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from functools import wraps
from public import public
from sympy import Expr
from pyecsca.ec.mod.base import Mod
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
@public
class SymbolicMod(Mod):
"""A symbolic element x of ℤₙ (implemented using sympy)."""
x: Expr
n: int
__slots__ = ("x", "n")
def __init__(self, x: Expr, n: int):
self.x = x
self.n = n
@_check
def __add__(self, other) -> "SymbolicMod":
return self.__class__((self.x + other.x), self.n)
@_check
def __radd__(self, other) -> "SymbolicMod":
return self + other
@_check
def __sub__(self, other) -> "SymbolicMod":
return self.__class__((self.x - other.x), self.n)
@_check
def __rsub__(self, other) -> "SymbolicMod":
return -self + other
def __neg__(self) -> "SymbolicMod":
return self.__class__(-self.x, self.n)
def bit_length(self) -> int:
raise NotImplementedError
def inverse(self) -> "SymbolicMod":
return self.__class__(self.x ** (-1), self.n)
def is_residue(self) -> bool:
raise NotImplementedError
def sqrt(self) -> "SymbolicMod":
raise NotImplementedError
def is_cubic_residue(self) -> bool:
raise NotImplementedError
def cube_root(self) -> "SymbolicMod":
raise NotImplementedError
def __invert__(self) -> "SymbolicMod":
return self.inverse()
@_check
def __mul__(self, other) -> "SymbolicMod":
return self.__class__(self.x * other.x, self.n)
@_check
def __rmul__(self, other) -> "SymbolicMod":
return self * other
@_check
def __truediv__(self, other) -> "SymbolicMod":
return self * ~other
@_check
def __rtruediv__(self, other) -> "SymbolicMod":
return ~self * other
@_check
def __floordiv__(self, other) -> "SymbolicMod":
return self * ~other
@_check
def __rfloordiv__(self, other) -> "SymbolicMod":
return ~self * other
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 == other % self.n
if type(other) is not SymbolicMod:
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(("SymbolicMod", self.x, self.n))
def __pow__(self, n, _=None) -> "SymbolicMod":
return self.__class__(pow(self.x, n), self.n)
from pyecsca.ec.mod.base import _mod_classes # noqa
_mod_classes["symbolic"] = SymbolicMod
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