Struct Fr

pub struct Fr(/* private fields */);

Trait Implementations

impl<'a> Add<Fr> for Poly

type Output = Poly

The resulting type after applying the + operator.

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

Performs the + operation.

impl Clone for Fr

fn clone(&self) -> Fr

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Fr

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

Formats the value using the given formatter.

impl Display for Fr

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

Formats the value using the given formatter.

impl Field for Fr

fn random<R>(rng: &mut R) -> Fr

where R: RngCore + ?Sized,

Computes a uniformly random element using rejection sampling.

fn zero() -> Fr

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

fn one() -> Fr

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: &Fr)

Adds another element to this element.

fn double(&mut self)

Doubles this element.

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

Subtracts another element from this element.

fn negate(&mut self)

Negates this element.

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

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: &Fr)

Multiplies another element by this element.

fn square(&mut self)

Squares this element.

fn pow<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

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

impl From<Fr> for FrRepr

fn from(e: Fr) -> FrRepr

Converts to this type from the input type.

impl IntoFr for Fr

fn into_fr(self) -> Fr

Converts self to a field element.

impl<'a> Mul<&'a Fr> for &'a Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: &Fr) -> Self::Output

Performs the * operation.

impl<'a> Mul<&'a Fr> for Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: &Fr) -> Self::Output

Performs the * operation.

impl<'a> Mul<Fr> for &'a Poly

type Output = Poly

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for Poly

type Output = Poly

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<Fr> for Poly

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl Ord for Fr

Elements are ordered lexicographically.

fn cmp(&self, other: &Fr) -> 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 PartialEq for Fr

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

fn partial_cmp(&self, other: &Fr) -> 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 PrimeField for Fr

const NUM_BITS: u32 = 255u32

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

const CAPACITY: u32 = 254u32

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

const S: u32 = 32u32

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

type Repr = FrRepr

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

fn from_repr(r: FrRepr) -> Result<Fr, PrimeFieldDecodingError>

Convert this prime field element into a biginteger representation.

fn into_repr(&self) -> FrRepr

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

fn char() -> FrRepr

Returns the field characteristic; the modulus.

fn multiplicative_generator() -> Fr

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

fn root_of_unity() -> Fr

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 SqrtField for Fr

fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol of the field element.

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

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

impl<'a> Sub<Fr> for Poly

type Output = Poly

The resulting type after applying the - operator.

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

Performs the - operation.

impl Copy for Fr

impl Eq for Fr