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import warnings
from functools import lru_cache, wraps, partial
from typing import Union
from public import public
from pyecsca.ec.error import (
raise_non_invertible,
raise_non_residue,
NonResidueError,
NonResidueWarning,
)
from pyecsca.ec.mod.base import Mod, cube_root_inner, square_root_inner
has_flint = False
try:
import flint
from flint.utils.flint_exceptions import DomainError
_major, _minor, *_ = flint.__version__.split(".")
if (int(_major), int(_minor)) >= (0, 5):
has_flint = True
else:
flint = None # type: ignore
except ImportError:
flint = None # type: ignore
if has_flint:
@lru_cache
def _fmpz_ctx(n: Union[int, flint.fmpz_mod_ctx]) -> flint.fmpz_mod_ctx:
if type(n) is flint.fmpz_mod_ctx:
return n
return flint.fmpz_mod_ctx(n) # type: ignore
@lru_cache
def _fmpz_is_prime(x: flint.fmpz) -> bool:
return x.is_probable_prime()
def _flint_check(func):
@wraps(func)
def method(self, other):
if self.__class__ is not type(other):
other = self.__class__(other, self.n)
elif self._ctx != other._ctx:
raise ValueError
return func(self, other)
return method
@public
class FlintMod(Mod["FlintMod"]):
"""An element x of ℤₙ. Implemented by flint."""
x: flint.fmpz_mod
_ctx: flint.fmpz_mod_ctx
__slots__ = ("x", "_ctx")
def __init__(
self,
x: Union[int, flint.fmpz_mod],
n: Union[int, flint.fmpz_mod_ctx],
ensure: bool = True,
):
if ensure:
self._ctx = _fmpz_ctx(n)
self.x = self._ctx(x)
else:
self._ctx = n # type: ignore
self.x = x # type: ignore
@property
def n(self) -> flint.fmpz:
return self._ctx.modulus()
def bit_length(self):
return int(self.x).bit_length()
def inverse(self) -> "FlintMod":
if self.x == 0:
raise_non_invertible()
if self.x == 1:
return FlintMod(self._ctx(1), self._ctx, ensure=False)
try:
res = self.x.inverse()
except ZeroDivisionError:
raise_non_invertible()
res = self._ctx(0)
return FlintMod(res, self._ctx, ensure=False)
def is_residue(self) -> bool:
try:
with warnings.catch_warnings(record=True) as warns:
self.sqrt()
if warns and isinstance(warns[0], NonResidueWarning):
return False
except NonResidueError:
return False
return True
def sqrt(self) -> "FlintMod":
mod = self.n
if not _fmpz_is_prime(mod):
raise NotImplementedError
try:
res = flint.fmpz(int(self.x)).sqrtmod(mod)
return FlintMod(self._ctx(res), self._ctx, ensure=False)
except (ValueError, DomainError):
raise_non_residue()
if self.x == 0:
return FlintMod(self._ctx(0), self._ctx, ensure=False)
return square_root_inner(self, self._ctx, lambda x: FlintMod(x, self._ctx, ensure=False))
def is_cubic_residue(self) -> bool:
if not _fmpz_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) -> "FlintMod":
if not _fmpz_is_prime(self.n):
raise NotImplementedError
if self.x == 0:
return FlintMod(self._ctx(0), self._ctx, ensure=False)
if self.x == 1:
return FlintMod(self._ctx(1), self._ctx, ensure=False)
if not self.is_cubic_residue():
raise_non_residue()
return cube_root_inner(self, self._ctx, lambda x: FlintMod(x, self._ctx, ensure=False))
@_flint_check
def __add__(self, other) -> "FlintMod":
return FlintMod(self.x + other.x, self._ctx, ensure=False)
@_flint_check
def __radd__(self, other) -> "Mod":
return self + other
@_flint_check
def __sub__(self, other) -> "FlintMod":
return FlintMod(self.x - other.x, self._ctx, ensure=False)
@_flint_check
def __rsub__(self, other) -> "Mod":
return -self + other
def __neg__(self) -> "FlintMod":
return FlintMod(-self.x, self._ctx, ensure=False)
@_flint_check
def __mul__(self, other) -> "FlintMod":
return FlintMod(self.x * other.x, self._ctx, ensure=False)
@_flint_check
def __rmul__(self, other) -> "Mod":
return self * other
@_flint_check
def __truediv__(self, other) -> "Mod":
return self * ~other
@_flint_check
def __rtruediv__(self, other) -> "Mod":
return ~self * other
@_flint_check
def __floordiv__(self, other) -> "Mod":
return self * ~other
@_flint_check
def __rfloordiv__(self, other) -> "Mod":
return ~self * other
def __bytes__(self):
return int(self.x).to_bytes(
(int(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 == other
if type(other) is not FlintMod:
return False
try:
return self.x == other.x
except ValueError:
return False
def __ne__(self, other):
return not self == other
def __repr__(self):
return str(int(self.x))
def __hash__(self):
return hash(("FlintMod", self.x, self.n))
def __pow__(self, n, _=None) -> "FlintMod":
if type(n) not in (int, flint.fmpz):
raise TypeError
if n == 0:
return FlintMod(self._ctx(1), self._ctx, ensure=False)
if n < 0:
return self.inverse() ** (-n)
if n == 1:
return FlintMod(self.x, self._ctx, ensure=False)
return FlintMod(self.x**n, self._ctx, ensure=False)
def __getstate__(self):
return {"x": int(self.x), "n": int(self.n)}
def __setstate__(self, state):
self._ctx = _fmpz_ctx(state["n"])
self.x = self._ctx(state["x"])
from pyecsca.ec.mod.base import _mod_classes
_mod_classes["flint"] = FlintMod
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