Type Alias Fp3

pub type Fp3<P> = CubicExtField<Fp3ConfigWrapper<P>>;

Aliased Type

struct Fp3<P> {
    pub c0: <Fp3ConfigWrapper<P> as CubicExtConfig>::BaseField,
    pub c1: <Fp3ConfigWrapper<P> as CubicExtConfig>::BaseField,
    pub c2: <Fp3ConfigWrapper<P> as CubicExtConfig>::BaseField,
}

Fields

c0: <Fp3ConfigWrapper<P> as CubicExtConfig>::BaseField

c1: <Fp3ConfigWrapper<P> as CubicExtConfig>::BaseField

c2: <Fp3ConfigWrapper<P> as CubicExtConfig>::BaseField

Implementations

impl<P: Fp3Config> Fp3<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: 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<P: Fp3Config> CyclotomicMultSubgroup for Fp3<P>

const INVERSE_IS_FAST: bool = false

Is the inverse fast to compute? For example, in quadratic extensions, the inverse can be computed at the cost of negating one coordinate, which is much faster than standard inversion. By default this is false, but should be set to true for quadratic extensions.

fn cyclotomic_square(&self) -> Self

Compute a square in the cyclotomic subgroup. By default this is computed using Field::square, but for degree 12 extensions, this can be computed faster than normal squaring.

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

Square self in place. By default this is computed using Field::square_in_place, but for degree 12 extensions, this can be computed faster than normal squaring.

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

Compute the inverse of self. See Self::INVERSE_IS_FAST for details. Returns None if self.is_zero(), and Some otherwise.

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

Compute the inverse of self. See Self::INVERSE_IS_FAST for details. Returns None if self.is_zero(), and Some otherwise.

fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self

Compute a cyclotomic exponentiation of self with respect to e.

fn cyclotomic_exp_in_place(&mut self, e: impl AsRef<[u64]>)

Set self to be the result of exponentiating self by e, using efficient cyclotomic algorithms.

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, 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<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<'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, 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<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, 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, 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<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, 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, 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<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,