Trait TowerField

pub trait TowerField: BinaryField + From<Self::Canonical>
where
    Self::Canonical: From<Self>,
{
    type Canonical: TowerField + SerializeBytes + DeserializeBytes;

    const TOWER_LEVEL: usize = _;

    // Provided methods
    fn basis(iota: usize, i: usize) -> Result<Self, Error> { ... }
    fn mul_primitive(self, iota: usize) -> Result<Self, Error> { ... }
}

A binary field isomorphic to a binary tower field.

The canonical binary field tower construction is specified in DP23, section 2.3. This is a family of binary fields with extension degree $2^{\iota}$ for any tower height $\iota$. This trait can be implemented on any binary field isomorphic to the canonical tower field.

Provided Associated Constants

const TOWER_LEVEL: usize = _

The level $\iota$ in the tower, where this field is isomorphic to $T_{\iota}$.

Required Associated Types

type Canonical: TowerField + SerializeBytes + DeserializeBytes

The canonical field isomorphic to this tower field. Currently for every tower field, the canonical field is Fan-Paar’s binary field of the same degree.

Provided Methods

fn basis(iota: usize, i: usize) -> Result<Self, Error>

fn mul_primitive(self, iota: usize) -> Result<Self, Error>

Multiplies a field element by the canonical primitive element of the extension $T_{\iota + 1} / T_{iota}$.

We represent the tower field $T_{\iota + 1}$ as a vector space over $T_{\iota}$ with the basis ${1, \beta^{(\iota)}_1}$. This operation multiplies the element by $\beta^{(\iota)}_1$.

Throws

• Error::ExtensionDegreeTooHigh if iota >= Self::TOWER_LEVEL

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl TowerField for AESTowerField8b

type Canonical = BinaryField8b

impl TowerField for AESTowerField16b

const TOWER_LEVEL: usize = 4usize

type Canonical = BinaryField16b

impl TowerField for AESTowerField32b

const TOWER_LEVEL: usize = 5usize

type Canonical = BinaryField32b

impl TowerField for AESTowerField64b

const TOWER_LEVEL: usize = 6usize

type Canonical = BinaryField64b

impl TowerField for AESTowerField128b

const TOWER_LEVEL: usize = 7usize

type Canonical = BinaryField128b

impl TowerField for BinaryField128bPolyval

type Canonical = BinaryField128b

impl TowerField for BinaryField1b

type Canonical = BinaryField1b

impl TowerField for BinaryField2b

const TOWER_LEVEL: usize = 1usize

type Canonical = BinaryField2b

impl TowerField for BinaryField4b

const TOWER_LEVEL: usize = 2usize

type Canonical = BinaryField4b

impl TowerField for BinaryField8b

const TOWER_LEVEL: usize = 3usize

type Canonical = BinaryField8b

impl TowerField for BinaryField16b

const TOWER_LEVEL: usize = 4usize

type Canonical = BinaryField16b

impl TowerField for BinaryField32b

const TOWER_LEVEL: usize = 5usize

type Canonical = BinaryField32b

impl TowerField for BinaryField64b

const TOWER_LEVEL: usize = 6usize

type Canonical = BinaryField64b

impl TowerField for BinaryField128b

const TOWER_LEVEL: usize = 7usize

type Canonical = BinaryField128b