Struct scuttlebutt::field::F63b

pub struct F63b(/* private fields */);

An element of the finite field $\textsf{GF}(2^{63})$ reduced over $x^{63} + x + 1$

Trait Implementations

impl<'a> Add<&'a F63b> for F63b

type Output = F63b

The resulting type after applying the + operator.

fn add(self, rhs: &'a F63b) -> Self::Output

Performs the + operation.

impl<'a> Add<F63b> for &'a F63b

type Output = F63b

The resulting type after applying the + operator.

fn add(self, rhs: F63b) -> Self::Output

Performs the + operation.

impl<'a> Add for &'a F63b

type Output = F63b

The resulting type after applying the + operator.

fn add(self, rhs: &'a F63b) -> Self::Output

Performs the + operation.

impl Add for F63b

type Output = F63b

The resulting type after applying the + operator.

fn add(self, rhs: F63b) -> Self::Output

Performs the + operation.

impl<'a> AddAssign<&'a F63b> for F63b

fn add_assign(&mut self, rhs: &'a F63b)

Performs the += operation.

impl AddAssign for F63b

fn add_assign(&mut self, rhs: F63b)

Performs the += operation.

impl CanonicalSerialize for F63b

type Serializer = ByteElementSerializer<F63b>

A way to serialize field elements of this type.

type Deserializer = ByteElementDeserializer<F63b>

A way to deserialize field elements of this type.

type ByteReprLen = <<UInt<UInt<UInt<UTerm, B1>, B1>, B1> as Add<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B1>, B1>, B1>>>::Output as Div<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>>>::Output

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( bytes: &GenericArray<u8, Self::ByteReprLen> ) -> Result<Self, Self::FromBytesError>

Deserialize an element from a byte array.

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

Serialize an element into a byte array.

impl Clone for F63b

fn clone(&self) -> F63b

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for F63b

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 F63b

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 F63b

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

Formats the value using the given formatter.

impl Default for F63b

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for F63b

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

Deserialize this value from the given Serde deserializer.

impl Distribution<F63b> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F63b

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 F63b> for F63b

type Output = F63b

The resulting type after applying the / operator.

fn div(self, rhs: &'a F63b) -> Self::Output

Performs the / operation.

impl<'a> Div<F63b> for &'a F63b

type Output = F63b

The resulting type after applying the / operator.

fn div(self, rhs: F63b) -> Self::Output

Performs the / operation.

impl<'a> Div for &'a F63b

type Output = F63b

The resulting type after applying the / operator.

fn div(self, rhs: &'a F63b) -> Self::Output

Performs the / operation.

impl Div for F63b

type Output = F63b

The resulting type after applying the / operator.

fn div(self, rhs: F63b) -> Self::Output

Performs the / operation.

impl<'a> DivAssign<&'a F63b> for F63b

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

Performs the /= operation.

impl DivAssign for F63b

fn div_assign(&mut self, rhs: F63b)

Performs the /= operation.

impl FiniteField for F63b

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<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B1>, B1>, 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 F63b

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

Construct an element from the given uniformly chosen random bytes.

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

Generate a random element.

const ZERO: Self = _

The additive identity element.

const ONE: Self = _

The multiplicative identity element.

fn random_nonzero<R: Rng + ?Sized>(rng: &mut R) -> Self

Generate a random non-zero element.

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 F63b

fn from(pf: F2) -> Self

Converts to this type from the input type.

impl Hash for F63b

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<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<'a> Mul<&'a F63b> for F63b

type Output = F63b

The resulting type after applying the * operator.

fn mul(self, rhs: &'a F63b) -> Self::Output

Performs the * operation.

impl<'a> Mul<F63b> for &'a F63b

type Output = F63b

The resulting type after applying the * operator.

fn mul(self, rhs: F63b) -> Self::Output

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<'a> Mul for &'a F63b

type Output = F63b

The resulting type after applying the * operator.

