Struct Gf2 

pub struct Gf2(/* private fields */);

The prime field GF(2) = {0, 1}, with addition given by XOR and multiplication by AND.

This is the base case of the characteristic-2 tower GF(2) ⊂ GF(4) ⊂ … ⊂ GF(2^128).

The serde encoding is canonical: every field element has exactly one valid byte representation (see the manual Deserialize impl below). #[serde(transparent)] makes the derived Serialize emit the backing integer itself, which is what that impl reads back.

Implementations

impl Gf2

pub const fn from_le_bytes(bytes: [u8; 1]) -> Self

Construct a field element from its little-endian byte representation.

Every byte is a valid input; only its least significant bit is used.

Trait Implementations

impl Add for Gf2

type Output = Gf2

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<BinaryField2> for Gf2

type Output = BinaryField2

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField2) -> Self::Output

Performs the + operation.

impl Add<BinaryField4> for Gf2

type Output = BinaryField4

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField4) -> Self::Output

Performs the + operation.

impl Add<BinaryField8> for Gf2

type Output = BinaryField8

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField8) -> Self::Output

Performs the + operation.

impl Add<BinaryField16> for Gf2

type Output = BinaryField16

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField16) -> Self::Output

Performs the + operation.

impl Add<BinaryField32> for Gf2

type Output = BinaryField32

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField32) -> Self::Output

Performs the + operation.

impl Add<BinaryField64> for Gf2

type Output = BinaryField64

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField64) -> Self::Output

Performs the + operation.

impl Add<BinaryField128> for Gf2

type Output = BinaryField128

The resulting type after applying the + operator.

fn add(self, rhs: BinaryField128) -> Self::Output

Performs the + operation.

impl<const N: usize> Add<Gf2> for PackedRijndael8b<N>

type Output = PackedRijndael8b<N>

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl<U: Underlier> Add<Gf2> for PackedGf2<U>

type Output = PackedGf2<U>

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for Ghash128

type Output = Ghash128

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for Poly192

type Output = Poly192

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for Poly64

type Output = Poly64

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField2

type Output = BinaryField2

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField4

type Output = BinaryField4

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField8

type Output = BinaryField8

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField16

type Output = BinaryField16

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField32

type Output = BinaryField32

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField64

type Output = BinaryField64

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Gf2> for BinaryField128

type Output = BinaryField128

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl Add<Ghash128> for Gf2

type Output = Ghash128

The resulting type after applying the + operator.

fn add(self, rhs: Ghash128) -> Self::Output

Performs the + operation.

impl Add<Poly64> for Gf2

type Output = Poly64

The resulting type after applying the + operator.

fn add(self, rhs: Poly64) -> Self::Output

Performs the + operation.

impl Add<Poly192> for Gf2

type Output = Poly192

The resulting type after applying the + operator.

fn add(self, rhs: Poly192) -> Self::Output

Performs the + operation.

impl Add<Rijndael8b> for Gf2

type Output = Rijndael8b

The resulting type after applying the + operator.

fn add(self, rhs: Rijndael8b) -> Self::Output

Performs the + operation.

impl<T: Into<Self>> AddAssign<T> for Gf2

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<const N: usize> Algebra<Gf2> for PackedRijndael8b<N>

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for Rijndael8b

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl<U: Underlier> Algebra<Gf2> for PackedGf2<U>

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for Ghash128

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for Poly192

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for Poly64

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField2

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField4

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField8

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField16

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField32

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField64

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Algebra<Gf2> for BinaryField128

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Clone for Gf2

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Gf2

impl Debug for Gf2

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

Formats the value using the given formatter.

impl Default for Gf2

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Gf2

fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error>

Deserialize this value from the given Serde deserializer.

impl Display for Gf2

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

Formats the value using the given formatter.

impl Distribution<Gf2> for StandardUniform

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Gf2

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl Div for Gf2

type Output = Gf2

The resulting type after applying the / operator.

fn div(self, rhs: Gf2) -> Self

Performs the / operation.

impl<U: Underlier> Div<Gf2> for PackedGf2<U>

type Output = PackedGf2<U>

The resulting type after applying the / operator.

fn div(self, rhs: Gf2) -> Self

Performs the / operation.

impl DivAssign for Gf2

fn div_assign(&mut self, rhs: Gf2)

Performs the /= operation.

impl<U: Underlier> DivAssign<Gf2> for PackedGf2<U>

fn div_assign(&mut self, rhs: Gf2)

Performs the /= operation.

impl Eq for Gf2

impl Field for Gf2

type Packing = Gf2

No packing: the packed-value contract needs a cast to an array of WIDTH scalars. Eight elements are eight bytes as scalars and one byte bit-sliced, so that cast lies.

