Struct scuttlebutt::field::F2

pub struct F2(/* private fields */);

A field element in the prime-order finite field $\textsf{GF}(2).$

Trait Implementations

impl<'a> Add<&'a F2> for F2

type Output = F2

The resulting type after applying the + operator.

fn add(self, rhs: &'a F2) -> Self::Output

Performs the + operation.

impl<'a> Add<F2> for &'a F2

type Output = F2

The resulting type after applying the + operator.

fn add(self, rhs: F2) -> Self::Output

Performs the + operation.

impl<'a> Add for &'a F2

type Output = F2

The resulting type after applying the + operator.

fn add(self, rhs: &'a F2) -> Self::Output

Performs the + operation.

impl Add for F2

type Output = F2

The resulting type after applying the + operator.

fn add(self, rhs: F2) -> Self::Output

Performs the + operation.

impl AddAssign<&F2> for F2

fn add_assign(&mut self, rhs: &F2)

Performs the += operation.

impl AddAssign for F2

fn add_assign(&mut self, rhs: F2)

Performs the += operation.

impl CanonicalSerialize for F2

fn to_bytes(&self) -> GenericArray<u8, Self::ByteReprLen>

Return the canonical byte representation (byte representation of the reduced field element).

type Serializer = F2BitSerializer

A way to serialize field elements of this type.

type Deserializer = F2BitDeserializer

A way to deserialize field elements of this type.

type ByteReprLen = UInt<UTerm, B1>

The number of bytes in the byte representation for this element.

type FromBytesError = BiggerThanModulus

The error that can result from trying to decode an invalid byte sequence.

fn from_bytes( buf: &GenericArray<u8, Self::ByteReprLen> ) -> Result<Self, BiggerThanModulus>

Deserialize an element from a byte array.

impl Clone for F2

fn clone(&self) -> F2

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for F2

fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for F2

fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl Debug for F2

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

Formats the value using the given formatter.

impl Default for F2

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for F2

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

Deserialize this value from the given Serde deserializer.

impl Distribution<F2> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F2

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

fn sample_iter<R>(self, rng: R) -> DistIter<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) -> DistMap<Self, F, T, S>

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

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<'a> Div<&'a F2> for F2

type Output = F2

The resulting type after applying the / operator.

fn div(self, rhs: &'a F2) -> Self::Output

Performs the / operation.

impl<'a> Div<F2> for &'a F2

type Output = F2

The resulting type after applying the / operator.

fn div(self, rhs: F2) -> Self::Output

Performs the / operation.

impl<'a> Div for &'a F2

type Output = F2

The resulting type after applying the / operator.

fn div(self, rhs: &'a F2) -> Self::Output

Performs the / operation.

impl Div for F2

type Output = F2

The resulting type after applying the / operator.

fn div(self, rhs: F2) -> Self::Output

Performs the / operation.

impl<'a> DivAssign<&'a F2> for F2

fn div_assign(&mut self, rhs: &Self)

Performs the /= operation.

impl DivAssign for F2

fn div_assign(&mut self, rhs: F2)

Performs the /= operation.

impl FiniteField for F2

type PrimeField = F2

The prime-order subfield of the finite field.

const GENERATOR: Self = _

The generator for the multiplicative group.

fn polynomial_modulus() -> Polynomial<Self::PrimeField>

Multiplication over field elements should be reduced over this polynomial.

type NumberOfBitsInBitDecomposition = UInt<UTerm, B1>

The number of bits in the bit decomposition of any element of this finite field.

fn bit_decomposition( &self ) -> GenericArray<bool, Self::NumberOfBitsInBitDecomposition>

Decompose the given field element into bits.

fn inverse(&self) -> Self

Compute the multiplicative inverse of self.

fn decompose<T: FiniteField + IsSubFieldOf<Self>>( &self ) -> GenericArray<T, DegreeModulo<T, Self>>

Decompose self into an array of T elements where T is a subfield of Self.

fn from_subfield<T: FiniteField + IsSubFieldOf<Self>>( arr: &GenericArray<T, DegreeModulo<T, Self>> ) -> Self

