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
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
|
"""This module provides an implementation of ECDSA (Elliptic Curve Digital Signature Algorithm)."""
import hashlib
from typing import Optional, Any
from asn1crypto.core import Sequence, SequenceOf, Integer
from public import public
from .context import Action
from .formula import AdditionFormula
from .mod import Mod
from .mult import ScalarMultiplier
from .params import DomainParameters
from .point import Point
@public
class SignatureResult(object):
"""ECDSA signature result (r, s)."""
r: int
s: int
def __init__(self, r: int, s: int):
self.r = r
self.s = s
@staticmethod
def from_DER(data: bytes) -> "SignatureResult":
"""Load an ECDSA signature from ASN.1 DER data."""
r, s = Sequence.load(data).native.values()
return SignatureResult(r, s)
def to_DER(self) -> bytes:
"""Output this signature into ASN.1 DER."""
obj = SequenceOf(spec=Integer)
obj.append(self.r)
obj.append(self.s)
return obj.dump()
def __eq__(self, other):
if not isinstance(other, SignatureResult):
return False
return self.r == other.r and self.s == other.s
def __str__(self):
return f"(r={self.r}, s={self.s})"
def __repr__(self):
return f"SignatureResult(r={self.r}, s={self.s})"
@public
class ECDSAAction(Action):
"""An ECDSA action base class."""
params: DomainParameters
hash_algo: Optional[Any]
msg: bytes
def __init__(self, params: DomainParameters, hash_algo: Optional[Any], msg: bytes):
super().__init__()
self.params = params
self.hash_algo = hash_algo
self.msg = msg
def __repr__(self):
return f"{self.__class__.__name__}({self.params}, {self.hash_algo}, {self.msg})"
@public
class ECDSASignAction(ECDSAAction):
"""ECDSA signing."""
privkey: Mod
def __init__(
self,
params: DomainParameters,
hash_algo: Optional[Any],
msg: bytes,
privkey: Mod,
):
super().__init__(params, hash_algo, msg)
self.privkey = privkey
def __repr__(self):
return f"{self.__class__.__name__}({self.params}, {self.hash_algo}, {self.msg}, {self.privkey})"
@public
class ECDSAVerifyAction(ECDSAAction):
"""ECDSA verification."""
signature: SignatureResult
pubkey: Point
def __init__(
self,
params: DomainParameters,
hash_algo: Optional[Any],
msg: bytes,
signature: SignatureResult,
pubkey: Point,
):
super().__init__(params, hash_algo, msg)
self.signature = signature
self.pubkey = pubkey
def __repr__(self):
return f"{self.__class__.__name__}({self.params}, {self.hash_algo}, {self.msg}, {self.signature}, {self.pubkey})"
@public
class Signature(object):
"""EC based signature primitive (ECDSA)."""
mult: ScalarMultiplier
params: DomainParameters
add: Optional[AdditionFormula]
pubkey: Optional[Point]
privkey: Optional[Mod]
hash_algo: Optional[Any]
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
hash_algo: Optional[Any] = None,
):
if pubkey is None and privkey is None:
raise ValueError
if add is None:
if "add" not in mult.formulas:
raise ValueError
elif isinstance(mult.formulas["add"], AdditionFormula):
add = mult.formulas["add"]
self.mult = mult
self.params = params
self.add = add
self.pubkey = pubkey
self.privkey = privkey
self.hash_algo = hash_algo
@property
def can_sign(self) -> bool:
"""Whether this instance can sign (has a private key)."""
return self.privkey is not None
@property
def can_verify(self) -> bool:
"""Whether this instance can verify (has a public key and add formula)."""
