Struct BinomialExtensionField 

pub struct BinomialExtensionField<F, const D: usize, A = F> { /* private fields */ }

Implementations

impl<R: PrimeCharacteristicRing> BinomialExtensionField<R, 2>

Convenience methods for complex extensions

pub const fn new_complex(real: R, imag: R) -> Self

pub const fn new_real(real: R) -> Self

pub const fn new_imag(imag: R) -> Self

pub fn real(&self) -> R

pub fn imag(&self) -> R

pub fn conjugate(&self) -> Self

pub fn norm(&self) -> R

pub fn to_array(&self) -> [R; 2]

pub fn rotate<Ext: Algebra<R>>(&self, rhs: &Complex<Ext>) -> Complex<Ext>

Trait Implementations

impl<F, A, const D: usize> Add<A> for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F, PF, const D: usize> Add<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedBinomialExtensionField<F, PF, D>

The resulting type after applying the + operator.

fn add(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the + operation.

impl<F, A, const D: usize> Add for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F, A, const D: usize> AddAssign<A> for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

fn add_assign(&mut self, rhs: A)

Performs the += operation.

impl<F, PF, const D: usize> AddAssign<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

fn add_assign(&mut self, rhs: BinomialExtensionField<F, D>)

Performs the += operation.

impl<F, A, const D: usize> AddAssign for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<F: BinomiallyExtendable<D>, A: Algebra<F>, const D: usize> BasedVectorSpace<A> for BinomialExtensionField<F, D, A>

const DIMENSION: usize = D

The dimension of the vector space, i.e. the number of elements in its basis.

fn as_basis_coefficients_slice(&self) -> &[A]

Fixes a basis for the algebra A and uses this to map an element of A to a slice of DIMENSION F elements.

fn from_basis_coefficients_fn<Fn: FnMut(usize) -> A>(f: Fn) -> Self

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A. Similar to core:array::from_fn, the DIMENSION F elements are given by Fn(0), ..., Fn(DIMENSION - 1) called in that order.

fn from_basis_coefficients_iter<I: ExactSizeIterator<Item = A>>( iter: I, ) -> Option<Self>

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A.

fn flatten_to_base(vec: Vec<Self>) -> Vec<A>

Convert from a vector of Self to a vector of F by flattening the basis coefficients.

fn reconstitute_from_base(vec: Vec<A>) -> Vec<Self>

Convert from a vector of F to a vector of Self by combining the basis coefficients.

fn from_basis_coefficients_slice(slice: &[F]) -> Option<Self>

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A.

fn ith_basis_element(i: usize) -> Option<Self>

Given a basis for the Algebra A, return the i’th basis element.

impl<F: Clone, const D: usize, A: Clone> Clone for BinomialExtensionField<F, D, A>

fn clone(&self) -> BinomialExtensionField<F, D, A>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug, const D: usize, A: Debug> Debug for BinomialExtensionField<F, D, A>

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

Formats the value using the given formatter.

impl<F: Field, A: Algebra<F>, const D: usize> Default for BinomialExtensionField<F, D, A>

fn default() -> Self

Returns the “default value” for a type.

impl<'de, F, const D: usize, A> Deserialize<'de> for BinomialExtensionField<F, D, A>

where A: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F, const D: usize> Display for BinomialExtensionField<F, D>

where F: BinomiallyExtendable<D>,

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

Formats the value using the given formatter.

impl<F: BinomiallyExtendable<D>, const D: usize> Distribution<BinomialExtensionField<F, D>> for StandardUniform

where Self: Distribution<F>,

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

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<F, const D: usize> Div for BinomialExtensionField<F, D>

where F: BinomiallyExtendable<D>,

type Output = BinomialExtensionField<F, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<F, const D: usize> DivAssign for BinomialExtensionField<F, D>

where F: BinomiallyExtendable<D>,

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<F: BinomiallyExtendable<D>, const D: usize> ExtensionField<F> for BinomialExtensionField<F, D>

type ExtensionPacking = PackedBinomialExtensionField<F, <F as Field>::Packing, D>

fn is_in_basefield(&self) -> bool

Determine if the given element lies in the base field.

fn as_base(&self) -> Option<F>

If the element lies in the base field project it down. Otherwise return None.

impl<F: BinomiallyExtendable<D>, const D: usize> Field for BinomialExtensionField<F, D>

const GENERATOR: Self

A generator of this field’s multiplicative group.

type Packing = BinomialExtensionField<F, D>

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

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

fn halve(&self) -> Self

The elementary function halve(a) = a/2.

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

Divide by a given power of two. div_2exp_u64(a, exp) = a/2^exp

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 order() -> BigUint

The number of elements in the 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 bits() -> usize

The number of bits required to define an element of this field.

impl<F: Field, A: Algebra<F>, const D: usize> From<A> for BinomialExtensionField<F, D, A>

fn from(x: A) -> Self

Converts to this type from the input type.

impl<F: Field, PF: PackedField<Scalar = F>, const D: usize> From<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

fn from(x: BinomialExtensionField<F, D>) -> Self

Converts to this type from the input type.

impl<F: BinomiallyExtendable<D>, const D: usize> HasFrobenius<F> for BinomialExtensionField<F, D>

fn frobenius(&self) -> Self

FrobeniusField automorphisms: x -> x^n, where n is the order of BaseField.

fn repeated_frobenius(&self, count: usize) -> Self

Repeated Frobenius automorphisms: x -> x^(n^count).

