Struct curve25519_dalek::scalar::Scalar

pub struct Scalar { /* private fields */ }

The Scalar struct holds an element of \(\mathbb Z / \ell\mathbb Z \).

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]) -> CtOption<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 modulo the group order \( \ell \);
• None if bytes is not a canonical byte representation.

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

👎Deprecated since 4.0.0: This constructor outputs scalars with undefined scalar-scalar arithmetic. See docs.

Available on crate feature legacy_compatibility only.

Construct a Scalar from the low 255 bits of a 256-bit integer. This breaks the invariant that scalars are always reduced. Scalar-scalar arithmetic, i.e., addition, subtraction, multiplication, does not work on scalars produced from this function. You may only use the output of this function for EdwardsPoint::mul, MontgomeryPoint::mul, and EdwardsPoint::vartime_double_scalar_mul_basepoint. Do not use this function unless you absolutely have to.

impl Scalar

pub const ZERO: Self = _

The scalar \( 0 \).

pub const ONE: Self = _

The scalar \( 1 \).

pub fn random<R: CryptoRngCore + ?Sized>(rng: &mut R) -> Self

Available on crate feature rand_core only.

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

Inputs

• rng: any RNG which implements CryptoRngCore (i.e. CryptoRng + RngCore) interface.

Returns

A random scalar within \(\mathbb{Z} / \ell\mathbb{Z}\).

Example

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,

Available on crate feature digest only.

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

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>,

Available on crate feature digest only.

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

use curve25519_dalek::digest::Update;

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_eq!(
    s.to_bytes(),
    [  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 const 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 const 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 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

Available on crate feature alloc only.

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());

Trait Implementations

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

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

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

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Scalar

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

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

Performs the += operation.

impl AddAssign for Scalar

fn add_assign(&mut self, rhs: Scalar)

Performs the += operation.

impl Clone for Scalar

fn clone(&self) -> Scalar

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Scalar

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

Select a or b according to choice.

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

Conditionally assign other to self, according to choice.

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

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 Debug for Scalar

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

Formats the value using the given formatter.

impl Default for Scalar

fn default() -> Scalar

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Scalar

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 Field for Scalar

Available on crate feature group only.

const ZERO: Self = Self::ZERO

The zero element of the field, the additive identity.

const ONE: Self = Self::ONE

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Self

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

fn square(&self) -> Self

Squares this element.

fn double(&self) -> Self

Doubles this element.

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

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

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

Computes:

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

Returns the square root of the field element, if it is quadratic residue.

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn cube(&self) -> Self

Cubes this element.

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

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

fn pow<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

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.

impl From<u128> for Scalar

fn from(x: u128) -> Scalar

Converts to this type from the input type.

impl From<u16> for Scalar

fn from(x: u16) -> Scalar

Converts to this type from the input type.

impl From<u32> for Scalar

fn from(x: u32) -> Scalar

Converts to this type from the input type.

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

fn from(x: u8) -> Scalar

Converts to this type from the input type.

impl FromUniformBytes<64> for Scalar

Available on crate feature group only.

fn from_uniform_bytes(bytes: &[u8; 64]) -> Self

Returns a field element that is congruent to the provided little endian unsigned byte representation of an integer.

impl Hash for Scalar

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

Feeds this value into the given Hasher.

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

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Index<usize> for Scalar

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

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

type Output = u8

The returned type after indexing.

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

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

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix128> for &'b Scalar

fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix128) -> EdwardsPoint

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix256> for &'b Scalar

fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix256) -> EdwardsPoint

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix32> for &'b Scalar

fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix32) -> EdwardsPoint

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a EdwardsBasepointTableRadix64> for &'b Scalar

fn mul(self, basepoint_table: &'a EdwardsBasepointTableRadix64) -> EdwardsPoint

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

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

Scalar multiplication: compute scalar * self.

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&MontgomeryPoint> for &Scalar

type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, point: &MontgomeryPoint) -> MontgomeryPoint

Performs the * operation.

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

type Output = MontgomeryPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

Available on crate feature precomputed-tables only.

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Scalar multiplication: compute self * scalar.

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

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 EdwardsBasepointTable

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

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix128

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

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix256

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

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix32

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

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTableRadix64

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

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

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

Scalar multiplication: compute scalar * self.