The bit-sliced packings therefore live beside this type rather than inside it.

fn bits() -> usize

An element of GF(2) is exactly one bit wide.

The default implementation returns order().bits(), which over-reports by one whenever the order is an exact power of two.

fn interpolation_node(i: usize) -> Self

The enumeration interpolation_node(0) = 0, interpolation_node(1) = 1 is the only injective enumeration of the two elements of GF(2) satisfying Field::interpolation_node’s contract.

Panics

Panics if i > 1. new keeps only the low bit, so a larger index would otherwise alias one of the two nodes and break an interpolation argument silently.

const GENERATOR: Self = Self::ONE

A generator of this field’s multiplicative group.

fn try_inverse(&self) -> Option<Self>

The multiplicative inverse of this field element, if it exists.

fn try_sqrt(&self) -> Option<Self>

A square root of this field element, if one exists.

fn order() -> BigUint

The number of elements in the field.

const BENEFITS_FROM_LOCKSTEP_EVALUATION: bool = false

Whether evaluating multiple packed vectors of this field in lockstep (to overlap independent dependency chains and hide packed-multiplication latency) is expected to help throughput for this field.

fn is_zero(&self) -> bool

Check if the given field element is equal to the unique additive identity (ZERO).

fn is_one(&self) -> bool

Check if the given field element is equal to the unique multiplicative identity (ONE).

fn inverse(&self) -> Self

The multiplicative inverse of this field element.

fn add_slices(slice_1: &mut [Self], slice_2: &[Self])

Add two slices of field elements together, returning the result in the first slice.

fn batched_columnwise_dot_product<EF, R, I, const N: usize>( acc: &mut [<EF as ExtensionField<Self>>::ExtensionPacking], items: I, )

where EF: ExtensionField<Self>, R: Iterator<Item = Self::Packing>, I: Iterator<Item = (R, [EF; N])>,

Accumulate acc[c * N + j] += scales[j] * row[c] over a stream of packed rows.

impl<const N: usize> From<Gf2> for PackedRijndael8b<N>

fn from(value: Gf2) -> Self

GF(2) is the prime subfield, embedded as {ZERO, ONE} in every position.

impl From<Gf2> for Rijndael8b

fn from(x: Gf2) -> Self

GF(2) is the prime subfield, embedded as {ZERO, ONE}.

impl<U: Underlier> From<Gf2> for PackedGf2<U>

fn from(value: Gf2) -> Self

Converts to this type from the input type.

impl From<Gf2> for Ghash128

fn from(x: Gf2) -> Self

GF(2) is the prime subfield, embedded as {ZERO, ONE}.

impl From<Gf2> for Poly192

fn from(x: Gf2) -> Self

GF(2) is the prime subfield, embedded as {ZERO, ONE}.

impl From<Gf2> for Poly64

fn from(x: Gf2) -> Self

GF(2) is the prime subfield, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField2

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField4

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField8

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField16

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField32

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField64

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl From<Gf2> for BinaryField128

fn from(x: Gf2) -> Self

GF(2) is the prime subfield of every level, embedded as {ZERO, ONE}.

impl Hash for Gf2

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, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for Gf2

type Output = Gf2

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<BinaryField2> for Gf2

type Output = BinaryField2

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField2) -> BinaryField2

Performs the * operation.

impl Mul<BinaryField4> for Gf2

type Output = BinaryField4

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField4) -> BinaryField4

Performs the * operation.

impl Mul<BinaryField8> for Gf2

type Output = BinaryField8

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField8) -> BinaryField8

Performs the * operation.

impl Mul<BinaryField16> for Gf2

type Output = BinaryField16

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField16) -> BinaryField16

Performs the * operation.

impl Mul<BinaryField32> for Gf2

type Output = BinaryField32

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField32) -> BinaryField32

Performs the * operation.

impl Mul<BinaryField64> for Gf2

type Output = BinaryField64

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField64) -> BinaryField64

Performs the * operation.

impl Mul<BinaryField128> for Gf2

type Output = BinaryField128

The resulting type after applying the * operator.

fn mul(self, rhs: BinaryField128) -> BinaryField128

Performs the * operation.