Create a field element from an array of subfield T elements.

impl FiniteRing for F2

fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self

This uniformly generates a field element either 0 or 1 for F2 type.

fn random_nonzero<R: RngCore + ?Sized>(_rng: &mut R) -> Self

Generate a random non-zero element.

const ZERO: Self = _

The additive identity element.

const ONE: Self = _

The multiplicative identity element.

fn from_uniform_bytes(x: &[u8; 16]) -> Self

Construct an element from the given uniformly chosen random bytes.

fn pow(&self, n: u128) -> Self

Compute self to the power of n.

fn pow_bounded(&self, n: u128, bound: u16) -> Self

Compute self to the power of n, where n is guaranteed to be <= 2^bound.

fn pow_var_time(&self, n: u128) -> Self

Compute self to the power of n, in non-constant time.

impl From<F2> for F128b

fn from(x: F2) -> Self

Converts to this type from the input type.

impl From<F2> for F40b

fn from(pf: F2) -> Self

Converts to this type from the input type.

impl From<F2> for F45b

fn from(pf: F2) -> Self

Converts to this type from the input type.

impl From<F2> for F56b

fn from(pf: F2) -> Self

Converts to this type from the input type.

impl From<F2> for F63b

fn from(pf: F2) -> Self

Converts to this type from the input type.

impl From<F2> for F64b

fn from(pf: F2) -> Self

Converts to this type from the input type.

impl From<F2> for bool

fn from(x: F2) -> Self

Converts to this type from the input type.

impl From<F2> for u8

This returns a canonical/reduced form of the field element.

fn from(x: F2) -> Self

Converts to this type from the input type.

impl From<bool> for F2

fn from(x: bool) -> Self

Converts to this type from the input type.

impl Hash for F2

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 IsSubFieldOf<F128b> for F2

type DegreeModulo = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>

The value $n$ from above.

fn decompose_superfield(fe: &F128b) -> GenericArray<Self, Self::DegreeModulo>

Turn FE into an array of Self, a subfield of FE.

fn form_superfield(components: &GenericArray<Self, Self::DegreeModulo>) -> F128b

Homomorphically lift an array of Self into an FE.

impl IsSubFieldOf<F40b> for F2

type DegreeModulo = UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B1>, B0>, B0>, B0>

The value $n$ from above.

fn decompose_superfield(fe: &F40b) -> GenericArray<Self, U40>

Turn FE into an array of Self, a subfield of FE.

fn form_superfield(components: &GenericArray<Self, Self::DegreeModulo>) -> F40b

Homomorphically lift an array of Self into an FE.

impl IsSubFieldOf<F45b> for F2

type DegreeModulo = UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B1>, B1>, B0>, B1>

The value $n$ from above.

fn decompose_superfield(fe: &F45b) -> GenericArray<Self, U45>

Turn FE into an array of Self, a subfield of FE.

fn form_superfield(components: &GenericArray<Self, Self::DegreeModulo>) -> F45b

Homomorphically lift an array of Self into an FE.

impl IsSubFieldOf<F56b> for F2

type DegreeModulo = UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B0>, B0>, B0>

The value $n$ from above.

fn decompose_superfield(fe: &F56b) -> GenericArray<Self, U56>

Turn FE into an array of Self, a subfield of FE.

fn form_superfield(components: &GenericArray<Self, Self::DegreeModulo>) -> F56b

Homomorphically lift an array of Self into an FE.

impl IsSubFieldOf<F63b> for F2

type DegreeModulo = UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B1>, B1>, B1>

The value $n$ from above.

fn decompose_superfield(fe: &F63b) -> GenericArray<Self, U63>

Turn FE into an array of Self, a subfield of FE.

fn form_superfield(components: &GenericArray<Self, Self::DegreeModulo>) -> F63b

Homomorphically lift an array of Self into an FE.

impl IsSubFieldOf<F64b> for F2

type DegreeModulo = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>

The value $n$ from above.

fn decompose_superfield(fe: &F64b) -> GenericArray<Self, Self::DegreeModulo>

Turn FE into an array of Self, a subfield of FE.