Follows precomputation suggestion in Section 11.3.3 of the Handbook of Elliptic and Hyperelliptic Curve Cryptography.

fn frobenius_inv(&self) -> Self

Compute the inverse of a given element making use of the Frobenius automorphism.

Algorithm 11.3.4 in Handbook of Elliptic and Hyperelliptic Curve Cryptography.

fn galois_orbit(self) -> Vec<Self>

Returns the full Galois orbit of the element under Frobenius.

impl<F: Hash, const D: usize, A: Hash> Hash for BinomialExtensionField<F, D, A>

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<F, A, const D: usize> Mul<A> for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<F, PF, const D: usize> Mul<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedBinomialExtensionField<F, PF, D>

The resulting type after applying the * operator.

fn mul(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the * operation.

impl<F, A, const D: usize> Mul for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<F, A, const D: usize> MulAssign<A> for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

fn mul_assign(&mut self, rhs: A)

Performs the *= operation.

impl<F, PF, const D: usize> MulAssign<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

fn mul_assign(&mut self, rhs: BinomialExtensionField<F, D>)

Performs the *= operation.

impl<F, A, const D: usize> MulAssign for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<F, A, const D: usize> Neg for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<F: Ord, const D: usize, A: Ord> Ord for BinomialExtensionField<F, D, A>

fn cmp(&self, other: &BinomialExtensionField<F, D, A>) -> 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.

impl<F, const D: usize> PackedFieldExtension<F, BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, F::Packing, D>

where F: BinomiallyExtendable<D>,

fn from_ext_slice(ext_slice: &[BinomialExtensionField<F, D>]) -> Self

Given a slice of extension field EF elements of length W, convert into the array [[F; D]; W] transpose to [[F; W]; D] and then pack to get [PF; D].

fn to_ext_iter( iter: impl IntoIterator<Item = Self>, ) -> impl Iterator<Item = BinomialExtensionField<F, D>>

Given a iterator of packed extension field elements, convert to an iterator of extension field elements.

fn packed_ext_powers(base: BinomialExtensionField<F, D>) -> Powers<Self>

Similar to packed_powers, construct an iterator which returns powers of base packed into PackedFieldExtension elements.

fn packed_ext_powers_capped( base: ExtField, unpacked_len: usize, ) -> impl Iterator<Item = Self>

Similar to packed_ext_powers but only returns unpacked_len powers of base.

impl<F: PartialEq, const D: usize, A: PartialEq> PartialEq for BinomialExtensionField<F, D, A>

fn eq(&self, other: &BinomialExtensionField<F, D, A>) -> bool

Tests for self and other values to be equal, and is used by ==.

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

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

impl<F: PartialOrd, const D: usize, A: PartialOrd> PartialOrd for BinomialExtensionField<F, D, A>

fn partial_cmp( &self, other: &BinomialExtensionField<F, D, A>, ) -> 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<F, A, const D: usize> PrimeCharacteristicRing for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

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 = <A as PrimeCharacteristicRing>::PrimeSubfield

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 square(&self) -> Self

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

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

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

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.

fn from_bool(b: bool) -> Self

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

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 double(&self) -> Self

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

fn cube(&self) -> Self

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

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

Computes the arithmetic generalization of boolean xor.

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 * (1 - x).

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.

impl<F, A, const D: usize> Product for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

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

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

impl<F: BinomiallyExtendable<D>, const D: usize> RawDataSerializable for BinomialExtensionField<F, D>

const NUM_BYTES: usize

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<F, const D: usize, A> Serialize for BinomialExtensionField<F, D, A>

where A: Serialize,

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<F, A, const D: usize> Sub<A> for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F, PF, const D: usize> Sub<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedBinomialExtensionField<F, PF, D>

The resulting type after applying the - operator.

fn sub(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the - operation.

impl<F, A, const D: usize> Sub for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

type Output = BinomialExtensionField<F, D, A>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F, A, const D: usize> SubAssign<A> for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

fn sub_assign(&mut self, rhs: A)

Performs the -= operation.

impl<F, PF, const D: usize> SubAssign<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

fn sub_assign(&mut self, rhs: BinomialExtensionField<F, D>)

Performs the -= operation.

impl<F, A, const D: usize> SubAssign for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<F, A, const D: usize> Sum for BinomialExtensionField<F, D, A>

where F: BinomiallyExtendable<D>, A: Algebra<F>,

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

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

impl<F: Field + HasTwoAdicBinomialExtension<D>, const D: usize> TwoAdicField for BinomialExtensionField<F, D>

const TWO_ADICITY: usize = F::EXT_TWO_ADICITY

The number of factors of two in this field’s multiplicative group.

fn two_adic_generator(bits: usize) -> Self

Returns a generator of the multiplicative group of order 2^bits. Assumes bits <= TWO_ADICITY, otherwise the result is undefined.

impl<F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>, const D: usize> Algebra<BinomialExtensionField<F, D>> for PackedBinomialExtensionField<F, PF, D>

impl<F: BinomiallyExtendable<D>, const D: usize> Algebra<F> for BinomialExtensionField<F, D>

impl<F: Copy, const D: usize, A: Copy> Copy for BinomialExtensionField<F, D, A>

impl<F: Eq, const D: usize, A: Eq> Eq for BinomialExtensionField<F, D, A>

impl<F: BinomiallyExtendable<D>, const D: usize> Packable for BinomialExtensionField<F, D>

impl<F, const D: usize, A> StructuralPartialEq for BinomialExtensionField<F, D, A>