impl<const N: usize> Mul<Gf2> for PackedRijndael8b<N>

type Output = PackedRijndael8b<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl<U: Underlier> Mul<Gf2> for PackedGf2<U>

type Output = PackedGf2<U>

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for Ghash128

type Output = Ghash128

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for Poly192

type Output = Poly192

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for Poly64

type Output = Poly64

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField2

type Output = BinaryField2

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField4

type Output = BinaryField4

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField8

type Output = BinaryField8

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField16

type Output = BinaryField16

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField32

type Output = BinaryField32

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField64

type Output = BinaryField64

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Gf2> for BinaryField128

type Output = BinaryField128

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl Mul<Ghash128> for Gf2

type Output = Ghash128

The resulting type after applying the * operator.

fn mul(self, rhs: Ghash128) -> Self::Output

Performs the * operation.

impl Mul<Poly64> for Gf2

type Output = Poly64

The resulting type after applying the * operator.

fn mul(self, rhs: Poly64) -> Self::Output

Performs the * operation.

impl Mul<Poly192> for Gf2

type Output = Poly192

The resulting type after applying the * operator.

fn mul(self, rhs: Poly192) -> Poly192

Performs the * operation.

impl Mul<Rijndael8b> for Gf2

type Output = Rijndael8b

The resulting type after applying the * operator.

fn mul(self, rhs: Rijndael8b) -> Self::Output

Performs the * operation.

impl<T: Into<Self>> MulAssign<T> for Gf2

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl Neg for Gf2

type Output = Gf2

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Ord for Gf2

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

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

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

where Self: Sized,

Restrict a value to a certain interval.

fn clamp_to<R>(self, range: R) -> Self

where Self: Sized, R: ClampBounds<Self>,

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

Restrict a value to a certain range.

impl Packable for Gf2

impl PartialEq for Gf2

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

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for Gf2

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

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

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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

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

impl PrimeCharacteristicRing for Gf2

fn halve(&self) -> Self

Panics

Always panics: 2 is not invertible in characteristic 2.

fn div_2exp_u64(&self, _exp: u64) -> Self

Panics

Always panics: 2 is not invertible in characteristic 2.

const ZERO: Self

The additive identity of the ring.

const ONE: Self

The multiplicative identity of the ring.

const TWO: Self

The element in the ring given by ONE + ONE.

const NEG_ONE: Self

The element in the ring given by -ONE.

type PrimeSubfield = Gf2

The field ℤ/p where the characteristic of this ring is p.

fn from_prime_subfield(f: Self::PrimeSubfield) -> Self

Embed an element of the prime field ℤ/p into the ring R.

fn from_bool(b: bool) -> Self

Return Self::ONE if b is true and Self::ZERO if b is false.

fn double(&self) -> Self

The elementary function double(a) = 2*a.

fn xor(&self, y: &Self) -> Self

Computes the arithmetic generalization of boolean xor.

fn mul_2exp_u64(&self, exp: u64) -> Self

The elementary function mul_2exp_u64(a, exp) = a * 2^{exp}.

fn square(&self) -> Self

The elementary function square(a) = a^2.

fn from_u8(int: u8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u16(int: u16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u32(int: u32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u64(int: u64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u128(int: u128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_usize(int: usize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i8(int: i8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i16(int: i16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i32(int: i32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i64(int: i64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i128(int: i128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_isize(int: isize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn cube(&self) -> Self

The elementary function cube(a) = a^3.

fn xor3(&self, y: &Self, z: &Self) -> Self

Computes the arithmetic generalization of a triple xor.

fn andn(&self, y: &Self) -> Self

Computes the arithmetic generalization of andnot.

fn bool_check(&self) -> Self

The vanishing polynomial for boolean values: x * (x - 1).

fn exp_u64(&self, power: u64) -> Self

Exponentiation by a u64 power.

fn exp_const_u64<const POWER: u64>(&self) -> Self

Exponentiation by a small constant power.

fn exp_power_of_2(&self, power_log: usize) -> Self

The elementary function exp_power_of_2(a, power_log) = a^{2^power_log}.

fn powers(&self) -> Powers<Self>

Construct an iterator which returns powers of self: self^0, self^1, self^2, ....

fn shifted_powers(&self, start: Self) -> Powers<Self>

Construct an iterator which returns powers of self shifted by start: start, start*self^1, start*self^2, ....

fn dot_product<const N: usize>(u: &[Self; N], v: &[Self; N]) -> Self

Compute the dot product of two vectors.

fn sum_array<const N: usize>(input: &[Self]) -> Self

Compute the sum of a slice of elements whose length is a compile time constant.

fn zero_vec(len: usize) -> Vec<Self>

Allocates a vector of zero elements of length len. Many operating systems zero pages before assigning them to a userspace process. In that case, our process should not need to write zeros, which would be redundant. However, the compiler may not always recognize this.

