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from functools import lru_cache, wraps, partial
from typing import Union
from public import public
from pyecsca.ec.mod.base import Mod, cube_root_inner, square_root_inner
from pyecsca.ec.error import (
raise_non_invertible,
raise_non_residue,
)
has_gmp = False
try:
import gmpy2
has_gmp = True
except ImportError:
gmpy2 = None
def _check(func):
@wraps(func)
def method(self, other):
if self.__class__ is not type(other):
other = self.__class__(other, self.n)
elif self.n != other.n:
raise ValueError
return func(self, other)
return method
if has_gmp:
@lru_cache
def _gmpy_is_prime(x) -> bool:
return gmpy2.is_prime(x)
@public
class GMPMod(Mod["GMPMod"]):
"""An element x of ℤₙ. Implemented by GMP."""
x: gmpy2.mpz
n: gmpy2.mpz
__slots__ = ("x", "n")
def __init__(
self,
x: Union[int, gmpy2.mpz],
n: Union[int, gmpy2.mpz],
ensure: bool = True,
):
if ensure:
self.n = gmpy2.mpz(n)
self.x = gmpy2.mpz(x % self.n)
else:
self.n = n
self.x = x
def bit_length(self):
return self.x.bit_length()
def inverse(self) -> "GMPMod":
if self.x == 0:
raise_non_invertible()
if self.x == 1:
return GMPMod(gmpy2.mpz(1), self.n, ensure=False)
try:
res = gmpy2.invert(self.x, self.n)
except ZeroDivisionError:
raise_non_invertible()
res = gmpy2.mpz(0)
return GMPMod(res, self.n, ensure=False)
def is_residue(self) -> bool:
if not _gmpy_is_prime(self.n):
raise NotImplementedError
if self.x == 0:
return True
if self.n == 2:
return self.x in (0, 1)
return gmpy2.legendre(self.x, self.n) == 1
def sqrt(self) -> "GMPMod":
if not _gmpy_is_prime(self.n):
raise NotImplementedError
if self.x == 0:
return GMPMod(gmpy2.mpz(0), self.n, ensure=False)
if not self.is_residue():
raise_non_residue()
return square_root_inner(self, gmpy2.mpz, lambda x: GMPMod(x, self.n, ensure=False))
def is_cubic_residue(self) -> bool:
if not _gmpy_is_prime(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) -> "GMPMod":
if not _gmpy_is_prime(self.n):
raise NotImplementedError
if self.x == 0:
return GMPMod(gmpy2.mpz(0), self.n, ensure=False)
if self.x == 1:
return GMPMod(gmpy2.mpz(1), self.n, ensure=False)
if not self.is_cubic_residue():
raise_non_residue()
return cube_root_inner(self, gmpy2.mpz, lambda x: GMPMod(x, self.n, ensure=False))
@_check
def __add__(self, other) -> "GMPMod":
return GMPMod((self.x + other.x) % self.n, self.n, ensure=False)
@_check
def __sub__(self, other) -> "GMPMod":
return GMPMod((self.x - other.x) % self.n, self.n, ensure=False)
def __neg__(self) -> "GMPMod":
return GMPMod(self.n - self.x, self.n, ensure=False)
@_check
def __mul__(self, other) -> "GMPMod":
return GMPMod((self.x * other.x) % self.n, self.n, ensure=False)
def __bytes__(self):
return int(self.x).to_bytes((self.n.bit_length() + 7) // 8, byteorder="big")
def __int__(self):
return int(self.x)
def __eq__(self, other):
if type(other) is int:
return self.x == (gmpy2.mpz(other) % self.n)
if type(other) is not GMPMod:
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(int(self.x))
def __hash__(self):
return hash(("GMPMod", self.x, self.n))
def __pow__(self, n, _=None) -> "GMPMod":
if type(n) not in (int, gmpy2.mpz):
raise TypeError
if n == 0:
return GMPMod(gmpy2.mpz(1), self.n, ensure=False)
if n < 0:
return self.inverse() ** (-n)
if n == 1:
return GMPMod(self.x, self.n, ensure=False)
return GMPMod(
gmpy2.powmod(self.x, gmpy2.mpz(n), self.n), self.n, ensure=False
)
from pyecsca.ec.mod.base import _mod_classes
_mod_classes["gmp"] = GMPMod
|
