Struct curv::elliptic::curves::Scalar

#[repr(transparent)]
pub struct Scalar<E: Curve> { /* fields omitted */ }

Scalar value in a prime field

Guarantees

• Modulus group order

  Denoting group order as n, any instance s of Scalar<E> is guaranteed to be non-negative integer modulo n: 0 <= s < n

Arithmetics

Supported operations:

• Unary: you can invert and negate a scalar
• Binary: you can add, subtract, and multiply two scalars

Example

fn expression(
   a: &Scalar<Secp256k1>,
   b: &Scalar<Secp256k1>,
   c: &Scalar<Secp256k1>
) -> Scalar<Secp256k1> {
   a + b * c
}

Implementations

impl<E: Curve> Scalar<E>

pub fn ensure_nonzero(&self) -> Result<(), ZeroScalarError>

Ensures that self is not zero, returns Err(_) otherwise

pub fn random() -> Self

Samples a random nonzero scalar

pub fn zero() -> Self

Constructs zero scalar

pub fn is_zero(&self) -> bool

Checks if a scalar is zero

pub fn to_bigint(&self) -> BigInt

Converts a scalar to BigInt

pub fn from_bigint(n: &BigInt) -> Self

Constructs a scalar n % curve_order from given n

pub fn to_bytes(&self) -> EncodedScalar<E>

Serializes a scalar to bytes

pub fn from_bytes(bytes: &[u8]) -> Result<Self, DeserializationError>

Constructs a scalar from bytes

pub fn group_order() -> &'static BigInt

Returns an order of generator point

pub fn invert(&self) -> Option<Self>

Returns inversion self^-1 mod group_order, or None if self is zero

pub fn from_raw(raw_scalar: E::Scalar) -> Self

Constructs a Scalar<E> from low-level ECScalar implementor

Typically, you don’t need to use this constructor. See random, from_bigint constructors, and From<T>, TryFrom<T> traits implemented for Scalar<E>.

pub fn as_raw(&self) -> &E::Scalar

Returns a reference to low-level scalar implementation

Typically, you don’t need to work with ECScalar trait directly. Scalar<E> wraps ECScalar and provides convenient utilities around it: it implements arithmetic operators, (de)serialization traits, etc. If you believe that some functionality is missing, please open an issue.

pub fn into_raw(self) -> E::Scalar

Converts a scalar into inner low-level scalar implementation

Typically, you don’t need to work with ECScalar trait directly. Scalar<E> wraps ECScalar and provides convenient utilities around it: it implements arithmetic operators, (de)serialization traits, etc. If you believe that some functionality is missing, please open an issue.

Trait Implementations

impl<E: Curve> Add<&'_ Scalar<E>> for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

fn add(self, rhs: &Scalar<E>) -> Self::Output

Performs the + operation.

impl<E: Curve> Add<&'_ Scalar<E>> for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

fn add(self, rhs: &Scalar<E>) -> Self::Output

Performs the + operation.

impl<E: Curve> Add<Scalar<E>> for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

fn add(self, rhs: Scalar<E>) -> Self::Output

Performs the + operation.

impl<E: Curve> Add<Scalar<E>> for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

fn add(self, rhs: Scalar<E>) -> Self::Output

Performs the + operation.

impl<E: Curve> Clone for Scalar<E>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<E: Curve> Debug for Scalar<E>

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

Formats the value using the given formatter.

impl<'de, E: Curve> Deserialize<'de> for Scalar<E>

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error> where
    D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<E: Curve> From<&'_ BigInt> for Scalar<E>

fn from(n: &BigInt) -> Self

Performs the conversion.

impl<'s, E: Curve> From<&'s Scalar<E>> for EncodedScalar<E>

fn from(s: &'s Scalar<E>) -> Self

Performs the conversion.

impl<E: Curve> From<BigInt> for Scalar<E>

fn from(n: BigInt) -> Self

Performs the conversion.

impl<E: Curve> From<Scalar<E>> for EncodedScalar<E>

fn from(s: Scalar<E>) -> Self

Performs the conversion.

impl<E: Curve> From<i32> for Scalar<E>

fn from(n: i32) -> Self

Performs the conversion.

impl<E: Curve> From<u16> for Scalar<E>

fn from(n: u16) -> Self

Performs the conversion.

impl<E: Curve> From<u32> for Scalar<E>

fn from(n: u32) -> Self

Performs the conversion.

impl<E: Curve> From<u64> for Scalar<E>

fn from(n: u64) -> Self

Performs the conversion.

impl<E: Curve> Mul<&'_ Point<E>> for Scalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Point<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Point<E>> for &Scalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Point<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Scalar<E>> for Point<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Scalar<E>> for &Point<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Scalar<E>> for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Scalar<E>> for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Scalar<E>> for Generator<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: &Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<&'_ Scalar<E>> for &Polynomial<E>

Multiplies polynomial f(x) at scalar s, returning resulting polynomial g(x) = s * f(x)

Example

use curv::elliptic::curves::{Secp256k1, Scalar};

let f = Polynomial::<Secp256k1>::sample_exact(3);

let s = Scalar::<Secp256k1>::random();
let g = &f * &s;

for (f_coef, g_coef) in f.coefficients().iter().zip(g.coefficients()) {
    assert_eq!(&(f_coef * &s), g_coef);
}

type Output = Polynomial<E>

The resulting type after applying the * operator.

fn mul(self, scalar: &Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Generator<E>> for &Scalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Generator<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Generator<E>> for Scalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Generator<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Point<E>> for Scalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Point<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Point<E>> for &Scalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Point<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Scalar<E>> for Point<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Scalar<E>> for &Point<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Scalar<E>> for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Scalar<E>> for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Mul<Scalar<E>> for Generator<E>

type Output = Point<E>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<E>) -> Self::Output

Performs the * operation.

impl<E: Curve> Neg for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<E: Curve> Neg for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<E: Curve> PartialEq<Scalar<E>> for Scalar<E>

fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<'s, E: Curve> Product<&'s Scalar<E>> for Scalar<E>

fn product<I: Iterator<Item = &'s Scalar<E>>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<E: Curve> Product<Scalar<E>> for Scalar<E>

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<E: Curve> Serialize for Scalar<E>

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error> where
    S: Serializer, 

Serialize this value into the given Serde serializer.

impl<E: Curve> Sub<&'_ Scalar<E>> for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

fn sub(self, rhs: &Scalar<E>) -> Self::Output

Performs the - operation.

impl<E: Curve> Sub<&'_ Scalar<E>> for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

fn sub(self, rhs: &Scalar<E>) -> Self::Output

Performs the - operation.

impl<E: Curve> Sub<Scalar<E>> for Scalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

fn sub(self, rhs: Scalar<E>) -> Self::Output

Performs the - operation.

impl<E: Curve> Sub<Scalar<E>> for &Scalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

fn sub(self, rhs: Scalar<E>) -> Self::Output

Performs the - operation.

impl<'s, E: Curve> Sum<&'s Scalar<E>> for Scalar<E>

fn sum<I: Iterator<Item = &'s Scalar<E>>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<E: Curve> Sum<Scalar<E>> for Scalar<E>

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.