Struct curve25519_dalek::scalar::Scalar

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pub struct Scalar { /* fields omitted */ }

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The Scalar struct holds an integer \(s < 2^{255} \) which represents an element of \(\mathbb Z / \ell\).

Implementations

impl Scalar[−]

pub fn from_bytes_mod_order(bytes: [u8; 32]) -> Scalar[−]

Construct a Scalar by reducing a 256-bit little-endian integer modulo the group order \( \ell \).

pub fn from_bytes_mod_order_wide(input: &[u8; 64]) -> Scalar[−]

Construct a Scalar by reducing a 512-bit little-endian integer modulo the group order \( \ell \).

pub fn from_canonical_bytes(bytes: [u8; 32]) -> Option<Scalar>[−]

Attempt to construct a Scalar from a canonical byte representation.

Return

• Some(s), where s is the Scalar corresponding to bytes, if bytes is a canonical byte representation;
• None if bytes is not a canonical byte representation.

pub const fn from_bits(bytes: [u8; 32]) -> Scalar[−]

Construct a Scalar from the low 255 bits of a 256-bit integer.

This function is intended for applications like X25519 which require specific bit-patterns when performing scalar multiplication.

impl Scalar[−]

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

Return a Scalar chosen uniformly at random using a user-provided RNG.

Inputs

• rng: any RNG which implements the RngCore + CryptoRng interface.

Returns

A random scalar within ℤ/lℤ.

Example

extern crate rand_core;
use curve25519_dalek::scalar::Scalar;

use rand_core::OsRng;

let mut csprng = OsRng;
let a: Scalar = Scalar::random(&mut csprng);

pub fn hash_from_bytes<D>(input: &[u8]) -> Scalar where
    D: Digest<OutputSize = U64> + Default, [−]

Hash a slice of bytes into a scalar.

Takes a type parameter D, which is any Digest producing 64 bytes (512 bits) of output.

Convenience wrapper around from_hash.

Example

extern crate sha2;

use sha2::Sha512;

let msg = "To really appreciate architecture, you may even need to commit a murder";
let s = Scalar::hash_from_bytes::<Sha512>(msg.as_bytes());

pub fn from_hash<D>(hash: D) -> Scalar where
    D: Digest<OutputSize = U64>, [−]

Construct a scalar from an existing Digest instance.

Use this instead of hash_from_bytes if it is more convenient to stream data into the Digest than to pass a single byte slice.

Example

extern crate sha2;

use sha2::Digest;
use sha2::Sha512;

let mut h = Sha512::new()
    .chain("To really appreciate architecture, you may even need to commit a murder.")
    .chain("While the programs used for The Manhattan Transcripts are of the most extreme")
    .chain("nature, they also parallel the most common formula plot: the archetype of")
    .chain("murder. Other phantasms were occasionally used to underline the fact that")
    .chain("perhaps all architecture, rather than being about functional standards, is")
    .chain("about love and death.");

let s = Scalar::from_hash(h);

println!("{:?}", s.to_bytes());
assert!(s == Scalar::from_bits([ 21,  88, 208, 252,  63, 122, 210, 152,
                                154,  38,  15,  23,  16, 167,  80, 150,
                                192, 221,  77, 226,  62,  25, 224, 148,
                                239,  48, 176,  10, 185,  69, 168,  11, ]));

pub fn to_bytes(&self) -> [u8; 32][−]

Convert this Scalar to its underlying sequence of bytes.

Example

use curve25519_dalek::scalar::Scalar;

let s: Scalar = Scalar::zero();

assert!(s.to_bytes() == [0u8; 32]);

pub fn as_bytes(&self) -> &[u8; 32][−]

View the little-endian byte encoding of the integer representing this Scalar.

Example

use curve25519_dalek::scalar::Scalar;

let s: Scalar = Scalar::zero();

assert!(s.as_bytes() == &[0u8; 32]);

pub fn zero() -> Self[−]

Construct the scalar \( 0 \).

pub fn one() -> Self[−]

Construct the scalar \( 1 \).

pub fn invert(&self) -> Scalar[−]

Given a nonzero Scalar, compute its multiplicative inverse.

Warning

self MUST be nonzero. If you cannot prove that this is the case, you SHOULD NOT USE THIS FUNCTION.

Returns

The multiplicative inverse of the this Scalar.

