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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
@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()
if self.n % 4 == 3:
return self ** int((self.n + 1) // 4)
q = self.n - 1
s = 0
while q % 2 == 0:
q //= 2
s += 1
z = 2
while RawMod(z, self.n).is_residue():
z += 1
m = s
c = RawMod(z, self.n) ** q
t = self**q
r_exp = (q + 1) // 2
r = self**r_exp
while t != 1:
i = 1
while not (t ** (2**i)) == 1:
i += 1
two_exp = m - (i + 1)
b = c ** int(RawMod(2, self.n) ** two_exp)
m = int(RawMod(i, self.n))
c = b**2
t *= c
r *= b
return r
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
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