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl Mul<&Scalar> for &MontgomeryPoint

Multiply this MontgomeryPoint by a Scalar.

fn mul(self, scalar: &Scalar) -> MontgomeryPoint

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

type Output = MontgomeryPoint

The resulting type after applying the * operator.

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

Available on crate feature precomputed-tables only.

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Scalar multiplication: compute scalar * self.

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&Scalar> for &SubgroupPoint

Available on crate feature group only.

fn mul(self, scalar: &Scalar) -> SubgroupPoint

Scalar multiplication: compute scalar * self.

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

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = MontgomeryPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

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 SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&SubgroupPoint> for &Scalar

Available on crate feature group only.

fn mul(self, point: &SubgroupPoint) -> SubgroupPoint

Scalar multiplication: compute scalar * self.

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

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the * operation.

impl Mul<EdwardsPoint> for Scalar

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

type Output = MontgomeryPoint

The resulting type after applying the * operator.

fn mul(self, rhs: MontgomeryPoint) -> MontgomeryPoint

Performs the * operation.

impl Mul<MontgomeryPoint> for Scalar

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

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the * operation.

impl Mul<RistrettoPoint> for Scalar

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 EdwardsPoint

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 MontgomeryPoint

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 RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

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 SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for MontgomeryPoint

type Output = MontgomeryPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = SubgroupPoint

The resulting type after applying the * operator.

fn mul(self, rhs: SubgroupPoint) -> SubgroupPoint

Performs the * operation.

impl Mul<SubgroupPoint> for Scalar

type Output = SubgroupPoint

The resulting type after applying the * operator.

fn mul(self, rhs: SubgroupPoint) -> SubgroupPoint

Performs the * operation.

impl Mul for Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl MulAssign<&Scalar> for MontgomeryPoint

fn mul_assign(&mut self, scalar: &Scalar)

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

impl MulAssign<&Scalar> for SubgroupPoint

Available on crate feature group only.

fn mul_assign(&mut self, scalar: &Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for EdwardsPoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for MontgomeryPoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for RistrettoPoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for SubgroupPoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MulAssign for Scalar

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl<'a> Neg for &'a Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the unary - operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the unary - operation.

impl PartialEq for Scalar

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 !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PrimeField for Scalar

Available on crate feature group only.

type Repr = [u8; 32]

The prime field can be converted back and forth into this binary representation.

fn from_repr(repr: Self::Repr) -> CtOption<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn from_repr_vartime(repr: Self::Repr) -> Option<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn to_repr(&self) -> Self::Repr

Converts an element of the prime field into the standard byte representation for this field.

fn is_odd(&self) -> Choice

Returns true iff this element is odd.

const MODULUS: &'static str = "0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed"

Modulus of the field written as a string for debugging purposes.

const NUM_BITS: u32 = 253u32

How many bits are needed to represent an element of this field.

const CAPACITY: u32 = 252u32

How many bits of information can be reliably stored in the field element.

const TWO_INV: Self = _

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self = _

A fixed multiplicative generator of modulus - 1 order. This element must also be a quadratic nonresidue.

const S: u32 = 2u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd.

const ROOT_OF_UNITY: Self = _

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self = _

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self = _

Generator of the t-order multiplicative subgroup.

fn from_str_vartime(s: &str) -> Option<Self>

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn is_even(&self) -> Choice

Returns true iff this element is even.

impl PrimeFieldBits for Scalar

Available on crate feature group-bits only.

type ReprBits = [u8; 32]

The backing store for a bit representation of a prime field element.

fn to_le_bits(&self) -> FieldBits<Self::ReprBits>

Converts an element of the prime field into a little-endian sequence of bits.

fn char_le_bits() -> FieldBits<Self::ReprBits>

Returns the bits of the field characteristic (the modulus) in little-endian order.

impl<T> Product<T> for Scalar

where T: Borrow<Scalar>,

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 Serialize for Scalar

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

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

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

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Scalar

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

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

Performs the -= operation.

impl SubAssign for Scalar

fn sub_assign(&mut self, rhs: Scalar)

Performs the -= operation.

impl<T> Sum<T> for Scalar

where T: Borrow<Scalar>,

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

Available on crate feature zeroize only.

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.

impl Copy for Scalar

impl Eq for Scalar