Example

use curve25519_dalek::scalar::Scalar;

// x = 2238329342913194256032495932344128051776374960164957527413114840482143558222
let X: Scalar = Scalar::from_bytes_mod_order([
        0x4e, 0x5a, 0xb4, 0x34, 0x5d, 0x47, 0x08, 0x84,
        0x59, 0x13, 0xb4, 0x64, 0x1b, 0xc2, 0x7d, 0x52,
        0x52, 0xa5, 0x85, 0x10, 0x1b, 0xcc, 0x42, 0x44,
        0xd4, 0x49, 0xf4, 0xa8, 0x79, 0xd9, 0xf2, 0x04,
    ]);
// 1/x = 6859937278830797291664592131120606308688036382723378951768035303146619657244
let XINV: Scalar = Scalar::from_bytes_mod_order([
        0x1c, 0xdc, 0x17, 0xfc, 0xe0, 0xe9, 0xa5, 0xbb,
        0xd9, 0x24, 0x7e, 0x56, 0xbb, 0x01, 0x63, 0x47,
        0xbb, 0xba, 0x31, 0xed, 0xd5, 0xa9, 0xbb, 0x96,
        0xd5, 0x0b, 0xcd, 0x7a, 0x3f, 0x96, 0x2a, 0x0f,
    ]);

let inv_X: Scalar = X.invert();
assert!(XINV == inv_X);
let should_be_one: Scalar = &inv_X * &X;
assert!(should_be_one == Scalar::one());

pub fn batch_invert(inputs: &mut [Scalar]) -> Scalar[−]

Given a slice of nonzero (possibly secret) Scalars, compute their inverses in a batch.

Return

Each element of inputs is replaced by its inverse.

The product of all inverses is returned.

Warning

All input Scalars MUST be nonzero. If you cannot prove that this is the case, you SHOULD NOT USE THIS FUNCTION.

Example

let mut scalars = [
    Scalar::from(3u64),
    Scalar::from(5u64),
    Scalar::from(7u64),
    Scalar::from(11u64),
];

let allinv = Scalar::batch_invert(&mut scalars);

assert_eq!(allinv, Scalar::from(3*5*7*11u64).invert());
assert_eq!(scalars[0], Scalar::from(3u64).invert());
assert_eq!(scalars[1], Scalar::from(5u64).invert());
assert_eq!(scalars[2], Scalar::from(7u64).invert());
assert_eq!(scalars[3], Scalar::from(11u64).invert());

pub fn reduce(&self) -> Scalar[−]

Reduce this Scalar modulo \(\ell\).

pub fn is_canonical(&self) -> bool[−]

Check whether this Scalar is the canonical representative mod \(\ell\).

This is intended for uses like input validation, where variable-time code is acceptable.

// 2^255 - 1, since `from_bits` clears the high bit
let _2_255_minus_1 = Scalar::from_bits([0xff;32]);
assert!(!_2_255_minus_1.is_canonical());

let reduced = _2_255_minus_1.reduce();
assert!(reduced.is_canonical());

Trait Implementations

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[−]

Performs the + operation.

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[−]

Performs the + operation.

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[−]

Performs the + operation.

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[−]

Performs the + operation.

impl<'b> AddAssign<&'b Scalar> for Scalar[+]

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fn add_assign(&mut self, _rhs: &'b Scalar)[−]

Performs the += operation.

impl AddAssign<Scalar> for Scalar[+]

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fn add_assign(&mut self, rhs: Scalar)[−]

Performs the += operation.

impl Clone for Scalar[+]

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fn clone(&self) -> Scalar[−]

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)[−]

Performs copy-assignment from source.

impl ConditionallySelectable for Scalar[+]

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fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self[−]

Select a or b according to choice.

pub fn conditional_assign(&mut self, other: &Self, choice: Choice)[−]

Conditionally assign other to self, according to choice.

pub fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)[−]

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for Scalar[+]

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

Determine if two items are equal.

impl Copy for Scalar

impl Debug for Scalar[+]

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

Formats the value using the given formatter.

impl Default for Scalar[+]

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fn default() -> Scalar[−]

Returns the “default value” for a type.

impl Eq for Scalar

impl From<u128> for Scalar[+]

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fn from(x: u128) -> Scalar[−]

Performs the conversion.

impl From<u16> for Scalar[+]

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fn from(x: u16) -> Scalar[−]

Performs the conversion.

impl From<u32> for Scalar[+]

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fn from(x: u32) -> Scalar[−]

Performs the conversion.

impl From<u64> for Scalar[+]

fn from(x: u64) -> Scalar[−]

Construct a scalar from the given u64.

