Struct Ed25519

pub struct Ed25519 {
    pub x: Fq,
    pub y: Fq,
    pub z: Fq,
    pub t: Fq,
}

Fields

x: Fq

y: Fq

z: Fq

t: Fq

Implementations

impl Ed25519

pub const fn identity() -> Self

Constructs an extended point from the neutral element (0, 1).

pub fn is_identity(&self) -> Choice

Determines if this point is the identity.

pub fn is_torsion_free(&self) -> Choice

Determines if this point is torsion free and so is contained in the prime order subgroup.

pub fn mul_by_cofactor(&self) -> Ed25519

Multiplies this element by the cofactor 8.

pub fn generator() -> Self

pub fn double(&self) -> Ed25519

Trait Implementations

impl<'a, 'b> Add<&'a Ed25519> for &'b Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: &'a Ed25519) -> Ed25519

Performs the + operation.

impl<'a, 'b> Add<&'a Ed25519> for &'b Ed25519Affine

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: &'a Ed25519) -> Ed25519

Performs the + operation.

impl<'b> Add<&'b Ed25519> for Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: &'b Ed25519) -> Ed25519

Performs the + operation.

impl<'b> Add<&'b Ed25519> for Ed25519Affine

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: &'b Ed25519) -> Ed25519

Performs the + operation.

impl<'a, 'b> Add<&'a Ed25519Affine> for &'b Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: &'a Ed25519Affine) -> Ed25519

Performs the + operation.

impl<'b> Add<&'b Ed25519Affine> for Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: &'b Ed25519Affine) -> Ed25519

Performs the + operation.

impl<'a> Add<Ed25519> for &'a Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: Ed25519) -> Ed25519

Performs the + operation.

impl<'a> Add<Ed25519> for &'a Ed25519Affine

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: Ed25519) -> Ed25519

Performs the + operation.

impl Add<Ed25519> for Ed25519Affine

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: Ed25519) -> Ed25519

Performs the + operation.

impl<'a> Add<Ed25519Affine> for &'a Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: Ed25519Affine) -> Ed25519

Performs the + operation.

impl Add<Ed25519Affine> for Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: Ed25519Affine) -> Ed25519

Performs the + operation.

impl Add for Ed25519

type Output = Ed25519

The resulting type after applying the + operator.

fn add(self, rhs: Ed25519) -> Ed25519

Performs the + operation.

impl<'b> AddAssign<&'b Ed25519> for Ed25519

fn add_assign(&mut self, rhs: &'b Ed25519)

Performs the += operation.

impl<'b> AddAssign<&'b Ed25519Affine> for Ed25519

fn add_assign(&mut self, rhs: &'b Ed25519Affine)

Performs the += operation.

impl AddAssign<Ed25519Affine> for Ed25519

fn add_assign(&mut self, rhs: Ed25519Affine)

Performs the += operation.

impl AddAssign for Ed25519

fn add_assign(&mut self, rhs: Ed25519)

Performs the += operation.

impl Clone for Ed25519

fn clone(&self) -> Ed25519

Returns a copy of the value.

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

Performs copy-assignment from source.

impl CofactorCurve for Ed25519

type Affine = Ed25519Affine

impl CofactorGroup for Ed25519

type Subgroup = Ed25519

The large prime-order subgroup in which cryptographic operations are performed. If Self implements PrimeGroup, then Self::Subgroup may be Self.

fn clear_cofactor(&self) -> Self

Maps self to the prime-order subgroup by multiplying this element by some k-multiple of the cofactor.

fn into_subgroup(self) -> CtOption<Self::Subgroup>

Returns self if it is contained in the prime-order subgroup.

fn is_torsion_free(&self) -> Choice

Determines if this element is “torsion free”, i.e., is contained in the prime-order subgroup.

fn is_small_order(&self) -> Choice

Determines if this element is of small order.

impl ConditionallySelectable for Ed25519

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 Ed25519

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 Curve for Ed25519

type AffineRepr = Ed25519Affine

The affine representation for this elliptic curve.

fn batch_normalize(p: &[Self], q: &mut [Self::AffineRepr])

Converts a batch of projective elements into affine elements. This function will panic if p.len() != q.len().

fn to_affine(&self) -> Self::AffineRepr

Converts this element into its affine representation.

impl CurveExt for Ed25519

const CURVE_ID: &'static str = "ed25519"

CURVE_ID used for hash-to-curve.

type ScalarExt = Fr

The scalar field of this elliptic curve.

type Base = Fq

The base field over which this elliptic curve is constructed.

type AffineExt = Ed25519Affine

The affine version of the curve

fn is_on_curve(&self) -> Choice

Returns whether or not this element is on the curve; should always be true unless an “unchecked” API was used.

fn endo(&self) -> Self

Apply the curve endomorphism by multiplying the x-coordinate by an element of multiplicative order 3.

fn jacobian_coordinates(&self) -> (Fq, Fq, Fq)

Return the Jacobian coordinates of this point.

fn hash_to_curve<'a>(_: &'a str) -> Box<dyn Fn(&[u8]) -> Self + 'a>

Requests a hasher that accepts messages and returns near-uniformly distributed elements in the group, given domain prefix domain_prefix.

fn a() -> Self::Base

Returns the curve constant a.

fn b() -> Self::Base

Returns the curve constant b.

fn new_jacobian( _x: Self::Base, _y: Self::Base, _z: Self::Base, ) -> CtOption<Self>

Obtains a point given Jacobian coordinates $X : Y : Z$, failing if the coordinates are not on the curve.

impl Debug for Ed25519

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

Formats the value using the given formatter.

