Trait Field 

pub trait Field:
    Sized
    + Eq
    + Copy
    + Clone
    + Default
    + Send
    + Sync
    + Debug
    + 'static
    + ConditionallySelectable
    + ConstantTimeEq
    + Neg<Output = Self>
    + Add<Output = Self, Output = Self>
    + Sub<Output = Self, Output = Self>
    + Mul<Output = Self, Output = Self>
    + Sum
    + Product
    + for<'a> Add<&'a Self>
    + for<'a> Sub<&'a Self>
    + for<'a> Mul<&'a Self>
    + for<'a> Sum<&'a Self>
    + for<'a> Product<&'a Self>
    + AddAssign
    + SubAssign
    + MulAssign
    + for<'a> AddAssign<&'a Self>
    + for<'a> SubAssign<&'a Self>
    + for<'a> MulAssign<&'a Self> {
    const ZERO: Self;
    const ONE: Self;

    // Required methods
    fn random(rng: impl RngCore) -> Self;
    fn square(&self) -> Self;
    fn double(&self) -> Self;
    fn invert(&self) -> CtOption<Self>;
    fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self);

    // Provided methods
    fn is_zero(&self) -> Choice { ... }
    fn is_zero_vartime(&self) -> bool { ... }
    fn cube(&self) -> Self { ... }
    fn sqrt_alt(&self) -> (Choice, Self) { ... }
    fn sqrt(&self) -> CtOption<Self> { ... }
    fn pow<S>(&self, exp: S) -> Self
       where S: AsRef<[u64]> { ... }
    fn pow_vartime<S>(&self, exp: S) -> Self
       where S: AsRef<[u64]> { ... }
}

This trait represents an element of a field.

Required Associated Constants

const ZERO: Self

The zero element of the field, the additive identity.

const ONE: Self

The one element of the field, the multiplicative identity.

Required Methods

fn random(rng: impl RngCore) -> Self

Returns an element chosen uniformly at random using a user-provided RNG.

fn square(&self) -> Self

Squares this element.

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

Computes:

• $(\textsf{true}, \sqrt{\textsf{num}/\textsf{div}})$, if $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a square in the field;
• $(\textsf{true}, 0)$, if $\textsf{num}$ is zero;
• $(\textsf{false}, 0)$, if $\textsf{num}$ is nonzero and $\textsf{div}$ is zero;
• $(\textsf{false}, \sqrt{G_S \cdot \textsf{num}/\textsf{div}})$, if $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a nonsquare in the field;

where $G_S$ is a non-square.

Warnings

• The choice of root from sqrt is unspecified.
• The value of $G_S$ is unspecified, and cannot be assumed to have any specific value in a generic context.

Provided Methods

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

Security

This method provides no constant-time guarantees. Implementors of the Field trait may optimise this method using non-constant-time logic.

fn cube(&self) -> Self

Cubes this element.

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

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

The provided method is implemented in terms of Self::sqrt_ratio.

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

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

The provided method is implemented in terms of Self::sqrt_ratio.

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

where S: AsRef<[u64]>,

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

Guarantees

This operation is constant time with respect to self, for all exponents with the same number of digits (exp.as_ref().len()). It is variable time with respect to the number of digits in the 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.

Guarantees

This operation is variable time with respect to self, for all exponent. If the exponent is fixed, this operation is effectively constant time. However, for stronger constant-time guarantees, Field::pow should be used.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl Field for Scalar

const ZERO: Scalar = Self::ZERO

const ONE: Scalar = Self::ONE

fn random(rng: impl RngCore) -> Scalar

fn square(&self) -> Scalar

fn double(&self) -> Scalar

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

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

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

impl Field for FieldElement

const ZERO: FieldElement

const ONE: FieldElement

fn random(rng: impl RngCore) -> FieldElement

fn square(&self) -> FieldElement

fn double(&self) -> FieldElement

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

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

fn sqrt_ratio(u: &FieldElement, v: &FieldElement) -> (Choice, FieldElement)

impl Field for Scalar

const ZERO: Scalar

const ONE: Scalar

fn random(rng: impl RngCore) -> Scalar

fn square(&self) -> Scalar

fn double(&self) -> Scalar

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

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

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

impl Field for Scalar

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

Tonelli-Shank’s algorithm for q mod 16 = 1 https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)

const ZERO: Scalar = Self::ZERO

const ONE: Scalar = Self::ONE

fn random(rng: impl RngCore) -> Scalar

fn square(&self) -> Scalar

fn double(&self) -> Scalar

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

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

impl Field for FieldElement

const ZERO: FieldElement

const ONE: FieldElement

fn random(rng: impl RngCore) -> FieldElement

fn square(&self) -> FieldElement

fn double(&self) -> FieldElement

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

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

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

impl Field for Scalar

const ZERO: Scalar

const ONE: Scalar

fn random(rng: impl RngCore) -> Scalar

fn square(&self) -> Scalar

fn double(&self) -> Scalar

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

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

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

impl Field for Scalar

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

Tonelli-Shank’s algorithm for q mod 16 = 1 https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)

const ZERO: Scalar = Self::ZERO

const ONE: Scalar = Self::ONE

fn random(rng: impl RngCore) -> Scalar

fn square(&self) -> Scalar

fn double(&self) -> Scalar

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

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

Implementors