Struct ark_ff::fields::models::quadratic_extension::QuadExtField

pub struct QuadExtField<P: QuadExtParameters> {
    pub c0: P::BaseField,
    pub c1: P::BaseField,
    // some fields omitted
}

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

Fields

c0: P::BaseField

c1: P::BaseField

Implementations

impl<P: Fp2Parameters> QuadExtField<Fp2ParamsWrapper<P>>

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

impl<P: Fp4Parameters> QuadExtField<Fp4ParamsWrapper<P>>

pub fn mul_by_fp(&mut self, element: &<P::Fp2Params as Fp2Parameters>::Fp)

pub fn mul_by_fp2(&mut self, element: &Fp2<P::Fp2Params>)

impl<P: Fp6Parameters> QuadExtField<Fp6ParamsWrapper<P>>

pub fn mul_by_034(
    &mut self,
    c0: &<P::Fp3Params as Fp3Parameters>::Fp,
    c3: &<P::Fp3Params as Fp3Parameters>::Fp,
    c4: &<P::Fp3Params as Fp3Parameters>::Fp
)

pub fn mul_by_014(
    &mut self,
    c0: &<P::Fp3Params as Fp3Parameters>::Fp,
    c1: &<P::Fp3Params as Fp3Parameters>::Fp,
    c4: &<P::Fp3Params as Fp3Parameters>::Fp
)

impl<P: Fp12Parameters> QuadExtField<Fp12ParamsWrapper<P>>

pub fn mul_by_fp(
    &mut self,
    element: &<<P::Fp6Params as Fp6Parameters>::Fp2Params as Fp2Parameters>::Fp
)

pub fn mul_by_034(
    &mut self,
    c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c3: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)

pub fn mul_by_014(
    &mut self,
    c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c1: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)

pub fn cyclotomic_square_in_place(&mut self)

pub fn cyclotomic_square(&self) -> Self

impl<P: QuadExtParameters> QuadExtField<P>

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

pub fn conjugate(&mut self)

This is only to be used when the element is known to be in the cyclotomic subgroup.

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

This is only to be used when the element is known to be in the cyclotomic subgroup.

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

Norm of QuadExtField over P::BaseField:Norm(a) = a * a.conjugate(). This simplifies to: Norm(a) = a.x^2 - P::NON_RESIDUE * a.y^2. This is alternatively expressed as Norm(a) = a^(1 + p).

pub fn mul_assign_by_basefield(&mut self, element: &P::BaseField)

Trait Implementations

impl<'a, P: QuadExtParameters> Add<&'a QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: QuadExtParameters> Add<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: QuadExtParameters> Add<QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: QuadExtParameters> AddAssign<&'a QuadExtField<P>> for QuadExtField<P>

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

Performs the += operation.

impl<'a, P: QuadExtParameters> AddAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

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

Performs the += operation.

impl<P: QuadExtParameters> AddAssign<QuadExtField<P>> for QuadExtField<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: QuadExtParameters> CanonicalDeserialize for QuadExtField<P>

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

Reads Self from reader.

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

Reads Self from reader without compression.

fn deserialize_unchecked<R>(reader: R) -> Result<Self, SerializationError> where
    R: Read, 

Reads self from reader without compression, and without performing validity checks. Should be used only when the input is trusted.

impl<P: QuadExtParameters> CanonicalDeserializeWithFlags for QuadExtField<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: QuadExtParameters> CanonicalSerialize for QuadExtField<P>

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

Serializes self into writer. It is left up to a particular type for how it strikes the serialization efficiency vs compression tradeoff. For standard types (e.g. bool, lengths, etc.) typically an uncompressed form is used, whereas for algebraic types compressed forms are used.

fn serialized_size(&self) -> usize

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

Serializes self into writer without compression.

fn serialize_unchecked<W>(&self, writer: W) -> Result<(), SerializationError> where
    W: Write, 

Serializes self into writer without compression, and without performing validity checks. Should be used only when there is no danger of adversarial manipulation of the output.

fn uncompressed_size(&self) -> usize

impl<P: QuadExtParameters> CanonicalSerializeWithFlags for QuadExtField<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: QuadExtParameters> Clone for QuadExtField<P> where
    P: QuadExtParameters, 

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: QuadExtParameters> Debug for QuadExtField<P> where
    P: QuadExtParameters, 

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

Formats the value using the given formatter.

impl<P: QuadExtParameters> Default for QuadExtField<P> where
    P: QuadExtParameters, 

fn default() -> Self

Returns the “default value” for a type.

impl<P: QuadExtParameters> Display for QuadExtField<P>

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

Formats the value using the given formatter.

impl<'a, P: QuadExtParameters> Div<&'a QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: QuadExtParameters> Div<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl<P: QuadExtParameters> Div<QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: QuadExtParameters> DivAssign<&'a QuadExtField<P>> for QuadExtField<P>

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

Performs the /= operation.

impl<'a, P: QuadExtParameters> DivAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

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

Performs the /= operation.

impl<P: QuadExtParameters> DivAssign<QuadExtField<P>> for QuadExtField<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: QuadExtParameters> Field for QuadExtField<P>

type BasePrimeField = P::BasePrimeField

fn extension_degree() -> u64

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

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 square(&self) -> Self

Returns self * self.