impl Default for Ed25519

fn default() -> Ed25519

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Ed25519

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<'a> From<&'a Ed25519> for Ed25519Affine

fn from(p: &'a Ed25519) -> Ed25519Affine

Converts to this type from the input type.

impl<'a> From<&'a Ed25519Affine> for Ed25519

fn from(p: &'a Ed25519Affine) -> Ed25519

Converts to this type from the input type.

impl From<Ed25519> for Ed25519Affine

fn from(p: Ed25519) -> Ed25519Affine

Converts to this type from the input type.

impl From<Ed25519Affine> for Ed25519

fn from(p: Ed25519Affine) -> Ed25519

Converts to this type from the input type.

impl Group for Ed25519

type Scalar = Fr

Scalars modulo the order of this group’s scalar field.

fn random(rng: impl RngCore) -> Self

Returns an element chosen uniformly at random from the non-identity elements of this group.

fn generator() -> Self

Returns a fixed generator of the prime-order subgroup.

fn identity() -> Self

Returns the additive identity, also known as the “neutral element”.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> Self

Doubles this element.

impl GroupEncoding for Ed25519

type Repr = Ed25519Compressed

The encoding of group elements.

fn from_bytes(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element from its encoding.

fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element, not checking if the element is valid.

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

Converts this element into its byte encoding. This may or may not support encoding the identity.

impl<'a, 'b> Mul<&'b Fr> for &'a Ed25519

type Output = Ed25519

The resulting type after applying the * operator.

fn mul(self, other: &'b Fr) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b Fr> for Ed25519

type Output = Ed25519

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fr) -> Ed25519

Performs the * operation.

impl<'a> Mul<Fr> for &'a Ed25519

type Output = Ed25519

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> Ed25519

Performs the * operation.

impl Mul<Fr> for Ed25519

type Output = Ed25519

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> Ed25519

Performs the * operation.

impl<'b> MulAssign<&'b Fr> for Ed25519

fn mul_assign(&mut self, rhs: &'b Fr)

Performs the *= operation.

impl MulAssign<Fr> for Ed25519

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl<'a> Neg for &'a Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn neg(self) -> Ed25519

Performs the unary - operation.

impl Neg for Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn neg(self) -> Ed25519

Performs the unary - operation.

impl PartialEq for Ed25519

fn eq(&self, other: &Self) -> 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 PrimeCurve for Ed25519

type Affine = Ed25519Affine

impl SerdeObject for Ed25519

fn from_raw_bytes_unchecked(bytes: &[u8]) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from bytes as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. As such this function should only be used internally as an extension of machine memory. It should not be used to deserialize externally provided data.

fn from_raw_bytes(bytes: &[u8]) -> Option<Self>

fn to_raw_bytes(&self) -> Vec<u8>

fn read_raw_unchecked<R: Read>(reader: &mut R) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from disk as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. This function should only be used internally when some machine state cannot be kept in memory (e.g., between runs) and needs to be reloaded as quickly as possible.

fn read_raw<R: Read>(reader: &mut R) -> Result<Self>

fn write_raw<W: Write>(&self, writer: &mut W) -> Result<()>

impl Serialize for Ed25519

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<&'a Ed25519> for &'b Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, other: &'a Ed25519) -> Ed25519

Performs the - operation.

impl<'a, 'b> Sub<&'a Ed25519> for &'b Ed25519Affine

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, other: &'a Ed25519) -> Ed25519

Performs the - operation.

impl<'b> Sub<&'b Ed25519> for Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Ed25519) -> Ed25519

Performs the - operation.

impl<'b> Sub<&'b Ed25519> for Ed25519Affine

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Ed25519) -> Ed25519

Performs the - operation.

impl<'a, 'b> Sub<&'a Ed25519Affine> for &'b Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, other: &'a Ed25519Affine) -> Ed25519

Performs the - operation.

impl<'b> Sub<&'b Ed25519Affine> for Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Ed25519Affine) -> Ed25519

Performs the - operation.

impl<'a> Sub<Ed25519> for &'a Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: Ed25519) -> Ed25519

Performs the - operation.

impl<'a> Sub<Ed25519> for &'a Ed25519Affine

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: Ed25519) -> Ed25519

Performs the - operation.

impl Sub<Ed25519> for Ed25519Affine

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: Ed25519) -> Ed25519

Performs the - operation.

impl<'a> Sub<Ed25519Affine> for &'a Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: Ed25519Affine) -> Ed25519

Performs the - operation.

impl Sub<Ed25519Affine> for Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: Ed25519Affine) -> Ed25519

Performs the - operation.

impl Sub for Ed25519

type Output = Ed25519

The resulting type after applying the - operator.

fn sub(self, rhs: Ed25519) -> Ed25519

Performs the - operation.

impl<'b> SubAssign<&'b Ed25519> for Ed25519

fn sub_assign(&mut self, rhs: &'b Ed25519)

Performs the -= operation.

impl<'b> SubAssign<&'b Ed25519Affine> for Ed25519

fn sub_assign(&mut self, rhs: &'b Ed25519Affine)

Performs the -= operation.

impl SubAssign<Ed25519Affine> for Ed25519

fn sub_assign(&mut self, rhs: Ed25519Affine)

Performs the -= operation.

impl SubAssign for Ed25519

fn sub_assign(&mut self, rhs: Ed25519)

Performs the -= operation.

impl<T> Sum<T> for Ed25519

where T: Borrow<Ed25519>,

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = T>,

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

impl TwistedEdwardsCurveExt for Ed25519

fn a() -> Fq

fn d() -> Fq

impl Copy for Ed25519

impl Eq for Ed25519

impl PrimeGroup for Ed25519