Struct dalek_ff_group::Scalar

pub struct Scalar(pub Scalar);

Wrapper around the dalek Scalar type.

Tuple Fields

0: Scalar

Implementations

impl Scalar

pub fn pow(&self, other: Scalar) -> Scalar

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

Perform wide reduction on a 64-byte array to create a Scalar without bias.

pub fn from_hash<D: Digest<OutputSize = U64> + HashMarker>(hash: D) -> Scalar

Derive a Scalar without bias from a digest via wide reduction.

Methods from Deref<Target = DScalar>

pub const ZERO: Scalar = _

pub const ONE: Scalar = _

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 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);

Trait Implementations

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

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, other: &'a Scalar) -> Self::Output

Performs the + operation.

impl Add for Scalar

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, other: Scalar) -> Self::Output

Performs the + operation.

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

fn add_assign(&mut self, other: &'a Scalar)

Performs the += operation.

impl AddAssign for Scalar

fn add_assign(&mut self, other: Scalar)

Performs the += operation.

impl Borrow<Scalar> for &Scalar

fn borrow(&self) -> &DScalar

Immutably borrows from an owned value.

impl Borrow<Scalar> for Scalar

fn borrow(&self) -> &DScalar

Immutably borrows from an owned value.

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 Deref for Scalar

type Target = Scalar

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl Field for Scalar

const ZERO: Scalar = _

The zero element of the field, the additive identity.

const ONE: Scalar = _

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(&self) -> CtOption<Self>

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

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

Computes:

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(a: u128) -> Scalar

Converts to this type from the input type.

impl From<u16> for Scalar

fn from(a: u16) -> Scalar

Converts to this type from the input type.

impl From<u32> for Scalar

fn from(a: u32) -> Scalar

Converts to this type from the input type.

impl From<u64> for Scalar

fn from(a: u64) -> Scalar

Converts to this type from the input type.

impl From<u8> for Scalar

fn from(a: u8) -> Scalar

Converts to this type from the input type.

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

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for &EdwardsBasepointTable

type Output = EdwardsPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for &RistrettoBasepointTable

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, other: Scalar) -> Self::Output

Performs the * operation.

impl Mul<Scalar> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, other: Scalar) -> Self::Output

Performs the * operation.

impl Mul for Scalar

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, other: Scalar) -> Self::Output

Performs the * operation.

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

fn mul_assign(&mut self, other: &'a Scalar)

Performs the *= operation.

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

fn mul_assign(&mut self, other: &'a Scalar)

Performs the *= operation.

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

fn mul_assign(&mut self, other: &'a Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for EdwardsPoint

fn mul_assign(&mut self, other: Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for RistrettoPoint

fn mul_assign(&mut self, other: Scalar)

Performs the *= operation.

impl MulAssign for Scalar

fn mul_assign(&mut self, other: Scalar)

Performs the *= operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for Scalar

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl PrimeField for Scalar

const MODULUS: &'static str = <DScalar as PrimeField>::MODULUS

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: Scalar = _

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Scalar = _

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: Scalar = _

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Scalar = _

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Scalar = _

Generator of the t-order multiplicative subgroup.

type Repr = [u8; 32]

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

fn from_repr(bytes: [u8; 32]) -> 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 to_repr(&self) -> [u8; 32]

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.

fn from_u128(num: u128) -> Self

Obtains a field element congruent to the integer v.

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_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 is_even(&self) -> Choice

Returns true iff this element is even.

impl PrimeFieldBits for Scalar

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<'a> Product<&'a Scalar> for Scalar

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

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

impl Product for Scalar

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

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

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

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, other: &'a Scalar) -> Self::Output

Performs the - operation.

impl Sub for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, other: Scalar) -> Self::Output

Performs the - operation.

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

fn sub_assign(&mut self, other: &'a Scalar)

Performs the -= operation.

impl SubAssign for Scalar

fn sub_assign(&mut self, other: Scalar)

Performs the -= operation.

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

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

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

impl Sum for Scalar

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

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

impl Zeroize for Scalar

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

impl StructuralPartialEq for Scalar

Layout

Note: Most layout information is completely unstable and may even differ between compilations. The only exception is types with certain repr(...) attributes. Please see the Rust Reference's “Type Layout” chapter for details on type layout guarantees.

Size: 32 bytes