fn form_superfield(components: &GenericArray<Self, Self::DegreeModulo>) -> F64b

Homomorphically lift an array of Self into an FE.

impl<'a> Mul<&'a F2> for F2

type Output = F2

The resulting type after applying the * operator.

fn mul(self, rhs: &'a F2) -> Self::Output

Performs the * operation.

impl Mul<F128b> for F2

type Output = F128b

The resulting type after applying the * operator.

fn mul(self, x: F128b) -> F128b

Performs the * operation.

impl<'a> Mul<F2> for &'a F2

type Output = F2

The resulting type after applying the * operator.

fn mul(self, rhs: F2) -> Self::Output

Performs the * operation.

impl Mul<F40b> for F2

type Output = F40b

The resulting type after applying the * operator.

fn mul(self, x: F40b) -> F40b

Performs the * operation.

impl Mul<F45b> for F2

type Output = F45b

The resulting type after applying the * operator.

fn mul(self, x: F45b) -> F45b

Performs the * operation.

impl Mul<F56b> for F2

type Output = F56b

The resulting type after applying the * operator.

fn mul(self, x: F56b) -> F56b

Performs the * operation.

impl Mul<F63b> for F2

type Output = F63b

The resulting type after applying the * operator.

fn mul(self, x: F63b) -> F63b

Performs the * operation.

impl Mul<F64b> for F2

type Output = F64b

The resulting type after applying the * operator.

fn mul(self, x: F64b) -> F64b

Performs the * operation.

impl<'a> Mul for &'a F2

type Output = F2

The resulting type after applying the * operator.

fn mul(self, rhs: &'a F2) -> Self::Output

Performs the * operation.

impl Mul for F2

type Output = F2

The resulting type after applying the * operator.

fn mul(self, rhs: F2) -> Self::Output

Performs the * operation.

impl MulAssign<&F2> for F2

fn mul_assign(&mut self, rhs: &F2)

Performs the *= operation.

impl MulAssign for F2

fn mul_assign(&mut self, rhs: F2)

Performs the *= operation.

impl Neg for F2

type Output = F2

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl One for F2

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl PartialEq for F2

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

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

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Product for F2

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Serialize for F2

fn serialize<S: Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error>

Serialize this value into the given Serde serializer.

impl<'a> Sub<&'a F2> for F2

type Output = F2

The resulting type after applying the - operator.

fn sub(self, rhs: &'a F2) -> Self::Output

Performs the - operation.

impl<'a> Sub<F2> for &'a F2

type Output = F2

The resulting type after applying the - operator.

fn sub(self, rhs: F2) -> Self::Output

Performs the - operation.

impl<'a> Sub for &'a F2

type Output = F2

The resulting type after applying the - operator.

fn sub(self, rhs: &'a F2) -> Self::Output

Performs the - operation.

impl Sub for F2

type Output = F2

The resulting type after applying the - operator.

fn sub(self, rhs: F2) -> Self::Output

Performs the - operation.

impl SubAssign<&F2> for F2

fn sub_assign(&mut self, rhs: &F2)

Performs the -= operation.

impl SubAssign for F2

fn sub_assign(&mut self, rhs: F2)

Performs the -= operation.

impl Sum for F2

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl TryFrom<u128> for F2

type Error = BiggerThanModulus

The type returned in the event of a conversion error.

fn try_from(value: u128) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<u8> for F2

type Error = BiggerThanModulus

The type returned in the event of a conversion error.

fn try_from(value: u8) -> Result<Self, Self::Error>

Performs the conversion.

impl Zero for F2

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Zeroable for F2

fn zeroed() -> Self

Calls zeroed.

impl Copy for F2

impl Eq for F2

impl IsSubRingOf<F128b> for F2

impl IsSubRingOf<F40b> for F2

impl IsSubRingOf<F45b> for F2

impl IsSubRingOf<F56b> for F2

impl IsSubRingOf<F63b> for F2

impl IsSubRingOf<F64b> for F2

impl PrimeFiniteField for F2