# [−][src]Struct bls12_381::Scalar

Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.

## Methods

`impl Scalar`

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`pub const fn zero() -> Scalar`

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Returns zero, the additive identity.

`pub const fn one() -> Scalar`

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Returns one, the multiplicative identity.

`pub const fn double(&self) -> Scalar`

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Doubles this field element.

`pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Scalar>`

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Attempts to convert a little-endian byte representation of
a scalar into a `Scalar`

, failing if the input is not canonical.

`pub fn to_bytes(&self) -> [u8; 32]`

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Converts an element of `Scalar`

into a byte representation in
little-endian byte order.

`pub fn from_bytes_wide(bytes: &[u8; 64]) -> Scalar`

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Converts a 512-bit little endian integer into
a `Scalar`

by reducing by the modulus.

`pub const fn from_raw(val: [u64; 4]) -> Self`

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Converts from an integer represented in little endian
into its (congruent) `Scalar`

representation.

`pub const fn square(&self) -> Scalar`

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Squares this element.

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

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Computes the square root of this element, if it exists.

`pub fn pow(&self, by: &[u64; 4]) -> Self`

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Exponentiates `self`

by `by`

, where `by`

is a
little-endian order integer exponent.

`pub fn pow_vartime(&self, by: &[u64; 4]) -> Self`

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Exponentiates `self`

by `by`

, where `by`

is a
little-endian order integer exponent.

**This operation is variable time with respect
to the exponent.** If the exponent is fixed,
this operation is effectively constant time.

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

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

`pub const fn mul(&self, rhs: &Self) -> Self`

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Multiplies `rhs`

by `self`

, returning the result.

`pub const fn sub(&self, rhs: &Self) -> Self`

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Subtracts `rhs`

from `self`

, returning the result.

`pub const fn add(&self, rhs: &Self) -> Self`

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Adds `rhs`

to `self`

, returning the result.

`pub const fn neg(&self) -> Self`

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Negates `self`

.

## Trait Implementations

`impl From<u64> for Scalar`

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`impl<'a> From<&'a Scalar> for [u8; 32]`

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`impl Debug for Scalar`

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`impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar`

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`type Output = Scalar`

The resulting type after applying the `-`

operator.

`fn sub(self, rhs: &'b Scalar) -> Scalar`

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`impl<'b> Sub<&'b Scalar> for Scalar`

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`type Output = Scalar`

The resulting type after applying the `-`

operator.

`fn sub(self, rhs: &'b Scalar) -> Scalar`

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`impl<'a> Sub<Scalar> for &'a Scalar`

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`type Output = Scalar`

The resulting type after applying the `-`

operator.

`fn sub(self, rhs: Scalar) -> Scalar`

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`impl Sub<Scalar> for Scalar`

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`type Output = Scalar`

The resulting type after applying the `-`

operator.

`fn sub(self, rhs: Scalar) -> Scalar`

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`impl PartialEq<Scalar> for Scalar`

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`impl Eq for Scalar`

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`impl<'a, 'b> Add<&'b Scalar> for &'a Scalar`

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`type Output = Scalar`

The resulting type after applying the `+`

operator.

`fn add(self, rhs: &'b Scalar) -> Scalar`

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`impl<'b> Add<&'b Scalar> for Scalar`

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`type Output = Scalar`

The resulting type after applying the `+`

operator.

`fn add(self, rhs: &'b Scalar) -> Scalar`

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`impl<'a> Add<Scalar> for &'a Scalar`

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`type Output = Scalar`

The resulting type after applying the `+`

operator.

`fn add(self, rhs: Scalar) -> Scalar`

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`impl Add<Scalar> for Scalar`

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`type Output = Scalar`

The resulting type after applying the `+`

operator.

`fn add(self, rhs: Scalar) -> Scalar`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a Scalar`

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`type Output = Scalar`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> Scalar`

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`impl<'b> Mul<&'b Scalar> for Scalar`

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`type Output = Scalar`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> Scalar`

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`impl<'a> Mul<Scalar> for &'a Scalar`

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`type Output = Scalar`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> Scalar`

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`impl Mul<Scalar> for Scalar`

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`type Output = Scalar`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> Scalar`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a G1Projective`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, other: &'b Scalar) -> Self::Output`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a G1Affine`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, other: &'b Scalar) -> Self::Output`

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`impl<'b> Mul<&'b Scalar> for G1Projective`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> G1Projective`

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`impl<'a> Mul<Scalar> for &'a G1Projective`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G1Projective`

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`impl Mul<Scalar> for G1Projective`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G1Projective`

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`impl<'b> Mul<&'b Scalar> for G1Affine`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> G1Projective`

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`impl<'a> Mul<Scalar> for &'a G1Affine`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G1Projective`