return self.pubkey is not None and self.add is not None
def _get_nonce(self, nonce: Optional[int]) -> Mod:
if nonce is None:
return Mod.random(self.params.order)
else:
return Mod(nonce, self.params.order)
def _do_sign(self, nonce: Mod, digest: bytes) -> SignatureResult:
z = int.from_bytes(digest, byteorder="big")
if len(digest) * 8 > self.params.order.bit_length():
z >>= len(digest) * 8 - self.params.order.bit_length()
self.mult.init(self.params, self.params.generator)
point = self.mult.multiply(int(nonce))
affine_point = point.to_affine()
r = Mod(int(affine_point.x), self.params.order)
s = nonce.inverse() * (Mod(z, self.params.order) + r * self.privkey)
return SignatureResult(int(r), int(s))
def sign_hash(self, digest: bytes, nonce: Optional[int] = None) -> SignatureResult:
"""Sign already hashed data."""
if not self.can_sign:
raise RuntimeError("This instance cannot sign.")
k = self._get_nonce(nonce)
return self._do_sign(k, digest)
def sign_data(self, data: bytes, nonce: Optional[int] = None) -> SignatureResult:
"""Sign data."""
if not self.can_sign or self.privkey is None:
raise RuntimeError("This instance cannot sign.")
with ECDSASignAction(self.params, self.hash_algo, data, self.privkey):
k = self._get_nonce(nonce)
if self.hash_algo is None:
digest = data
else:
digest = self.hash_algo(data).digest()
return self._do_sign(k, digest)
def _do_verify(self, signature: SignatureResult, digest: bytes) -> bool:
if self.pubkey is None or self.add is None:
return False
z = int.from_bytes(digest, byteorder="big")
if len(digest) * 8 > self.params.order.bit_length():
z >>= len(digest) * 8 - self.params.order.bit_length()
c = Mod(signature.s, self.params.order).inverse()
u1 = Mod(z, self.params.order) * c
u2 = Mod(signature.r, self.params.order) * c
self.mult.init(self.params, self.params.generator)
p1 = self.mult.multiply(int(u1))
self.mult.init(self.params, self.pubkey)
p2 = self.mult.multiply(int(u2))
p = self.add(self.params.curve.prime, p1, p2, **self.params.curve.parameters)[0]
affine = p.to_affine()
v = Mod(int(affine.x), self.params.order)
return signature.r == int(v)
def verify_hash(self, signature: SignatureResult, digest: bytes) -> bool:
"""Verify already hashed data."""
if not self.can_verify:
raise RuntimeError("This instance cannot verify.")
return self._do_verify(signature, digest)
def verify_data(self, signature: SignatureResult, data: bytes) -> bool:
"""Verify data."""
if not self.can_verify or self.pubkey is None:
raise RuntimeError("This instance cannot verify.")
with ECDSAVerifyAction(
self.params, self.hash_algo, data, signature, self.pubkey
):
if self.hash_algo is None:
digest = data
else:
digest = self.hash_algo(data).digest()
return self._do_verify(signature, digest)
@public
class ECDSA_NONE(Signature):
"""ECDSA with raw message input."""
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
):
super().__init__(mult, params, add, pubkey, privkey)
@public
class ECDSA_SHA1(Signature):
"""ECDSA with SHA1."""
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
):
super().__init__(mult, params, add, pubkey, privkey, hashlib.sha1)
@public
class ECDSA_SHA224(Signature):
"""ECDSA with SHA224."""
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
):
super().__init__(mult, params, add, pubkey, privkey, hashlib.sha224)
@public
class ECDSA_SHA256(Signature):
"""ECDSA with SHA256."""
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
):
super().__init__(mult, params, add, pubkey, privkey, hashlib.sha256)
@public
class ECDSA_SHA384(Signature):
"""ECDSA with SHA384."""
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
):
super().__init__(mult, params, add, pubkey, privkey, hashlib.sha384)
@public
class ECDSA_SHA512(Signature):
"""ECDSA with SHA512."""
def __init__(
self,
mult: ScalarMultiplier,
params: DomainParameters,
add: Optional[AdditionFormula] = None,
pubkey: Optional[Point] = None,
privkey: Optional[Mod] = None,
):
super().__init__(mult, params, add, pubkey, privkey, hashlib.sha512)
|
