Struct SecretScalar 

pub struct SecretScalar<E: Curve>(/* private fields */);

Scalar representing sensitive information (like secret key)

Secret scalar should be treated with an extra care. You shouldn’t do any branching (e.g. Eq, Ord) on the secret to avoid timing side-channel attacks, so it implements only constant time traits (like ConstantTimeEq).

Also, when alloc feature is enabled, we enforce extra measures:

• Secret scalar leaves no trace in RAM after it’s dropped
  Memory is zeroized after use
• All clones of secret scalar refer to the same region in the memory
  I.e. there will always be only one instance of the scalar in the memory no matter how many clones you make

All these guarantees can be bypassed by calling .as_ref() and obtaining &Scalar<E> that is not protected from timing attacks, leaving traces in the memory, etc.

Implementations

impl<E: Curve> SecretScalar<E>

pub fn new(scalar: &mut Scalar<E>) -> Self

Constructs a new secret scalar

Takes the original scalar by mutable reference instead of taking by value to avoid leaving copies of the scalar on stack. Scalar behind the reference will be zeroized after the function has returned.

pub fn zero() -> Self

Returns scalar $S = 0$

pub fn one() -> Self

Returns scalar $S = 1$

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

Returns scalar inverse

pub fn random<R: RngCore + CryptoRng>(rng: &mut R) -> Self

Generates random secret scalar

pub fn from_hash<D: Digest>(data: &impl Digestable) -> Self

Available on crate feature hash-to-scalar only.

Hashes the input and outputs scalar

Input can be any structured data that implements Digestable trait (see udigest crate).

How it works

It works by instantiating HashRng CSPRNG seeded from provided data. Then it’s used to derive the scalar.

Security considerations

It’s not constant time. It doesn’t follow any existing standards for hash to scalar primitive.

Example

use generic_ec::{SecretScalar, curves::Secp256k1};
use sha2::Sha256;

#[derive(udigest::Digestable)]
struct Data<'a> {
    nonce: &'a [u8],
    param_a: &'a str,
    param_b: u128,
    // ...
}

let scalar = SecretScalar::<Secp256k1>::from_hash::<Sha256>(&Data {
    nonce: b"some data",
    param_a: "some other data",
    param_b: 12345,
    // ...
});

pub fn as_nonsecret(&self) -> &Scalar<E>

Obtain the reference to the scalar, which you can use for any operations necessary. This bypasses all the secrecy guarantees, so be careful when handling the resulting value; ideally this reference should not be held for longer than one expression

The AsRef impl uses this method under the hood, and is provided as a less explicit but very convenient alternative

pub fn to_be_bytes(&self) -> EncodedSecretScalar<E>

Encodes scalar as bytes in big-endian order

pub fn to_le_bytes(&self) -> EncodedSecretScalar<E>

Encodes scalar as bytes in little-endian order

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

Decodes scalar from its bytes representation in big-endian order

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

Decodes scalar from its bytes representation in little-endian order

Trait Implementations

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<&NonZero<SecretScalar<E>>> for SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<&NonZero<SecretScalar<E>>> for &SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<&SecretScalar<E>> for NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<&SecretScalar<E>> for &NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<NonZero<SecretScalar<E>>> for SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<NonZero<SecretScalar<E>>> for &SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<SecretScalar<E>> for NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> Add<SecretScalar<E>> for &NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<E: Curve> AddAssign<&SecretScalar<E>> for Scalar<E>

fn add_assign(&mut self, rhs: &SecretScalar<E>)

Performs the += operation.

impl<E: Curve> AddAssign<SecretScalar<E>> for Scalar<E>

fn add_assign(&mut self, rhs: SecretScalar<E>)

Performs the += operation.

impl<E: Curve> AsRef<Scalar<E>> for SecretScalar<E>

fn as_ref(&self) -> &Scalar<E>

Converts this type into a shared reference of the (usually inferred) input type.

impl<E: Curve> Clone for SecretScalar<E>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<E: Curve> ConstantTimeEq for SecretScalar<E>

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

Determine if two items are equal.

