1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
|
"""Provides Comb-like scalar multipliers, such as BGMW or Lim-Lee."""
from copy import copy
from math import ceil
from typing import MutableMapping, Optional
from public import public
from pyecsca.ec.formula import AdditionFormula, DoublingFormula, ScalingFormula
from pyecsca.ec.mult import (
AccumulatorMultiplier,
ScalarMultiplier,
ProcessingDirection,
AccumulationOrder,
PrecomputationAction,
ScalarMultiplicationAction,
)
from pyecsca.ec.params import DomainParameters
from pyecsca.ec.point import Point
from pyecsca.ec.scalar import convert_base
@public
class BGMWMultiplier(AccumulatorMultiplier, ScalarMultiplier):
"""
Brickell, Gordon, McCurley and Wilson (BGMW) scalar multiplier,
or rather, its one parametrization.
Algorithm 3.41 from [GECC]_
:param width: Window width.
:param direction: Whether it is LTR or RTL.
:param accumulation_order: The order of accumulation of points.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
direction: ProcessingDirection
"""Whether it is LTR or RTL."""
width: int
"""Window width."""
_points: MutableMapping[int, Point]
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
width: int,
scl: Optional[ScalingFormula] = None,
direction: ProcessingDirection = ProcessingDirection.LTR,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
accumulation_order=accumulation_order,
add=add,
dbl=dbl,
scl=scl,
)
self.direction = direction
self.width = width
def __hash__(self):
return hash(
(
BGMWMultiplier,
super().__hash__(),
self.width,
self.direction,
self.accumulation_order,
)
)
def __eq__(self, other):
if not isinstance(other, BGMWMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.width == other.width
and self.direction == other.direction
and self.accumulation_order == other.accumulation_order
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, width={self.width}, direction={self.direction.name}, accumulation_order={self.accumulation_order.name})"
def init(self, params: DomainParameters, point: Point):
with PrecomputationAction(params, point):
super().init(params, point)
d = ceil(params.order.bit_length() / self.width)
self._points = {}
current_point = point
for i in range(d):
self._points[i] = current_point
if i != d - 1:
for _ in range(self.width):
current_point = self._dbl(current_point)
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))
a = copy(self._params.curve.neutral)
b = copy(self._params.curve.neutral)
recoded = convert_base(scalar, 2**self.width)
for j in range(2**self.width - 1, 0, -1):
if self.direction == ProcessingDirection.RTL:
for i, ki in enumerate(recoded):
if ki == j:
b = self._accumulate(b, self._points[i])
elif self.direction == ProcessingDirection.LTR:
for i, ki in reversed(list(enumerate(recoded))):
if ki == j:
b = self._accumulate(b, self._points[i])
if self.short_circuit and a == b:
# TODO: Double necessary here for incomplete formulas, maybe another param and not reuse short_cirtuit?
a = self._dbl(b)
else:
a = self._accumulate(a, b)
if "scl" in self.formulas:
a = self._scl(a)
return action.exit(a)
@public
class CombMultiplier(AccumulatorMultiplier, ScalarMultiplier):
"""
Comb multiplier.
Algorithm 3.44 from [GECC]_
:param width: Window width (number of comb teeth).
:param accumulation_order: The order of accumulation of points.
"""
requires = {AdditionFormula, DoublingFormula}
optionals = {ScalingFormula}
width: int
"""Window width."""
_points: MutableMapping[int, Point]
def __init__(
self,
add: AdditionFormula,
dbl: DoublingFormula,
width: int,
scl: Optional[ScalingFormula] = None,
accumulation_order: AccumulationOrder = AccumulationOrder.PeqPR,
short_circuit: bool = True,
):
super().__init__(
short_circuit=short_circuit,
accumulation_order=accumulation_order,
add=add,
dbl=dbl,
scl=scl,
)
self.width = width
def __hash__(self):
return hash(
(CombMultiplier, super().__hash__(), self.width, self.accumulation_order)
)
def __eq__(self, other):
if not isinstance(other, CombMultiplier):
return False
return (
self.formulas == other.formulas
and self.short_circuit == other.short_circuit
and self.width == other.width
and self.accumulation_order == other.accumulation_order
)
def __repr__(self):
return f"{self.__class__.__name__}({', '.join(map(str, self.formulas.values()))}, short_circuit={self.short_circuit}, width={self.width}, accumulation_order={self.accumulation_order.name})"
def init(self, params: DomainParameters, point: Point):
with PrecomputationAction(params, point):
super().init(params, point)
d = ceil(params.order.bit_length() / self.width)
base_points = {}
current_point = point
for i in range(self.width):
base_points[i] = current_point
if i != d - 1:
for _ in range(d):
current_point = self._dbl(current_point)
self._points = {}
for j in range(1, 2**self.width):
points = []
for i in range(self.width):
if j & (1 << i):
points.append(base_points[i])
self._points[j] = points[0]
for other in points[1:]:
self._points[j] = self._accumulate(self._points[j], other)
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 = copy(self._params.curve.neutral)
d = ceil(self._params.order.bit_length() / self.width)
recoded = convert_base(scalar, 2**d)
if len(recoded) != self.width:
recoded.extend([0] * (self.width - len(recoded)))
for i in range(d - 1, -1, -1):
q = self._dbl(q)
word = 0
for j in range(self.width):
# get i-th bit of recoded[j] and set it into the j-th bit of word
bit = (recoded[j] >> i) & 1
word |= bit << j
if word:
q = self._accumulate(q, self._points[word])
# TODO always
if "scl" in self.formulas:
q = self._scl(q)
return action.exit(q)
|
