Struct CubicExtField

pub struct CubicExtField<P: CubicExtConfig> {
    pub c0: P::BaseField,
    pub c1: P::BaseField,
    pub c2: P::BaseField,
}

An element of a cubic extension field F_p[X]/(X^3 - P::NONRESIDUE) is represented as c0 + c1 * X + c2 * X^2, for c0, c1, c2 in P::BaseField.

Fields

c0: P::BaseField

c1: P::BaseField

c2: P::BaseField

Implementations

impl<P: Fp3Config> CubicExtField<Fp3ConfigWrapper<P>>

pub fn mul_assign_by_fp(&mut self, value: &P::Fp)

In-place multiply all coefficients c0, c1, and c2 of self by an element from Fp.

Examples

use ark_mnt6_753::{Fq as Fp, Fq3 as Fp3};
let c0: Fp = Fp::rand(&mut test_rng());
let c1: Fp = Fp::rand(&mut test_rng());
let c2: Fp = Fp::rand(&mut test_rng());
let mut ext_element: Fp3 = Fp3::new(c0, c1, c2);

let base_field_element: Fp = Fp::rand(&mut test_rng());
ext_element.mul_assign_by_fp(&base_field_element);

assert_eq!(ext_element.c0, c0 * base_field_element);
assert_eq!(ext_element.c1, c1 * base_field_element);
assert_eq!(ext_element.c2, c2 * base_field_element);

impl<P: Fp6Config> CubicExtField<Fp6ConfigWrapper<P>>

pub fn mul_assign_by_fp2(&mut self, other: Fp2<P::Fp2Config>)

pub fn mul_by_fp(&mut self, element: &<P::Fp2Config as Fp2Config>::Fp)

pub fn mul_by_fp2(&mut self, element: &Fp2<P::Fp2Config>)

pub fn mul_by_1(&mut self, c1: &Fp2<P::Fp2Config>)

pub fn mul_by_01(&mut self, c0: &Fp2<P::Fp2Config>, c1: &Fp2<P::Fp2Config>)

impl<P: CubicExtConfig> CubicExtField<P>

pub const fn new(c0: P::BaseField, c1: P::BaseField, c2: P::BaseField) -> Self

Create a new field element from coefficients c0, c1 and c2 so that the result is of the form c0 + c1 * X + c2 * X^2.

Examples

use ark_ff::models::cubic_extension::CubicExtField;

let c0: Fp2 = Fp2::rand(&mut test_rng());
let c1: Fp2 = Fp2::rand(&mut test_rng());
let c2: Fp2 = Fp2::rand(&mut test_rng());
// `Fp6` a degree-3 extension over `Fp2`.
let c: CubicExtField<Config> = Fp6::new(c0, c1, c2);

pub fn mul_assign_by_base_field(&mut self, value: &P::BaseField)

pub fn norm(&self) -> P::BaseField

Calculate the norm of an element with respect to the base field P::BaseField. The norm maps an element a in the extension field Fq^m to an element in the BaseField Fq. Norm(a) = a * a^q * a^(q^2)

Trait Implementations

impl<'a, 'b, P: CubicExtConfig> Add<&'a CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the + operation.

impl<'a, P: CubicExtConfig> Add<&'a CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &Self) -> Self

Performs the + operation.

impl<'a, 'b, P: CubicExtConfig> Add<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the + operation.

impl<'a, P: CubicExtConfig> Add<&'a mut CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<'b, P: CubicExtConfig> Add<CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: CubicExtField<P>) -> CubicExtField<P>

Performs the + operation.

impl<P: CubicExtConfig> Add for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: CubicExtConfig> AddAssign<&'a CubicExtField<P>> for CubicExtField<P>

fn add_assign(&mut self, other: &Self)

Performs the += operation.

impl<'a, P: CubicExtConfig> AddAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: CubicExtConfig> AddAssign for CubicExtField<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: CubicExtConfig> CanonicalDeserialize for CubicExtField<P>

fn deserialize_with_mode<R: Read>( reader: R, compress: Compress, validate: Validate, ) -> Result<Self, SerializationError>

The general deserialize method that takes in customization flags.

fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_compressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

impl<P: CubicExtConfig> CanonicalDeserializeWithFlags for CubicExtField<P>

fn deserialize_with_flags<R: Read, F: Flags>( reader: R, ) -> Result<(Self, F), SerializationError>

Reads Self and Flags from reader. Returns empty flags by default.

impl<P: CubicExtConfig> CanonicalSerialize for CubicExtField<P>

fn serialize_with_mode<W: Write>( &self, writer: W, _compress: Compress, ) -> Result<(), SerializationError>

The general serialize method that takes in customization flags.

