Struct isochronous_finite_fields::GF

pub struct GF(pub u8);

Galois field wrapper struct.

It is wrapped around an u8 type, to guarantee at compile time that all elements are in the finite field GF(2⁸).

Methods

impl GF

pub fn multiplicative_inverse(self) -> Self

Calculates the multiplicative inverse. The multiplicative inverse is the element in the Galois field that results in a product of 1.

Example

let element = GF(148);
let inverse = element.multiplicative_inverse();

assert_eq!(element * inverse, GF(1));

Trait Implementations

impl Add<GF> for GF

Adding two elements in the Galois field GF(2⁸) is equal to doing an exclusive or (XOR) between the two elements. It is also equal to subtracting two elements.

type Output = Self

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl AddAssign<GF> for GF

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for GF

fn clone(&self) -> GF

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for GF

impl Debug for GF

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

Formats the value using the given formatter.

impl Eq for GF

impl From<u8> for GF

fn from(x: u8) -> Self

Performs the conversion.

impl Hash for GF

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given [Hasher].

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given [Hasher].

impl Mul<GF> for GF

Multiplication in this finite field is multiplication modulo AES standardized irreducible polynomial x⁸ + x⁴ + x³ + x + 1 (or 0b1_0001_1011).

type Output = Self

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl MulAssign<GF> for GF

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Ord for GF

fn cmp(&self, other: &GF) -> Ordering

This method returns an [Ordering] between self and other.

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

🔬 This is a nightly-only experimental API. (clamp)

Restrict a value to a certain interval.

impl PartialEq<GF> for GF

fn eq(&self, other: &GF) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &GF) -> bool

This method tests for !=.

impl PartialOrd<GF> for GF

fn partial_cmp(&self, other: &GF) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &GF) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &GF) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &GF) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &GF) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl StructuralEq for GF

impl StructuralPartialEq for GF

impl Sub<GF> for GF

Subtracting two elements in the Galois field GF(2⁸) is equal to doing an exclusive or (XOR) between the two elements. It is also equal to adding two elements.

type Output = Self

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl SubAssign<GF> for GF

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.