fn mul(self, rhs: &'a F63b) -> Self::Output

Performs the * operation.

impl Mul for F63b

type Output = F63b

The resulting type after applying the * operator.

fn mul(self, rhs: F63b) -> Self::Output

Performs the * operation.

impl<'a> MulAssign<&'a F63b> for F63b

fn mul_assign(&mut self, rhs: &'a F63b)

Performs the *= operation.

impl MulAssign for F63b

fn mul_assign(&mut self, rhs: F63b)

Performs the *= operation.

impl Neg for F63b

type Output = F63b

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl One for F63b

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 F63b

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 F63b

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 F63b

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

Serialize this value into the given Serde serializer.

impl SmallBinaryField for F63b

fn from_lower_bits(x: u64) -> Self

Produce a field element of Self by zeroing the upper bits of x.

fn reduce(product: U64x2) -> Self

Reduce the result of a single 128-bit carryless multiply of two Self values modulo [FiniteField::reduce_multiplication_over()]

fn reduce_vectored<const N: usize>( uppers: [U64x2; N], lowers: [U64x2; N] ) -> [U64x2; N]

where ArrayUnrolledOps: UnrollableArraySize<N>,

Reduce the result of several 128-bit carryless multiply operations over [FiniteField::reduce_multiplication_over()].

impl<'a> Sub<&'a F63b> for F63b

type Output = F63b

The resulting type after applying the - operator.

fn sub(self, rhs: &'a F63b) -> Self::Output

Performs the - operation.

impl<'a> Sub<F63b> for &'a F63b

type Output = F63b

The resulting type after applying the - operator.

fn sub(self, rhs: F63b) -> Self::Output

Performs the - operation.

impl<'a> Sub for &'a F63b

type Output = F63b

The resulting type after applying the - operator.

fn sub(self, rhs: &'a F63b) -> Self::Output

Performs the - operation.

impl Sub for F63b

type Output = F63b

The resulting type after applying the - operator.

fn sub(self, rhs: F63b) -> Self::Output

Performs the - operation.

impl<'a> SubAssign<&'a F63b> for F63b

fn sub_assign(&mut self, rhs: &'a F63b)

Performs the -= operation.

impl SubAssign for F63b

fn sub_assign(&mut self, rhs: F63b)

Performs the -= operation.

impl Sum for F63b

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 TransparentWrapper<u64> for F63b

fn wrap(s: Inner) -> Self

where Self: Sized,

Convert the inner type into the wrapper type.

fn wrap_ref(s: &Inner) -> &Self

Convert a reference to the inner type into a reference to the wrapper type.

fn wrap_mut(s: &mut Inner) -> &mut Self

Convert a mutable reference to the inner type into a mutable reference to the wrapper type.

fn wrap_slice(s: &[Inner]) -> &[Self]

where Self: Sized,

Convert a slice to the inner type into a slice to the wrapper type.

fn wrap_slice_mut(s: &mut [Inner]) -> &mut [Self]

where Self: Sized,

Convert a mutable slice to the inner type into a mutable slice to the wrapper type.

fn peel(s: Self) -> Inner

where Self: Sized,

Convert the wrapper type into the inner type.

fn peel_ref(s: &Self) -> &Inner

Convert a reference to the wrapper type into a reference to the inner type.

fn peel_mut(s: &mut Self) -> &mut Inner

Convert a mutable reference to the wrapper type into a mutable reference to the inner type.

fn peel_slice(s: &[Self]) -> &[Inner]

where Self: Sized,

Convert a slice to the wrapped type into a slice to the inner type.

fn peel_slice_mut(s: &mut [Self]) -> &mut [Inner]

where Self: Sized,

Convert a mutable slice to the wrapped type into a mutable slice to the inner type.

impl Zero for F63b

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 F63b

fn zeroed() -> Self

Calls zeroed.

impl Copy for F63b

impl Eq for F63b

impl IsSubRingOf<F63b> for F2