fn serialized_size(&self, _compress: Compress) -> usize

fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn compressed_size(&self) -> usize

fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn uncompressed_size(&self) -> usize

impl<P: CubicExtConfig> CanonicalSerializeWithFlags for CubicExtField<P>

fn serialize_with_flags<W: Write, F: Flags>( &self, writer: W, flags: F, ) -> Result<(), SerializationError>

Serializes self and flags into writer.

fn serialized_size_with_flags<F: Flags>(&self) -> usize

Serializes self and flags into writer.

impl<P> Clone for CubicExtField<P>

where P: CubicExtConfig,

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P> Debug for CubicExtField<P>

where P: CubicExtConfig,

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

Formats the value using the given formatter.

impl<P> Default for CubicExtField<P>

where P: CubicExtConfig,

fn default() -> Self

Returns the “default value” for a type.

impl<P: CubicExtConfig> Display for CubicExtField<P>

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

Formats the value using the given formatter.

impl<P: CubicExtConfig> Distribution<CubicExtField<P>> for Standard

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

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, 'b, P: CubicExtConfig> Div<&'a CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'a, P: CubicExtConfig> Div<&'a CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &Self) -> Self

Performs the / operation.

impl<'a, 'b, P: CubicExtConfig> Div<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'a, P: CubicExtConfig> Div<&'a mut CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut Self) -> Self

Performs the / operation.

impl<'b, P: CubicExtConfig> Div<CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<P: CubicExtConfig> Div for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: CubicExtConfig> DivAssign<&'a CubicExtField<P>> for CubicExtField<P>

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

Performs the /= operation.

impl<'a, P: CubicExtConfig> DivAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

fn div_assign(&mut self, other: &'a mut Self)

Performs the /= operation.

impl<P: CubicExtConfig> DivAssign for CubicExtField<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: CubicExtConfig> Field for CubicExtField<P>

fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol.

const SQRT_PRECOMP: Option<SqrtPrecomputation<Self>> = P::SQRT_PRECOMP

Determines the algorithm for computing square roots.

const ZERO: Self = _

The additive identity of the field.

const ONE: Self = _

The multiplicative identity of the field.

type BasePrimeField = <P as CubicExtConfig>::BasePrimeField

type BasePrimeFieldIter = Chain<<<P as CubicExtConfig>::BaseField as Field>::BasePrimeFieldIter, Chain<<<P as CubicExtConfig>::BaseField as Field>::BasePrimeFieldIter, <<P as CubicExtConfig>::BaseField as Field>::BasePrimeFieldIter>>

fn extension_degree() -> u64

Returns the extension degree of this field with respect to Self::BasePrimeField.

fn from_base_prime_field(elem: Self::BasePrimeField) -> Self

Constructs a field element from a single base prime field elements.

fn to_base_prime_field_elements(&self) -> Self::BasePrimeFieldIter

fn from_base_prime_field_elems(elems: &[Self::BasePrimeField]) -> Option<Self>

Convert a slice of base prime field elements into a field element. If the slice length != Self::extension_degree(), must return None.

fn double(&self) -> Self

Returns self + self.

fn double_in_place(&mut self) -> &mut Self

Doubles self in place.

fn neg_in_place(&mut self) -> &mut Self

Negates self in place.

fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>

Attempt to deserialize a field element, splitting the bitflags metadata according to F specification. Returns None if the deserialization fails.

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Attempt to deserialize a field element. Returns None if the deserialization fails.

fn square(&self) -> Self

Returns self * self.

fn square_in_place(&mut self) -> &mut Self

Squares self in place.

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

Computes the multiplicative inverse of self if self is nonzero.

fn inverse_in_place(&mut self) -> Option<&mut Self>

If self.inverse().is_none(), this just returns None. Otherwise, it sets self to self.inverse().unwrap().

fn frobenius_map_in_place(&mut self, power: usize)

Sets self to self^s, where s = Self::BasePrimeField::MODULUS^power. This is also called the Frobenius automorphism.

fn characteristic() -> &'static [u64]

Returns the characteristic of the field, in little-endian representation.

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

Returns the square root of self, if it exists.

fn sqrt_in_place(&mut self) -> Option<&mut Self>

Sets self to be the square root of self, if it exists.

fn sum_of_products<const T: usize>(a: &[Self; T], b: &[Self; T]) -> Self

Returns sum([a_i * b_i]).

fn frobenius_map(&self, power: usize) -> Self

Returns self^s, where s = Self::BasePrimeField::MODULUS^power. This is also called the Frobenius automorphism.

fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self

Returns self^exp, where exp is an integer represented with u64 limbs, least significant limb first.

fn pow_with_table<S: AsRef<[u64]>>(powers_of_2: &[Self], exp: S) -> Option<Self>

Exponentiates a field element f by a number represented with u64 limbs, using a precomputed table containing as many powers of 2 of f as the 1 + the floor of log2 of the exponent exp, starting from the 1st power. That is, powers_of_2 should equal &[p, p^2, p^4, ..., p^(2^n)] when exp has at most n bits.