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

Returns a field element with an extra sign bit used for group parsing if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

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

Returns a field element if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

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>

fn frobenius_map(&mut self, power: usize)

Exponentiates this element by a power of the base prime modulus via the Frobenius automorphism.

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

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

#[must_use]

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

Exponentiates this element by a number 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: QuadExtParameters> From<bool> for QuadExtField<P>

fn from(other: bool) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<i128> for QuadExtField<P>

fn from(val: i128) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<i16> for QuadExtField<P>

fn from(val: i16) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<i32> for QuadExtField<P>

fn from(val: i32) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<i64> for QuadExtField<P>

fn from(val: i64) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<i8> for QuadExtField<P>

fn from(val: i8) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<u128> for QuadExtField<P>

fn from(other: u128) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<u16> for QuadExtField<P>

fn from(other: u16) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<u32> for QuadExtField<P>

fn from(other: u32) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<u64> for QuadExtField<P>

fn from(other: u64) -> Self

Performs the conversion.

impl<P: QuadExtParameters> From<u8> for QuadExtField<P>

fn from(other: u8) -> Self

Performs the conversion.

impl<P: QuadExtParameters> FromBytes for QuadExtField<P>

fn read<R: Read>(reader: R) -> IoResult<Self>

Reads Self from reader.

impl<P: QuadExtParameters> Hash for QuadExtField<P> where
    P: QuadExtParameters, 

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, 

Feeds a slice of this type into the given Hasher.

impl<'a, P: QuadExtParameters> Mul<&'a QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: QuadExtParameters> Mul<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: QuadExtParameters> Mul<QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: QuadExtParameters> MulAssign<&'a QuadExtField<P>> for QuadExtField<P>

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

Performs the *= operation.

impl<'a, P: QuadExtParameters> MulAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

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

Performs the *= operation.

impl<P: QuadExtParameters> MulAssign<QuadExtField<P>> for QuadExtField<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: QuadExtParameters> Neg for QuadExtField<P>

type Output = Self

The resulting type after applying the - operator.

#[must_use]

fn neg(self) -> Self

Performs the unary - operation.

impl<P: QuadExtParameters> One for QuadExtField<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: QuadExtParameters> Ord for QuadExtField<P>

QuadExtField elements are ordered lexicographically.

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

#[must_use]

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

Compares and returns the maximum of two values.

#[must_use]

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

Compares and returns the minimum of two values.

#[must_use]

fn clamp(self, min: Self, max: Self) -> Self

Restrict a value to a certain interval.

impl<P: QuadExtParameters> PartialEq<QuadExtField<P>> for QuadExtField<P> where
    P: QuadExtParameters, 

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

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

#[must_use]

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

This method tests for !=.

impl<P: QuadExtParameters> PartialOrd<QuadExtField<P>> for QuadExtField<P>

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

#[must_use]

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

This method tests less than (for self and other) and is used by the < operator.

#[must_use]

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

#[must_use]

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

This method tests greater than (for self and other) and is used by the > operator.

#[must_use]

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<'a, P: QuadExtParameters> Product<&'a QuadExtField<P>> for QuadExtField<P>

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

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

impl<P: QuadExtParameters> Product<QuadExtField<P>> for QuadExtField<P>

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<'a, P: QuadExtParameters> SquareRootField for QuadExtField<P> where
    P::BaseField: SquareRootField, 

fn legendre(&self) -> LegendreSymbol

Returns a LegendreSymbol, which indicates whether this field element is 1 : a quadratic residue 0 : equal to 0 -1 : a quadratic non-residue

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.

impl<'a, P: QuadExtParameters> Sub<&'a QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: QuadExtParameters> Sub<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: QuadExtParameters> Sub<QuadExtField<P>> for QuadExtField<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: QuadExtParameters> SubAssign<&'a QuadExtField<P>> for QuadExtField<P>

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

Performs the -= operation.

impl<'a, P: QuadExtParameters> SubAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

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

Performs the -= operation.

impl<P: QuadExtParameters> SubAssign<QuadExtField<P>> for QuadExtField<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: QuadExtParameters> Sum<&'a QuadExtField<P>> for QuadExtField<P>

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

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

impl<P: QuadExtParameters> Sum<QuadExtField<P>> for QuadExtField<P>

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<P: QuadExtParameters> ToBytes for QuadExtField<P>

fn write<W: Write>(&self, writer: W) -> IoResult<()>

Serializes self into writer.

impl<P: QuadExtParameters> ToConstraintField<<P as QuadExtParameters>::BasePrimeField> for QuadExtField<P> where
    P::BaseField: ToConstraintField<P::BasePrimeField>, 

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

impl<P: QuadExtParameters> Zero for QuadExtField<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: QuadExtParameters> Zeroize for QuadExtField<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: QuadExtParameters> Copy for QuadExtField<P> where
    P: QuadExtParameters, 

impl<P: QuadExtParameters> Eq for QuadExtField<P> where
    P: QuadExtParameters,