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

Determine if two items are NOT equal.

impl<E: Curve> Debug for SecretScalar<E>

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

Formats the value using the given formatter.

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

Available on crate feature serde only.

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<'de, E: Curve> DeserializeAs<'de, SecretScalar<E>> for Compact

Available on crate feature serde only.

fn deserialize_as<D>(deserializer: D) -> Result<SecretScalar<E>, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<E: Curve> From<NonZero<SecretScalar<E>>> for SecretScalar<E>

fn from(secret_scalar: NonZero<SecretScalar<E>>) -> Self

Converts to this type from the input type.

impl<E: Curve> Mul<&Generator<E>> for SecretScalar<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 &SecretScalar<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<&NonZero<Point<E>>> for SecretScalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<&NonZero<Point<E>>> for &SecretScalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<&SecretScalar<E>> for NonZero<Point<E>>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<&SecretScalar<E>> for &NonZero<Point<E>>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<Generator<E>> for SecretScalar<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 &SecretScalar<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<NonZero<Point<E>>> for SecretScalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<NonZero<Point<E>>> for &SecretScalar<E>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<SecretScalar<E>> for NonZero<Point<E>>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> Mul<SecretScalar<E>> for &NonZero<Point<E>>

type Output = Point<E>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<E: Curve> MulAssign<&SecretScalar<E>> for Point<E>

fn mul_assign(&mut self, rhs: &SecretScalar<E>)

Performs the *= operation.

impl<E: Curve> MulAssign<&SecretScalar<E>> for Scalar<E>

fn mul_assign(&mut self, rhs: &SecretScalar<E>)

Performs the *= operation.

impl<E: Curve> MulAssign<SecretScalar<E>> for Point<E>

fn mul_assign(&mut self, rhs: SecretScalar<E>)

Performs the *= operation.

impl<E: Curve> MulAssign<SecretScalar<E>> for Scalar<E>

fn mul_assign(&mut self, rhs: SecretScalar<E>)

Performs the *= operation.

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

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

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

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

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

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

impl<E: Curve> Samplable for SecretScalar<E>

fn random<R: RngCore>(rng: &mut R) -> Self

Uniformly samples an instance of Self from source of randomness using constant-time method

fn random_vartime<R: RngCore>(rng: &mut R) -> Self

Uniformly samples an instance of Self from source of randomness using vartime method

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

Available on crate feature serde only.

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> SerializeAs<SecretScalar<E>> for Compact

Available on crate feature serde only.

fn serialize_as<S>( source: &SecretScalar<E>, serializer: S, ) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<&NonZero<SecretScalar<E>>> for SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<&NonZero<SecretScalar<E>>> for &SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<&SecretScalar<E>> for NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<&SecretScalar<E>> for &NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<NonZero<SecretScalar<E>>> for SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<NonZero<SecretScalar<E>>> for &SecretScalar<E>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<SecretScalar<E>> for NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> Sub<SecretScalar<E>> for &NonZero<SecretScalar<E>>

type Output = Scalar<E>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<E: Curve> SubAssign<&SecretScalar<E>> for Scalar<E>

fn sub_assign(&mut self, rhs: &SecretScalar<E>)

Performs the -= operation.

impl<E: Curve> SubAssign<SecretScalar<E>> for Scalar<E>

fn sub_assign(&mut self, rhs: SecretScalar<E>)

Performs the -= operation.

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

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

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

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

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

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

impl<E: Curve> Sum<NonZero<SecretScalar<E>>> for SecretScalar<E>

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

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

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

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

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

impl<E: Curve> TryFrom<SecretScalar<E>> for NonZero<SecretScalar<E>>

type Error = ZeroScalar

The type returned in the event of a conversion error.

fn try_from(secret_scalar: SecretScalar<E>) -> Result<Self, Self::Error>

Performs the conversion.