Inputs

An u64 to convert to a Scalar.

Returns

A Scalar corresponding to the input u64.

Example

use curve25519_dalek::scalar::Scalar;

let fourtytwo = Scalar::from(42u64);
let six = Scalar::from(6u64);
let seven = Scalar::from(7u64);

assert!(fourtytwo == six * seven);

impl From<u8> for Scalar[+]

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fn from(x: u8) -> Scalar[−]

Performs the conversion.

impl Hash for Scalar[+]

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fn hash<__H: Hasher>(&self, state: &mut __H)[−]

Feeds this value into the given Hasher.

pub fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, [−]

Feeds a slice of this type into the given Hasher.

impl Index<usize> for Scalar[+]

type Output = u8

The returned type after indexing.

fn index(&self, _index: usize) -> &u8[−]

Index the bytes of the representative for this Scalar. Mutation is not permitted.

impl<'a, 'b> Mul<&'a EdwardsBasepointTable> for &'b Scalar[+]

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, basepoint_table: &'a EdwardsBasepointTable) -> EdwardsPoint[−]

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

impl<'a, 'b> Mul<&'a RistrettoBasepointTable> for &'b Scalar[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, basepoint_table: &'a RistrettoBasepointTable) -> RistrettoPoint[−]

Performs the * operation.

impl<'b> Mul<&'b EdwardsPoint> for Scalar[+]

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type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b EdwardsPoint) -> EdwardsPoint[−]

Performs the * operation.

impl<'a, 'b> Mul<&'b EdwardsPoint> for &'a Scalar[+]

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, point: &'b EdwardsPoint) -> EdwardsPoint[−]

Scalar multiplication: compute scalar * self.

For scalar multiplication of a basepoint, EdwardsBasepointTable is approximately 4x faster.

impl<'b> Mul<&'b MontgomeryPoint> for Scalar[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b MontgomeryPoint) -> MontgomeryPoint[−]

Performs the * operation.

impl<'a, 'b> Mul<&'b MontgomeryPoint> for &'a Scalar[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, point: &'b MontgomeryPoint) -> MontgomeryPoint[−]

Performs the * operation.

impl<'a, 'b> Mul<&'b RistrettoPoint> for &'a Scalar[+]

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, point: &'b RistrettoPoint) -> RistrettoPoint[−]

Scalar multiplication: compute self * scalar.

impl<'b> Mul<&'b RistrettoPoint> for Scalar[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b RistrettoPoint) -> RistrettoPoint[−]

Performs the * operation.

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[−]

Performs the * operation.

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[−]

Performs the * operation.

impl<'b> Mul<&'b Scalar> for MontgomeryPoint[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Scalar) -> MontgomeryPoint[−]

Performs the * operation.

impl<'a, 'b> Mul<&'b Scalar> for &'a MontgomeryPoint[+]

Multiply this MontgomeryPoint by a Scalar.

type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> MontgomeryPoint[−]

Given self \( = u_0(P) \), and a Scalar \(n\), return \( u_0([n]P) \).

impl<'b> Mul<&'b Scalar> for EdwardsPoint[+]

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type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Scalar) -> EdwardsPoint[−]

Performs the * operation.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsPoint[+]

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> EdwardsPoint[−]

Scalar multiplication: compute scalar * self.

For scalar multiplication of a basepoint, EdwardsBasepointTable is approximately 4x faster.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTable[+]

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> EdwardsPoint[−]

Construct an EdwardsPoint from a Scalar \(a\) by computing the multiple \(aB\) of this basepoint \(B\).

impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoPoint[+]

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> RistrettoPoint[−]

Scalar multiplication: compute scalar * self.

impl<'b> Mul<&'b Scalar> for RistrettoPoint[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Scalar) -> RistrettoPoint[−]

Performs the * operation.

impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoBasepointTable[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> RistrettoPoint[−]

Performs the * operation.

impl<'a> Mul<EdwardsPoint> for &'a Scalar[+]

