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"""Provides ladder-based scalar multipliers, either using the ladder formula, or (diffadd, dbl) or (add, dbl)."""
from copy import copy
from typing import Optional
from public import public
from pyecsca.ec.mult.base import ScalarMultiplier, ScalarMultiplicationAction
from pyecsca.ec.formula import (
AdditionFormula,
DoublingFormula,
ScalingFormula,
LadderFormula,
DifferentialAdditionFormula,
)
from pyecsca.ec.point import Point
@public
class LadderMultiplier(ScalarMultiplier):
"""
Montgomery ladder multiplier, using a three input, two output ladder formula.
Optionally takes a doubling formula, and if both `complete` and `full` is false, it requires one.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param complete: Whether it starts processing at full order-bit-length.
:param full: Whether it start processing at top bit of the scalar.
"""
requires = {LadderFormula}
optionals = {DoublingFormula, ScalingFormula}
complete: bool
"""Whether it starts processing at full order-bit-length."""
full: bool
"""Whether it start processing at top bit of the scalar."""
def __init__(
self,
ladd: LadderFormula,
dbl: Optional[DoublingFormula] = None,
scl: Optional[ScalingFormula] = None,
complete: bool = True,
short_circuit: bool = True,
full: bool = False,
):
super().__init__(short_circuit=short_circuit, ladd=ladd, dbl=dbl, scl=scl)
self.complete = complete
self.full = full
if complete and full:
raise ValueError("Only one of `complete` and `full` can be set.")
if dbl is None:
if short_circuit:
raise ValueError(
"When `short_circuit` is set LadderMultiplier requires a doubling formula."
)
if not (complete or full):
raise ValueError(
"When neither `complete` nor `full` is not set LadderMultiplier requires a doubling formula."
)
def __hash__(self):
return hash((LadderMultiplier, super().__hash__(), self.complete, self.full))
def __eq__(self, other):
if not isinstance(other, LadderMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.complete == other.complete
and self.full == other.full
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, complete={self.complete}, full={self.full})"
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
if self.complete:
p0 = copy(self._params.curve.neutral)
p1 = self._point
top = self._bits - 1
elif self.full:
p0 = copy(self._params.curve.neutral)
p1 = self._point
top = scalar.bit_length() - 1
else:
p0 = copy(q)
p1 = self._dbl(q)
top = scalar.bit_length() - 2
for i in range(top, -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 action.exit(p0)
@public
class SimpleLadderMultiplier(ScalarMultiplier):
"""
Montgomery ladder multiplier, using addition and doubling formulas.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param complete: Whether it starts processing at full order-bit-length.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
complete: bool
"""Whether it starts processing at full order-bit-length."""
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
scl: Optional[ScalingFormula] = None,
complete: bool = True,
short_circuit: bool = True,
):
super().__init__(short_circuit=short_circuit, add=add, dbl=dbl, scl=scl)
self.complete = complete
def __hash__(self):
return hash((SimpleLadderMultiplier, super().__hash__(), self.complete))
def __eq__(self, other):
if not isinstance(other, SimpleLadderMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.complete == other.complete
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, complete={self.complete})"
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.complete:
top = self._bits - 1
else:
top = scalar.bit_length() - 1
p0 = copy(self._params.curve.neutral)
p1 = copy(self._point)
for i in range(top, -1, -1):
if scalar & (1 << i) == 0:
p1 = self._add(p0, p1)
p0 = self._dbl(p0)
else:
p0 = self._add(p0, p1)
p1 = self._dbl(p1)
if "scl" in self.formulas:
p0 = self._scl(p0)
return action.exit(p0)
@public
class DifferentialLadderMultiplier(ScalarMultiplier):
"""
Montgomery ladder multiplier, using differential addition and doubling formulas.
:param short_circuit: Whether the use of formulas will be guarded by short-circuit on inputs
of the point at infinity.
:param complete: Whether it starts processing at full order-bit-length.
"""
requires = {DifferentialAdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
complete: bool
"""Whether it starts processing at full order-bit-length."""
full: bool
"""Whether it start processing at top bit of the scalar."""
def __init__(
self,
dadd: DifferentialAdditionFormula,
dbl: DoublingFormula,
scl: Optional[ScalingFormula] = None,
complete: bool = True,
short_circuit: bool = True,
full: bool = False,
):
super().__init__(short_circuit=short_circuit, dadd=dadd, dbl=dbl, scl=scl)
self.complete = complete
self.full = full
if complete and full:
raise ValueError("Only one of `complete` and `full` can be set.")
def __hash__(self):
return hash(
(DifferentialLadderMultiplier, super().__hash__(), self.complete, self.full)
)
def __eq__(self, other):
if not isinstance(other, DifferentialLadderMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.complete == other.complete
and self.full == other.full
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, complete={self.complete}, full={self.full})"
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
if self.complete:
p0 = copy(self._params.curve.neutral)
p1 = copy(q)
top = self._bits - 1
elif self.full:
p0 = copy(self._params.curve.neutral)
p1 = copy(q)
top = scalar.bit_length() - 1
else:
p0 = copy(q)
p1 = self._dbl(q)
top = scalar.bit_length() - 2
for i in range(top, -1, -1):
if scalar & (1 << i) == 0:
p1 = self._dadd(q, p0, p1)
p0 = self._dbl(p0)
else:
p0 = self._dadd(q, p0, p1)
p1 = self._dbl(p1)
if "scl" in self.formulas:
p0 = self._scl(p0)
return action.exit(p0)
|