impl PrimeField for Gf2

fn as_canonical_biguint(&self) -> BigUint

Return the representative of value in canonical form which lies in the range 0 <= x < self.order().

impl PrimeField32 for Gf2

const ORDER_U32: u32 = 2

fn as_canonical_u32(&self) -> u32

Return the representative of value in canonical form which lies in the range 0 <= x < ORDER_U64.

fn to_unique_u32(&self) -> u32

Convert a field element to a u32 such that any two field elements are converted to the same u32 if and only if they represent the same value.

impl PrimeField64 for Gf2

const ORDER_U64: u64 = 2

fn as_canonical_u64(&self) -> u64

Return the representative of value in canonical form which lies in the range 0 <= x < ORDER_U64.

fn to_unique_u64(&self) -> u64

Convert a field element to a u64 such that any two field elements are converted to the same u64 if and only if they represent the same value.

impl Product for Gf2

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl QuotientMap<i8> for Gf2

fn from_int(int: i8) -> Self

Convert a given i8 integer into an element of the Gf2 field.

fn from_canonical_checked(int: i8) -> Option<Self>

Convert a given i8 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range [0, 1].

unsafe fn from_canonical_unchecked(int: i8) -> Self

Convert a given i8 integer into an element of the Gf2 field.

Safety

The caller must guarantee that int lies in [0, 1].

impl QuotientMap<i16> for Gf2

fn from_int(int: i16) -> Gf2

Convert a given i16 integer into an element of the Gf2 field.

This checks the sign and then makes use of the equivalent method for unsigned integers. This should be avoided in performance critical locations.

fn from_canonical_checked(int: i16) -> Option<Gf2>

Convert a given u16 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: i16) -> Gf2

Convert a given u16 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<i32> for Gf2

fn from_int(int: i32) -> Gf2

Convert a given i32 integer into an element of the Gf2 field.

This checks the sign and then makes use of the equivalent method for unsigned integers. This should be avoided in performance critical locations.

fn from_canonical_checked(int: i32) -> Option<Gf2>

Convert a given u32 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: i32) -> Gf2

Convert a given u32 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<i64> for Gf2

fn from_int(int: i64) -> Gf2

Convert a given i64 integer into an element of the Gf2 field.

This checks the sign and then makes use of the equivalent method for unsigned integers. This should be avoided in performance critical locations.

fn from_canonical_checked(int: i64) -> Option<Gf2>

Convert a given u64 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: i64) -> Gf2

Convert a given u64 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<i128> for Gf2

fn from_int(int: i128) -> Gf2

Convert a given i128 integer into an element of the Gf2 field.

This checks the sign and then makes use of the equivalent method for unsigned integers. This should be avoided in performance critical locations.

fn from_canonical_checked(int: i128) -> Option<Gf2>

Convert a given u128 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: i128) -> Gf2

Convert a given u128 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<u8> for Gf2

fn from_int(int: u8) -> Self

Convert a given u8 integer into an element of the Gf2 field.

fn from_canonical_checked(int: u8) -> Option<Self>

Convert a given u8 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range [0, 1].

unsafe fn from_canonical_unchecked(int: u8) -> Self

Convert a given u8 integer into an element of the Gf2 field.

Safety

The caller must guarantee that int < 2.

impl QuotientMap<u16> for Gf2

fn from_int(int: u16) -> Gf2

Convert a given u16 integer into an element of the Gf2 field.

Uses a modular reduction to reduce to canonical form. This should be avoided in performance critical locations.

fn from_canonical_checked(int: u16) -> Option<Gf2>

Convert a given u16 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: u16) -> Gf2

Convert a given u16 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<u32> for Gf2

fn from_int(int: u32) -> Gf2

Convert a given u32 integer into an element of the Gf2 field.

Uses a modular reduction to reduce to canonical form. This should be avoided in performance critical locations.

fn from_canonical_checked(int: u32) -> Option<Gf2>

Convert a given u32 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: u32) -> Gf2

Convert a given u32 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<u64> for Gf2

fn from_int(int: u64) -> Gf2

Convert a given u64 integer into an element of the Gf2 field.

Uses a modular reduction to reduce to canonical form. This should be avoided in performance critical locations.

fn from_canonical_checked(int: u64) -> Option<Gf2>

Convert a given u64 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: u64) -> Gf2

Convert a given u64 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl QuotientMap<u128> for Gf2

fn from_int(int: u128) -> Gf2

Convert a given u128 integer into an element of the Gf2 field.

Uses a modular reduction to reduce to canonical form. This should be avoided in performance critical locations.

fn from_canonical_checked(int: u128) -> Option<Gf2>

Convert a given u128 integer into an element of the Gf2 field.

