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from functools import (
total_ordering,
)
from typing import (
TYPE_CHECKING,
Any,
List,
Sequence,
Tuple,
Type,
TypeVar,
Union,
cast,
)
from py_ecc.utils import (
deg,
poly_rounded_div,
prime_field_inv,
)
if TYPE_CHECKING:
from py_ecc.typing import (
FQ2_modulus_coeffs_type,
FQ12_modulus_coeffs_type,
)
# These new TypeVars are needed because these classes are kind of base classes and
# we need the output type to correspond to the type of the inherited class
T_FQ = TypeVar("T_FQ", bound="FQ")
T_FQP = TypeVar("T_FQP", bound="FQP")
T_FQ2 = TypeVar("T_FQ2", bound="FQ2")
T_FQ12 = TypeVar("T_FQ12", bound="FQ12")
IntOrFQ = Union[int, "FQ"]
@total_ordering
class FQ:
"""
A class for field elements in FQ. Wrap a number in this class,
and it becomes a field element.
"""
n: int
field_modulus: int
def __init__(self: T_FQ, val: IntOrFQ) -> None:
if not hasattr(self, "field_modulus"):
raise AttributeError("Field Modulus hasn't been specified")
if isinstance(val, FQ):
self.n = val.n
elif isinstance(val, int):
self.n = val % self.field_modulus
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(val)}"
)
def __add__(self: T_FQ, other: IntOrFQ) -> T_FQ:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return type(self)((self.n + on) % self.field_modulus)
def __mul__(self: T_FQ, other: IntOrFQ) -> T_FQ:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return type(self)((self.n * on) % self.field_modulus)
def __rmul__(self: T_FQ, other: IntOrFQ) -> T_FQ:
return self * other
def __radd__(self: T_FQ, other: IntOrFQ) -> T_FQ:
return self + other
def __rsub__(self: T_FQ, other: IntOrFQ) -> T_FQ:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return type(self)((on - self.n) % self.field_modulus)
def __sub__(self: T_FQ, other: IntOrFQ) -> T_FQ:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return type(self)((self.n - on) % self.field_modulus)
def __div__(self: T_FQ, other: IntOrFQ) -> T_FQ:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return type(self)(
self.n * prime_field_inv(on, self.field_modulus) % self.field_modulus
)
def __truediv__(self: T_FQ, other: IntOrFQ) -> T_FQ:
return self.__div__(other)
def __rdiv__(self: T_FQ, other: IntOrFQ) -> T_FQ:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return type(self)(
prime_field_inv(self.n, self.field_modulus) * on % self.field_modulus
)
def __rtruediv__(self: T_FQ, other: IntOrFQ) -> T_FQ:
return self.__rdiv__(other)
def __pow__(self: T_FQ, other: int) -> T_FQ:
if other == 0:
return type(self)(1)
elif other == 1:
return type(self)(self.n)
elif other % 2 == 0:
return (self * self) ** (other // 2)
else:
return ((self * self) ** int(other // 2)) * self
def __eq__(self: T_FQ, other: Any) -> bool:
if isinstance(other, FQ):
return self.n == other.n
elif isinstance(other, int):
return self.n == other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
def __ne__(self: T_FQ, other: Any) -> bool:
return not self == other
def __neg__(self: T_FQ) -> T_FQ:
return type(self)(-self.n)
def __repr__(self: T_FQ) -> str:
return repr(self.n)
def __int__(self: T_FQ) -> int:
return self.n
def __lt__(self: T_FQ, other: IntOrFQ) -> bool:
if isinstance(other, FQ):
on = other.n
elif isinstance(other, int):
on = other
else:
raise TypeError(
f"Expected an int or FQ object, but got object of type {type(other)}"
)
return self.n < on
@classmethod
def one(cls: Type[T_FQ]) -> T_FQ:
return cls(1)
@classmethod
def zero(cls: Type[T_FQ]) -> T_FQ:
return cls(0)
int_types_or_FQ = (int, FQ)
class FQP:
"""
A class for elements in polynomial extension fields
"""
degree: int = 0
field_modulus: int
def __init__(
self, coeffs: Sequence[IntOrFQ], modulus_coeffs: Sequence[IntOrFQ] = ()
) -> None:
if not hasattr(self, "field_modulus"):
raise AttributeError("Field Modulus hasn't been specified")
if len(coeffs) != len(modulus_coeffs):
raise Exception("coeffs and modulus_coeffs aren't of the same length")
# Encoding all coefficients in the corresponding type FQ
self.FQP_corresponding_FQ_class = type(
"FQP_corresponding_FQ_class", (FQ,), {"field_modulus": self.field_modulus}
)
self.coeffs: Tuple[IntOrFQ, ...] = tuple(
self.FQP_corresponding_FQ_class(c) for c in coeffs
)
# The coefficients of the modulus, without the leading [1]
self.modulus_coeffs: Tuple[IntOrFQ, ...] = tuple(modulus_coeffs)
# The degree of the extension field
self.degree = len(self.modulus_coeffs)
def __add__(self: T_FQP, other: T_FQP) -> T_FQP:
if not isinstance(other, type(self)):
raise TypeError(
f"Expected an FQP object, but got object of type {type(other)}"
)
return type(self)([x + y for x, y in zip(self.coeffs, other.coeffs)])
def __sub__(self: T_FQP, other: T_FQP) -> T_FQP:
if not isinstance(other, type(self)):
raise TypeError(
f"Expected an FQP object, but got object of type {type(other)}"
)
return type(self)([x - y for x, y in zip(self.coeffs, other.coeffs)])
def __mul__(self: T_FQP, other: Union[int, T_FQ, T_FQP]) -> T_FQP:
if isinstance(other, int_types_or_FQ):
return type(self)([c * other for c in self.coeffs])
elif isinstance(other, FQP):
b = [self.FQP_corresponding_FQ_class(0) for i in range(self.degree * 2 - 1)]
for i in range(self.degree):
for j in range(self.degree):
b[i + j] += self.coeffs[i] * other.coeffs[j]
while len(b) > self.degree:
exp, top = len(b) - self.degree - 1, b.pop()
for i in range(self.degree):
b[exp + i] -= top * self.FQP_corresponding_FQ_class(
self.modulus_coeffs[i]
)
return type(self)(b)
else:
raise TypeError(
"Expected an int or FQ object or FQP object, "
f"but got object of type {type(other)}"
)
def __rmul__(self: T_FQP, other: Union[int, T_FQ, T_FQP]) -> T_FQP:
return self * other
def __div__(self: T_FQP, other: Union[int, T_FQ, T_FQP]) -> T_FQP:
if isinstance(other, int_types_or_FQ):
return type(self)(
[
c / other if isinstance(c, FQ) else c // int(other)
for c in self.coeffs
]
)
elif isinstance(other, type(self)):
return self * other.inv()
else:
raise TypeError(
"Expected an int or FQ object or FQP object, "
f"but got object of type {type(other)}"
)
def __truediv__(self: T_FQP, other: Union[int, T_FQ, T_FQP]) -> T_FQP:
return self.__div__(other)
def __pow__(self: T_FQP, other: int) -> T_FQP:
if other == 0:
return type(self)([1] + [0] * (self.degree - 1))
elif other == 1:
return type(self)(self.coeffs)
elif other % 2 == 0:
return (self * self) ** (other // 2)
else:
return ((self * self) ** int(other // 2)) * self
# Extended euclidean algorithm used to find the modular inverse
def inv(self: T_FQP) -> T_FQP:
lm, hm = (
[1] + [0] * self.degree,
[0] * (self.degree + 1),
)
low, high = (
cast(List[IntOrFQ], list(self.coeffs + (0,))),
cast(List[IntOrFQ], list(self.modulus_coeffs + (1,))),
)
while deg(low):
r = cast(List[IntOrFQ], list(poly_rounded_div(high, low)))
r += [0] * (self.degree + 1 - len(r))
nm = [x for x in hm]
new = [x for x in high]
if len(lm) != self.degree + 1:
raise Exception(f"Length of lm is not {self.degree + 1}")
elif len(hm) != self.degree + 1:
raise Exception(f"Length of hm is not {self.degree + 1}")
elif len(nm) != self.degree + 1:
raise Exception(f"Length of nm is not {self.degree + 1}")
elif len(low) != self.degree + 1:
raise Exception(f"Length of low is not {self.degree + 1}")
elif len(high) != self.degree + 1:
raise Exception(f"Length of high is not {self.degree + 1}")
elif len(new) != self.degree + 1:
raise Exception(f"Length of new is not {self.degree + 1}")
for i in range(self.degree + 1):
for j in range(self.degree + 1 - i):
nm[i + j] -= lm[i] * int(r[j])
new[i + j] -= low[i] * int(r[j])
lm, low, hm, high = nm, new, lm, low
return type(self)(lm[: self.degree]) / int(low[0])
def __repr__(self: T_FQP) -> str:
return repr(self.coeffs)
def __eq__(self: T_FQP, other: Any) -> bool:
if not isinstance(other, type(self)):
raise TypeError(
f"Expected an FQP object, but got object of type {type(other)}"
)
for c1, c2 in zip(self.coeffs, other.coeffs):
if c1 != c2:
return False
return True
def __ne__(self: T_FQP, other: Any) -> bool:
return not self == other
def __neg__(self: T_FQP) -> T_FQP:
return type(self)([-c for c in self.coeffs])
@classmethod
def one(cls: Type[T_FQP]) -> T_FQP:
return cls([1] + [0] * (cls.degree - 1))
@classmethod
def zero(cls: Type[T_FQP]) -> T_FQP:
return cls([0] * cls.degree)
class FQ2(FQP):
"""
The quadratic extension field
"""
degree: int = 2
FQ2_MODULUS_COEFFS: "FQ2_modulus_coeffs_type"
def __init__(self, coeffs: Sequence[IntOrFQ]) -> None:
if not hasattr(self, "FQ2_MODULUS_COEFFS"):
raise AttributeError("FQ2 Modulus Coeffs haven't been specified")
super().__init__(coeffs, self.FQ2_MODULUS_COEFFS)
class FQ12(FQP):
"""
The 12th-degree extension field
"""
degree: int = 12
FQ12_MODULUS_COEFFS: "FQ12_modulus_coeffs_type"
def __init__(self, coeffs: Sequence[IntOrFQ]) -> None:
if not hasattr(self, "FQ12_MODULUS_COEFFS"):
raise AttributeError("FQ12 Modulus Coeffs haven't been specified")
super().__init__(coeffs, self.FQ12_MODULUS_COEFFS)
|