impl<P: CubicExtConfig> From<bool> for CubicExtField<P>

fn from(other: bool) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<i128> for CubicExtField<P>

fn from(val: i128) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<i16> for CubicExtField<P>

fn from(val: i16) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<i32> for CubicExtField<P>

fn from(val: i32) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<i64> for CubicExtField<P>

fn from(val: i64) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<i8> for CubicExtField<P>

fn from(val: i8) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<u128> for CubicExtField<P>

fn from(other: u128) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<u16> for CubicExtField<P>

fn from(other: u16) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<u32> for CubicExtField<P>

fn from(other: u32) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<u64> for CubicExtField<P>

fn from(other: u64) -> Self

Converts to this type from the input type.

impl<P: CubicExtConfig> From<u8> for CubicExtField<P>

fn from(other: u8) -> Self

Converts to this type from the input type.

impl<P> Hash for CubicExtField<P>

where P: CubicExtConfig,

fn hash<__HP>(&self, __state: &mut __HP)

where __HP: Hasher,

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<'a, 'b, P: CubicExtConfig> Mul<&'a CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the * operation.

impl<'a, P: CubicExtConfig> Mul<&'a CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &Self) -> Self

Performs the * operation.

impl<'a, 'b, P: CubicExtConfig> Mul<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the * operation.

impl<'a, P: CubicExtConfig> Mul<&'a mut CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut Self) -> Self

Performs the * operation.

impl<'b, P: CubicExtConfig> Mul<CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: CubicExtField<P>) -> CubicExtField<P>

Performs the * operation.

impl<P: CubicExtConfig> Mul for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: CubicExtConfig> MulAssign<&'a CubicExtField<P>> for CubicExtField<P>

fn mul_assign(&mut self, other: &Self)

Performs the *= operation.

impl<'a, P: CubicExtConfig> MulAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

fn mul_assign(&mut self, other: &'a mut Self)

Performs the *= operation.

impl<P: CubicExtConfig> MulAssign for CubicExtField<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: CubicExtConfig> Neg for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: CubicExtConfig> One for CubicExtField<P>

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<P: CubicExtConfig> Ord for CubicExtField<P>

CubicExtField elements are ordered lexicographically.

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.

impl<P> PartialEq for CubicExtField<P>

where P: CubicExtConfig,

fn eq(&self, other: &Self) -> 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<P: CubicExtConfig> PartialOrd for CubicExtField<P>

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<'a, P: CubicExtConfig> Product<&'a CubicExtField<P>> for CubicExtField<P>

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

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

impl<P: CubicExtConfig> Product for CubicExtField<P>

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

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

impl<'a, 'b, P: CubicExtConfig> Sub<&'a CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the - operation.

impl<'a, P: CubicExtConfig> Sub<&'a CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &Self) -> Self

Performs the - operation.

impl<'a, 'b, P: CubicExtConfig> Sub<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the - operation.

impl<'a, P: CubicExtConfig> Sub<&'a mut CubicExtField<P>> for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<'b, P: CubicExtConfig> Sub<CubicExtField<P>> for &'b CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: CubicExtField<P>) -> CubicExtField<P>

Performs the - operation.

impl<P: CubicExtConfig> Sub for CubicExtField<P>

type Output = CubicExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: CubicExtConfig> SubAssign<&'a CubicExtField<P>> for CubicExtField<P>

fn sub_assign(&mut self, other: &Self)

Performs the -= operation.

impl<'a, P: CubicExtConfig> SubAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: CubicExtConfig> SubAssign for CubicExtField<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: CubicExtConfig> Sum<&'a CubicExtField<P>> for CubicExtField<P>

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

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

impl<P: CubicExtConfig> Sum for CubicExtField<P>

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

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

impl<P: CubicExtConfig> ToConstraintField<<P as CubicExtConfig>::BasePrimeField> for CubicExtField<P>

where P::BaseField: ToConstraintField<P::BasePrimeField>,

fn to_field_elements(&self) -> Option<Vec<P::BasePrimeField>>

impl<P: CubicExtConfig> Valid for CubicExtField<P>

fn check(&self) -> Result<(), SerializationError>

fn batch_check<'a>( batch: impl Iterator<Item = &'a Self> + Send, ) -> Result<(), SerializationError>

where Self: 'a,

impl<P: CubicExtConfig> Zero for CubicExtField<P>

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<P: CubicExtConfig> Zeroize for CubicExtField<P>

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl<P> Copy for CubicExtField<P>

where P: CubicExtConfig,

impl<P> Eq for CubicExtField<P>

where P: CubicExtConfig,