Returns None if the input does not lie in the range:[0, 1].

unsafe fn from_canonical_unchecked(int: u128) -> Gf2

Convert a given u128 integer into an element of the Gf2 field.

Safety

The input must lie in the range:[0, 1].

impl RawDataSerializable for Gf2

const NUM_BYTES: usize = 1

The number of bytes which this field element occupies in memory. Must be equal to the length of self.into_bytes().

fn into_bytes(self) -> impl IntoIterator<Item = u8>

Convert a field element into a collection of bytes.

fn into_byte_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u8>

Convert an iterator of field elements into an iterator of bytes.

fn into_u32_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u32>

Convert an iterator of field elements into an iterator of u32s.

fn into_u64_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u64>

Convert an iterator of field elements into an iterator of u64s.

fn into_parallel_byte_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u8; N]>

Convert an iterator of field element arrays into an iterator of byte arrays.

fn into_parallel_u32_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u32; N]>

Convert an iterator of field element arrays into an iterator of u32 arrays.

fn into_parallel_u64_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u64; N]>

Convert an iterator of field element arrays into an iterator of u64 arrays.

impl Serialize for Gf2

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for Gf2

impl Sub for Gf2

type Output = Gf2

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<BinaryField2> for Gf2

type Output = BinaryField2

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField2) -> Self::Output

Performs the - operation.

impl Sub<BinaryField4> for Gf2

type Output = BinaryField4

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField4) -> Self::Output

Performs the - operation.

impl Sub<BinaryField8> for Gf2

type Output = BinaryField8

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField8) -> Self::Output

Performs the - operation.

impl Sub<BinaryField16> for Gf2

type Output = BinaryField16

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField16) -> Self::Output

Performs the - operation.

impl Sub<BinaryField32> for Gf2

type Output = BinaryField32

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField32) -> Self::Output

Performs the - operation.

impl Sub<BinaryField64> for Gf2

type Output = BinaryField64

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField64) -> Self::Output

Performs the - operation.

impl Sub<BinaryField128> for Gf2

type Output = BinaryField128

The resulting type after applying the - operator.

fn sub(self, rhs: BinaryField128) -> Self::Output

Performs the - operation.

impl<const N: usize> Sub<Gf2> for PackedRijndael8b<N>

type Output = PackedRijndael8b<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl<U: Underlier> Sub<Gf2> for PackedGf2<U>

type Output = PackedGf2<U>

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for Ghash128

type Output = Ghash128

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for Poly192

type Output = Poly192

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for Poly64

type Output = Poly64

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField2

type Output = BinaryField2

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField4

type Output = BinaryField4

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField8

type Output = BinaryField8

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField16

type Output = BinaryField16

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField32

type Output = BinaryField32

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField64

type Output = BinaryField64

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Gf2> for BinaryField128

type Output = BinaryField128

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl Sub<Ghash128> for Gf2

type Output = Ghash128

The resulting type after applying the - operator.

fn sub(self, rhs: Ghash128) -> Self::Output

Performs the - operation.

impl Sub<Poly64> for Gf2

type Output = Poly64

The resulting type after applying the - operator.

fn sub(self, rhs: Poly64) -> Self::Output

Performs the - operation.

impl Sub<Poly192> for Gf2

type Output = Poly192

The resulting type after applying the - operator.

fn sub(self, rhs: Poly192) -> Self::Output

Performs the - operation.

impl Sub<Rijndael8b> for Gf2

type Output = Rijndael8b

The resulting type after applying the - operator.

fn sub(self, rhs: Rijndael8b) -> Self::Output

Performs the - operation.

impl<T: Into<Self>> SubAssign<T> for Gf2

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl Sum for Gf2

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl TowerLevel for Gf2

fn mul_alpha(self) -> Self

X_{−1} = 1, so at the base of the tower this is the identity.

fn cantor_basis(i: usize) -> Self

GF(2) holds only v_0 = 1.

const LOG_BITS: usize = 0

The k in GF(2^(2^k)).

type Repr = u8

The backing integer of an element.

fn from_repr(r: Self::Repr) -> Self

Build an element from a bit pattern, discarding the bits above 2^LOG_BITS.

fn to_repr(self) -> Self::Repr

The bit pattern of this element, zero above 2^LOG_BITS.

fn from_le_byte_iter(bytes: impl Iterator<Item = u8>) -> Self

Build an element from the next RawDataSerializable::NUM_BYTES bytes of a little-endian byte stream, discarding the bits above 2^LOG_BITS.