Struct FieldElementCore 

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

Trait Implementations

impl<'r> Add<&'r FieldElementCore> for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'r> AddAssign<&'r FieldElementCore> for FieldElementCore

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

Performs the += operation.

impl AddAssign for FieldElementCore

fn add_assign(&mut self, other: FieldElementCore)

Performs the += operation.

impl Clone for FieldElementCore

fn clone(&self) -> FieldElementCore

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for FieldElementCore

fn conditional_select( a: &FieldElementCore, b: &FieldElementCore, choice: Choice, ) -> FieldElementCore

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for FieldElementCore

fn ct_eq(&self, other: &FieldElementCore) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl Debug for FieldElementCore

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

Formats the value using the given formatter.

impl Default for FieldElementCore

fn default() -> FieldElementCore

Returns the “default value” for a type.

impl Field for FieldElementCore

fn random(rng: impl RngCore) -> Self

Computes a uniformly random element using rejection sampling.

const ZERO: Self

The zero element of the field, the additive identity.

const ONE: Self = R

The one element of the field, the multiplicative identity.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn double(&self) -> Self

Doubles this element.

fn invert(&self) -> CtOption<Self>

Computes the multiplicative inverse of this element, failing if the element is zero.

fn square(&self) -> Self

Squares this element.

fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes:

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

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

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn cube(&self) -> Self

Cubes this element.

fn sqrt_alt(&self) -> (Choice, Self)

Equivalent to Self::sqrt_ratio(self, one()).

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

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

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

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

impl<'a> From<&'a FieldElementCore> for FieldElementCoreRepr

fn from(e: &'a FieldElementCore) -> FieldElementCoreRepr

Converts to this type from the input type.

impl From<FieldElementCore> for FieldElementCoreRepr

fn from(e: FieldElementCore) -> FieldElementCoreRepr

Converts to this type from the input type.

impl From<u64> for FieldElementCore

fn from(val: u64) -> FieldElementCore

Converts to this type from the input type.

impl<'r> Mul<&'r FieldElementCore> for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'r> MulAssign<&'r FieldElementCore> for FieldElementCore

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

Performs the *= operation.

impl MulAssign for FieldElementCore

fn mul_assign(&mut self, other: FieldElementCore)

Performs the *= operation.

impl Neg for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the - operator.

fn neg(self) -> FieldElementCore

Performs the unary - operation.

impl Ord for FieldElementCore

Elements are ordered lexicographically.

fn cmp(&self, other: &FieldElementCore) -> 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 FieldElementCore

fn eq(&self, other: &FieldElementCore) -> 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 FieldElementCore

fn partial_cmp(&self, other: &FieldElementCore) -> 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 FieldElementCore

const MODULUS: &'static str = MODULUS_STR

Modulus of the field written as a string for debugging purposes.

const NUM_BITS: u32 = 252u32

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

const CAPACITY: u32 = 251u32

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

const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self = GENERATOR

A fixed multiplicative generator of modulus - 1 order. This element must also be a quadratic nonresidue.

const S: u32 = 192u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd.

const ROOT_OF_UNITY: Self = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self = DELTA

Generator of the t-order multiplicative subgroup.

type Repr = FieldElementCoreRepr

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

fn from_repr(r: FieldElementCoreRepr) -> CtOption<FieldElementCore>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn from_repr_vartime(r: FieldElementCoreRepr) -> Option<FieldElementCore>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn to_repr(&self) -> FieldElementCoreRepr

Converts an element of the prime field into the standard byte representation for this field.

fn is_odd(&self) -> Choice

Returns true iff this element is odd.

fn from_str_vartime(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.

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn is_even(&self) -> Choice

Returns true iff this element is even.

impl<T: Borrow<FieldElementCore>> Product<T> for FieldElementCore

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

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

impl<'r> Sub<&'r FieldElementCore> for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for FieldElementCore

type Output = FieldElementCore

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'r> SubAssign<&'r FieldElementCore> for FieldElementCore

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

Performs the -= operation.

impl SubAssign for FieldElementCore

fn sub_assign(&mut self, other: FieldElementCore)

Performs the -= operation.

impl<T: Borrow<FieldElementCore>> Sum<T> for FieldElementCore

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

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

impl Copy for FieldElementCore

impl Eq for FieldElementCore