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type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: EdwardsPoint) -> EdwardsPoint[−]

Performs the * operation.

impl Mul<EdwardsPoint> for Scalar[+]

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type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: EdwardsPoint) -> EdwardsPoint[−]

Performs the * operation.

impl<'a> Mul<MontgomeryPoint> for &'a Scalar[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: MontgomeryPoint) -> MontgomeryPoint[−]

Performs the * operation.

impl Mul<MontgomeryPoint> for Scalar[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: MontgomeryPoint) -> MontgomeryPoint[−]

Performs the * operation.

impl<'a> Mul<RistrettoPoint> for &'a Scalar[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint[−]

Performs the * operation.

impl Mul<RistrettoPoint> for Scalar[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint[−]

Performs the * operation.

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[−]

Performs the * operation.

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[−]

Performs the * operation.

impl<'a> Mul<Scalar> for &'a MontgomeryPoint[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> MontgomeryPoint[−]

Performs the * operation.

impl Mul<Scalar> for MontgomeryPoint[+]

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type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> MontgomeryPoint[−]

Performs the * operation.

impl<'a> Mul<Scalar> for &'a EdwardsPoint[+]

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type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> EdwardsPoint[−]

Performs the * operation.

impl Mul<Scalar> for EdwardsPoint[+]

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type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> EdwardsPoint[−]

Performs the * operation.

impl<'a> Mul<Scalar> for &'a RistrettoPoint[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> RistrettoPoint[−]

Performs the * operation.

impl Mul<Scalar> for RistrettoPoint[+]

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type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> RistrettoPoint[−]

Performs the * operation.

impl<'b> MulAssign<&'b Scalar> for Scalar[+]

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fn mul_assign(&mut self, _rhs: &'b Scalar)[−]

Performs the *= operation.

impl<'b> MulAssign<&'b Scalar> for MontgomeryPoint[+]

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fn mul_assign(&mut self, scalar: &'b Scalar)[−]

Performs the *= operation.

impl<'b> MulAssign<&'b Scalar> for EdwardsPoint[+]

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fn mul_assign(&mut self, scalar: &'b Scalar)[−]

Performs the *= operation.

impl<'b> MulAssign<&'b Scalar> for RistrettoPoint[+]

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fn mul_assign(&mut self, scalar: &'b Scalar)[−]

Performs the *= operation.

impl MulAssign<Scalar> for Scalar[+]

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fn mul_assign(&mut self, rhs: Scalar)[−]

Performs the *= operation.

impl MulAssign<Scalar> for MontgomeryPoint[+]

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fn mul_assign(&mut self, rhs: Scalar)[−]

Performs the *= operation.

impl MulAssign<Scalar> for EdwardsPoint[+]

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fn mul_assign(&mut self, rhs: Scalar)[−]

Performs the *= operation.

impl MulAssign<Scalar> for RistrettoPoint[+]

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fn mul_assign(&mut self, rhs: Scalar)[−]

Performs the *= operation.

impl<'a> Neg for &'a Scalar[+]

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type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar[−]

Performs the unary - operation.

impl<'a> Neg for Scalar[+]

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type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar[−]

Performs the unary - operation.

impl PartialEq<Scalar> for Scalar[+]

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fn eq(&self, other: &Self) -> bool[−]

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

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#[must_use]pub fn ne(&self, other: &Rhs) -> bool[−]

This method tests for !=.

impl<T> Product<T> for Scalar where
    T: Borrow<Scalar>, [+]

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fn product<I>(iter: I) -> Self where
    I: Iterator<Item = T>, [−]

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

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[−]

Performs the - operation.

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[−]

Performs the - operation.

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[−]

Performs the - operation.

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[−]

Performs the - operation.

impl<'b> SubAssign<&'b Scalar> for Scalar[+]

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fn sub_assign(&mut self, _rhs: &'b Scalar)[−]

Performs the -= operation.

impl SubAssign<Scalar> for Scalar[+]

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fn sub_assign(&mut self, rhs: Scalar)[−]

Performs the -= operation.

impl<T> Sum<T> for Scalar where
    T: Borrow<Scalar>, [+]

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fn sum<I>(iter: I) -> Self where
    I: Iterator<Item = T>, [−]

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

impl Zeroize for Scalar[+]

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fn zeroize(&mut self)[−]

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.