Struct Binary 

pub struct Binary<R: EuclideanRing> { /* private fields */ }

Binary field structure for the field GF(2^m) that contains the XOR ring and irreducible value.

See crate::gf::binary for the full example.

Implementations

impl<R: EuclideanRing> Binary<R>

pub fn new(ring: R, irreducible: R::Item) -> Self

Create a binary field object from the given XOR ring and the irreducible value.

pub fn ring(&self) -> &R

Get ring.

pub fn irreducible(&self) -> &R::Item

Get irreducible.

Trait Implementations

impl<R: Clone + EuclideanRing> Clone for Binary<R>

where R::Item: Clone,

fn clone(&self) -> Binary<R>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<R: Debug + EuclideanRing> Debug for Binary<R>

where R::Item: Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<R: EuclideanRing> Field for Binary<R>

type Item = <R as EuclideanRing>::Item

The type of the field elements.

fn zero(&self) -> Self::Item

Get the zero element of the field (the identity by addition).

fn one(&self) -> Self::Item

Get the one element of the field (the identity by multiplication).

fn eq(&self, a: &Self::Item, b: &Self::Item) -> bool

Perform the equity operation in the field.

fn add(&self, a: &Self::Item, b: &Self::Item) -> Self::Item

Perform addition operation in the field.

fn sub(&self, a: &Self::Item, b: &Self::Item) -> Self::Item

Perform sub operation. By default it is implemented through add and neg but it can be overridden for optimization purposes.

fn mul(&self, a: &Self::Item, b: &Self::Item) -> Self::Item

Perform multiplication operation in the field.

fn neg(&self, a: &Self::Item) -> Self::Item

Get inversed element by addition.

fn inv(&self, a: &Self::Item) -> Option<Self::Item>

Get inversed element by multiplication.

fn add_assign(&self, a: &mut Self::Item, b: &Self::Item)

Perform add_assign operation. By default it is implemented through add but it can be overridden for optimization purposes.

fn sub_assign(&self, a: &mut Self::Item, b: &Self::Item)

Perform sub_assign operation. By default it is implemented through sub but it can be overridden for optimization purposes.

fn neg_assign(&self, a: &mut Self::Item)

Perform neg_assign operation. By default it is implemented through neg but it can be overridden for optimization purposes.

fn mul_scalar<I>(&self, a: &Self::Item, bits_iter: I) -> Self::Item

where I: Iterator<Item = bool>,

Perform multiplication in the group by a scalar given as an iterator of bits according to the double and add algorithm.

fn pow_scalar<I>(&self, a: &Self::Item, bits_iter: I) -> Self::Item

where I: Iterator<Item = bool>,

Perform multiplication in the group by a scalar given as an iterator of bits according to the exponentiation by squaring algorithm.

fn div(&self, a: &Self::Item, b: &Self::Item) -> Option<Self::Item>

Perform div operation. By default it is implemented through mul and inv but it can be overridden for optimization purposes.

fn mul_assign(&self, a: &mut Self::Item, b: &Self::Item)

Perform mul_assign operation. By default it is implemented through mul but it can be overridden for optimization purposes.

fn div_assign(&self, a: &mut Self::Item, b: &Self::Item) -> Option<()>

Perform div_assign operation. By default it is implemented through div but it can be overridden for optimization purposes.

fn inv_assign(&self, a: &mut Self::Item) -> Option<()>

Perform inv_assign operation. By default it is implemented through inv but it can be overridden for optimization purposes.

fn mul_scalar_assign<I>(&self, a: &mut Self::Item, bits_iter: I)

where I: Iterator<Item = bool>,

Perform mul_scalar_assign operation. By default it is implemented
through mul_scalar but it can be overridden for optimization purposes.

fn pow_scalar_assign<I>(&self, a: &mut Self::Item, bits_iter: I)

where I: Iterator<Item = bool>,

Perform pow_scalar_assign operation. By default it is implemented
through pow_scalar but it can be overridden for optimization purposes.

fn as_add_group(&self) -> FieldAddGroup<'_, Self>

Represent the field as a group by addition.

fn as_mul_group(&self) -> FieldMulGroup<'_, Self>

Represent the field as a group by multiplication.