._dbl(p0)
else:
if self._differential:
p0 = self._dadd(q, p0, p1)
else:
p0 = self._add(p0, p1)
p1 = self._dbl(p1)
if "scl" in self.formulas:
p0 = self._scl(p0)
return p0
@public
class BinaryNAFMultiplier(ScalarMultiplier):
"""
Binary NAF (Non Adjacent Form) multiplier, left-to-right.
"""
_point_neg: Point
def __init__(self, group: AbelianGroup, add: AdditionFormula, dbl: DoublingFormula,
neg: NegationFormula, scl: ScalingFormula = None):
super().__init__(group, add=add, dbl=dbl, neg=neg, 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:
if scalar == 0:
return copy(self.group.neutral)
self._init_multiply(point)
bnaf = naf(scalar)
q = copy(self.group.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)
if "scl" in self.formulas:
q = self._scl(q)
return q
@public
class WindowNAFMultiplier(ScalarMultiplier):
"""
Window NAF (Non Adjacent Form) multiplier, left-to-right.
"""
_points: MutableMapping[int, Point]
_points_neg: MutableMapping[int, Point]
_precompute_neg: bool = False
_width: int
def __init__(self, group: AbelianGroup, add: AdditionFormula, dbl: DoublingFormula,
neg: NegationFormula, width: int, scl: ScalingFormula = None,
precompute_negation: bool = False):
super().__init__(group, add=add, dbl=dbl, neg=neg, scl=scl)
self._width = width
self._precompute_neg = precompute_negation
def init(self, point: Point):
self._point = point
self._points = {}
self._points_neg = {}
current_point = point
double_point = self._dbl(point)
for i in range(1, (self._width + 1) // 2 + 1):
self._points[2 ** i - 1] = current_point
if self._precompute_neg:
self._points_neg[2 ** i - 1] = self._neg(current_point)
current_point = self._add(current_point, double_point)
def multiply(self, scalar: int, point: Optional[Point] = None):
if scalar == 0:
return copy(self.group.neutral)
self._init_multiply(point)
naf = wnaf(scalar, self._width)
q = copy(self.group.neutral)
for val in naf:
q = self._dbl(q)
if val > 0:
q = self._add(q, self._points[val])
elif val < 0:
if self._precompute_neg:
neg = self._points_neg[-val]
else:
neg = self._neg(self._points[-val])
q = self._add(q, neg)
if "scl" in self.formulas:
q = self._scl(q)
return q
|
