Struct pairing_ce::bn256::fq::Fq

pub struct Fq(_);

Trait Implementations

impl Clone for Fq

fn clone(&self) -> Fq

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Fq

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

Formats the value using the given formatter.

impl Default for Fq

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Fq

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

Deserialize this value from the given Serde deserializer.

impl Display for Fq

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

Formats the value using the given formatter.

impl Field for Fq

fn zero() -> Self

Returns the zero element of the field, the additive identity.

fn one() -> Self

Returns the one element of the field, the multiplicative identity.

fn is_zero(&self) -> bool

Returns true iff this element is zero.

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

Adds another element to this element.

fn double(&mut self)

Doubles this element.

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

Subtracts another element from this element.

fn negate(&mut self)

Negates this element.

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

Computes the multiplicative inverse of this element, if nonzero.

fn frobenius_map(&mut self, _: usize)

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

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

Multiplies another element by this element.

fn square(&mut self)

Squares this element.

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

Exponentiates this element by a number represented with u64 limbs, least significant digit first.

impl From<Fq> for FqRepr

fn from(e: Fq) -> FqRepr

Converts to this type from the input type.

impl Hash for Fq

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 Ord for Fq

Elements are ordered lexicographically.

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

This method returns an Ordering between self and other.

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

Compares and returns the maximum of two values.

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

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Selfwhere
    Self: Sized + PartialOrd<Self>,

Restrict a value to a certain interval.

impl PartialEq<Fq> for Fq

fn eq(&self, other: &Fq) -> 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 PartialOrd<Fq> for Fq

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

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

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

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

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

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

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

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

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 PrimeField for Fq

type Repr = FqRepr

The prime field can be converted back and forth into this biginteger representation.

fn from_repr(r: FqRepr) -> Result<Fq, PrimeFieldDecodingError>

Convert this prime field element into a biginteger representation.

fn from_raw_repr(r: FqRepr) -> Result<Self, PrimeFieldDecodingError>

Creates an element from raw representation in Montgommery form.

fn into_repr(&self) -> FqRepr

Convert a biginteger representation into a prime field element, if the number is an element of the field.

fn into_raw_repr(&self) -> FqRepr

Expose Montgommery represendation.

fn char() -> FqRepr

Returns the field characteristic; the modulus.

const NUM_BITS: u32 = 254u32

How many bits are needed to represent an element of this field.

const CAPACITY: u32 = 253u32

How many bits of information can be reliably stored in the field element.

fn multiplicative_generator() -> Self

Returns the multiplicative generator of char() - 1 order. This element must also be quadratic nonresidue.

const S: u32 = 1u32

2^s * t = char() - 1 with t odd.

fn root_of_unity() -> Self

Returns the 2^s root of unity computed by exponentiating the multiplicative_generator() by t.

fn from_str(s: &str) -> Option<Self>

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.

impl Rand for Fq

fn rand<R: Rng>(rng: &mut R) -> Self

Computes a uniformly random element using rejection sampling.

impl Serialize for Fq

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

Serialize this value into the given Serde serializer.

impl SqrtField for Fq

fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol of the field element.

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

Returns the square root of the field element, if it is quadratic residue.

impl Copy for Fq

impl Eq for Fq