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`impl Mul<Scalar> for G1Affine`

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`type Output = G1Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G1Projective`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a G2Projective`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, other: &'b Scalar) -> Self::Output`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a G2Affine`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, other: &'b Scalar) -> Self::Output`

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`impl<'b> Mul<&'b Scalar> for G2Projective`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> G2Projective`

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`impl<'a> Mul<Scalar> for &'a G2Projective`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G2Projective`

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`impl Mul<Scalar> for G2Projective`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G2Projective`

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`impl<'b> Mul<&'b Scalar> for G2Affine`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> G2Projective`

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`impl<'a> Mul<Scalar> for &'a G2Affine`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G2Projective`

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`impl Mul<Scalar> for G2Affine`

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`type Output = G2Projective`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> G2Projective`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a Gt`

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`type Output = Gt`

The resulting type after applying the `*`

operator.

`fn mul(self, other: &'b Scalar) -> Self::Output`

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`impl<'b> Mul<&'b Scalar> for Gt`

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`type Output = Gt`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: &'b Scalar) -> Gt`

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`impl<'a> Mul<Scalar> for &'a Gt`

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`type Output = Gt`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> Gt`

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`impl Mul<Scalar> for Gt`

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`type Output = Gt`

The resulting type after applying the `*`

operator.

`fn mul(self, rhs: Scalar) -> Gt`

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`impl<'a> Neg for &'a Scalar`

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`impl Neg for Scalar`

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`impl AddAssign<Scalar> for Scalar`

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`fn add_assign(&mut self, rhs: Scalar)`

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`impl<'b> AddAssign<&'b Scalar> for Scalar`

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`fn add_assign(&mut self, rhs: &'b Scalar)`

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`impl SubAssign<Scalar> for Scalar`

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`fn sub_assign(&mut self, rhs: Scalar)`

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`impl<'b> SubAssign<&'b Scalar> for Scalar`

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`fn sub_assign(&mut self, rhs: &'b Scalar)`

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`impl MulAssign<Scalar> for Scalar`

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`fn mul_assign(&mut self, rhs: Scalar)`

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`impl<'b> MulAssign<&'b Scalar> for Scalar`

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`fn mul_assign(&mut self, rhs: &'b Scalar)`

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`impl MulAssign<Scalar> for G1Projective`

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`fn mul_assign(&mut self, rhs: Scalar)`

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`impl<'b> MulAssign<&'b Scalar> for G1Projective`

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`fn mul_assign(&mut self, rhs: &'b Scalar)`

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`impl MulAssign<Scalar> for G2Projective`

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`fn mul_assign(&mut self, rhs: Scalar)`

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`impl<'b> MulAssign<&'b Scalar> for G2Projective`

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`fn mul_assign(&mut self, rhs: &'b Scalar)`

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`impl MulAssign<Scalar> for Gt`

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`fn mul_assign(&mut self, rhs: Scalar)`

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`impl<'b> MulAssign<&'b Scalar> for Gt`

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`fn mul_assign(&mut self, rhs: &'b Scalar)`

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`impl Copy for Scalar`

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`impl StructuralEq for Scalar`

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`impl Clone for Scalar`

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`fn clone(&self) -> Scalar`

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

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`impl Default for Scalar`

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`impl ConstantTimeEq for Scalar`

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`impl ConditionallySelectable for Scalar`

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

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

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

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## Auto Trait Implementations

## Blanket Implementations

`impl<T> From<T> for T`

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`impl<T, U> TryFrom<U> for T where`

U: Into<T>,

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U: Into<T>,

`type Error = Infallible`

The type returned in the event of a conversion error.

`fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>`

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`impl<T, U> Into<U> for T where`

U: From<T>,

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U: From<T>,

`impl<T, U> TryInto<U> for T where`

U: TryFrom<T>,

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U: TryFrom<T>,

`type Error = <U as TryFrom<T>>::Error`

The type returned in the event of a conversion error.

`fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>`

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`impl<T> Borrow<T> for T where`

T: ?Sized,

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T: ?Sized,

`impl<T> BorrowMut<T> for T where`

T: ?Sized,

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T: ?Sized,

`fn borrow_mut(&mut self) -> &mut T`

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`impl<T> Any for T where`

T: 'static + ?Sized,

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T: 'static + ?Sized,

`impl<T> ToOwned for T where`

T: Clone,

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T: Clone,

`type Owned = T`

The resulting type after obtaining ownership.

`fn to_owned(&self) -> T`

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`fn clone_into(&self, target: &mut T)`

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`impl<T> ConditionallyNegatable for T where`

T: ConditionallySelectable,

&'a T: Neg,

<&'a T as Neg>::Output == T,

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T: ConditionallySelectable,

&'a T: Neg,

<&'a T as Neg>::Output == T,