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
|
from public import public
from pyecsca.ec.error import (
raise_non_invertible,
raise_non_residue,
)
from pyecsca.ec.mod.base import Mod, extgcd, miller_rabin, jacobi, cube_root_inner, square_root_inner
@public
class RawMod(Mod):
"""An element x of ℤₙ (implemented using Python integers)."""
x: int
n: int
__slots__ = ("x", "n")
def __init__(self, x: int, n: int):
self.x = x % n
self.n = n
def bit_length(self):
return self.x.bit_length()
def inverse(self) -> "RawMod":
if self.x == 0:
raise_non_invertible()
x, _, d = extgcd(self.x, self.n)
if d != 1:
raise_non_invertible()
return RawMod(x, self.n)
def is_residue(self):
if not miller_rabin(self.n):
raise NotImplementedError
if self.x == 0:
return True
if self.n == 2:
return self.x in (0, 1)
legendre_symbol = jacobi(self.x, self.n)
return legendre_symbol == 1
def sqrt(self) -> "RawMod":
if not miller_rabin(self.n):
raise NotImplementedError
if self.x == 0:
return RawMod(0, self.n)
if not self.is_residue():
raise_non_residue()
return square_root_inner(self, int, lambda x: RawMod(x, self.n))
def is_cubic_residue(self):
if not miller_rabin(self.n):
raise NotImplementedError
if self.x in (0, 1):
return True
if self.n % 3 == 2:
return True
pm1 = self.n - 1
r = self ** (pm1 // 3)
return r == 1
def cube_root(self) -> "RawMod":
if not miller_rabin(self.n):
raise NotImplementedError
if self.x == 0:
return RawMod(0, self.n)
if self.x == 1:
return RawMod(1, self.n)
if not self.is_cubic_residue():
raise_non_residue()
return cube_root_inner(self, int, lambda x: RawMod(x, self.n))
def __bytes__(self):
return self.x.to_bytes((self.n.bit_length() + 7) // 8, byteorder="big")
def __int__(self):
return self.x
def __eq__(self, other):
if type(other) is int:
return self.x == (other % self.n)
if type(other) is not RawMod:
return False
return self.x == other.x and self.n == other.n
def __ne__(self, other):
return not self == other
def __repr__(self):
return str(self.x)
def __hash__(self):
return hash(("RawMod", self.x, self.n))
def __pow__(self, n, _=None) -> "RawMod":
if type(n) is not int:
raise TypeError
if n == 0:
return RawMod(1, self.n)
if n < 0:
return self.inverse() ** (-n)
if n == 1:
return RawMod(self.x, self.n)
return RawMod(pow(self.x, n, self.n), self.n)
from pyecsca.ec.mod.base import _mod_classes # noqa
_mod_classes["python"] = RawMod
|
