Trait Field

Source

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]> { ... }
}

Expand description

This trait represents an element of a field.

Required Associated Constants§

Source

const ZERO: Self

The zero element of the field, the additive identity.

Source

const ONE: Self

The one element of the field, the multiplicative identity.

Required Methods§

Source

fn random(rng: impl RngCore) -> Self

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

Source

fn square(&self) -> Self

Squares this element.

Source

fn double(&self) -> Self

Doubles this element.

Source

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

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

Source

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§

Source

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

Source

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.

Source

fn cube(&self) -> Self

Cubes this element.

Source

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

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

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

Source

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.

Source

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.

Source

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.

Trait FieldCopy item path

Required Associated Constants§

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)

§Warnings

Provided Methods§

fn is_zero(&self) -> Choice

fn is_zero_vartime(&self) -> bool

§Security

fn cube(&self) -> Self

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

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

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

§Guarantees

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

§Guarantees

Dyn Compatibility§

Implementations on Foreign Types§

impl Field for Fp2

const ZERO: Fp2 = _

const ONE: Fp2 = _

fn random(rng: impl RngCore) -> Fp2

fn is_zero(&self) -> Choice

fn square(&self) -> Fp2

fn double(&self) -> Fp2

fn sqrt(&self) -> CtOption<Fp2>

fn invert(&self) -> CtOption<Fp2>

fn sqrt_ratio(num: &Fp2, div: &Fp2) -> (Choice, Fp2)

impl Field for Fp12

const ZERO: Fp12 = _

const ONE: Fp12 = _

fn random(rng: impl RngCore) -> Fp12

fn is_zero(&self) -> Choice

fn square(&self) -> Fp12

fn double(&self) -> Fp12

fn sqrt(&self) -> CtOption<Fp12>

fn invert(&self) -> CtOption<Fp12>

fn sqrt_ratio(_num: &Fp12, _div: &Fp12) -> (Choice, Fp12)

impl Field for Fp

const ZERO: Fp = _

const ONE: Fp = _

fn random(rng: impl RngCore) -> Fp

fn square(&self) -> Fp

fn double(&self) -> Fp

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

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

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

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_ratio(num: &Scalar, div: &Scalar) -> (Choice, Scalar)

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

fn is_zero_vartime(&self) -> bool

impl Field for Fq2

const ZERO: Fq2 = _

const ONE: Fq2 = _

fn random(rng: impl RngCore) -> Fq2

fn is_zero(&self) -> Choice

fn square(&self) -> Fq2

fn double(&self) -> Fq2

fn sqrt(&self) -> CtOption<Fq2>

fn sqrt_ratio(num: &Fq2, div: &Fq2) -> (Choice, Fq2)

fn invert(&self) -> CtOption<Fq2>

impl Field for Fq6

const ZERO: Fq6 = _

const ONE: Fq6 = _

fn random(rng: impl RngCore) -> Fq6

fn is_zero(&self) -> Choice

fn square(&self) -> Fq6

fn double(&self) -> Fq6

Trait Field

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

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

fn pow_vartime<S>(&self, exp: S) -> Fq
where S: AsRef<[u64]>,

fn pow_vartime<S>(&self, exp: S) -> Fr
where S: AsRef<[u64]>,