Struct Jubjub 

pub struct Jubjub { /* private fields */ }

This represents an extended point (U, V, Z, T1, T2) with Z nonzero, corresponding to the affine point (U/Z, V/Z). We always have T1 * T2 = UV/Z.

You can do the following things with a point in this form:

• Convert it into a point in the affine form.
• Add it to an ExtendedPoint, AffineNielsPoint or ExtendedNielsPoint.
• Double it using double().
• Compare it with another extended point using PartialEq or ct_eq().

Implementations

impl JubjubExtended

pub const fn identity() -> JubjubExtended

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_small_order(&self) -> Choice

Determines if this point is of small order.

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 is_prime_order(&self) -> Choice

Determines if this point is prime order, or in other words that the smallest scalar multiplied by this point that produces the identity is r. This is equivalent to checking that the point is both torsion free and not the identity.

pub fn mul_by_cofactor(&self) -> JubjubExtended

Multiplies this element by the cofactor 8.

pub fn to_niels(&self) -> ExtendedNielsPoint

Performs a pre-processing step that produces an ExtendedNielsPoint for use in multiple additions.

pub fn double(&self) -> JubjubExtended

Computes the doubling of a point more efficiently than a point can be added to itself.

Trait Implementations

impl<'b> Add<&'b ExtendedNielsPoint> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, other: &'b ExtendedNielsPoint) -> JubjubExtended

Performs the + operation.

impl<'b> Add<&'b ExtendedNielsPoint> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b> Add<&'b JubjubAffine> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, other: &'b JubjubAffine) -> JubjubExtended

Performs the + operation.

impl<'b> Add<&'b JubjubAffine> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b> Add<&'b JubjubAffineNiels> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, other: &'b JubjubAffineNiels) -> JubjubExtended

Performs the + operation.

impl<'b> Add<&'b JubjubAffineNiels> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, other: &'b JubjubExtended) -> JubjubExtended

Performs the + operation.

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

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b> Add<&'b JubjubSubgroup> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, other: &'b JubjubSubgroup) -> JubjubExtended

Performs the + operation.

impl<'b> Add<&'b JubjubSubgroup> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a> Add<ExtendedNielsPoint> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: ExtendedNielsPoint) -> JubjubExtended

Performs the + operation.

impl Add<ExtendedNielsPoint> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: ExtendedNielsPoint) -> JubjubExtended

Performs the + operation.

impl<'a> Add<JubjubAffine> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: JubjubAffine) -> JubjubExtended

Performs the + operation.

impl Add<JubjubAffine> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: JubjubAffine) -> JubjubExtended

Performs the + operation.

impl<'a> Add<JubjubAffineNiels> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: JubjubAffineNiels) -> JubjubExtended

Performs the + operation.

impl Add<JubjubAffineNiels> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: JubjubAffineNiels) -> JubjubExtended

Performs the + operation.

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

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a> Add<JubjubSubgroup> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: JubjubSubgroup) -> JubjubExtended

Performs the + operation.

impl Add<JubjubSubgroup> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

fn add(self, rhs: JubjubSubgroup) -> JubjubExtended

Performs the + operation.

impl Add for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b> AddAssign<&'b ExtendedNielsPoint> for JubjubExtended

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

Performs the += operation.

impl<'b> AddAssign<&'b JubjubAffine> for JubjubExtended

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

Performs the += operation.

impl<'b> AddAssign<&'b JubjubAffineNiels> for JubjubExtended

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

Performs the += operation.

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

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

Performs the += operation.

impl<'b> AddAssign<&'b JubjubSubgroup> for JubjubExtended

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

Performs the += operation.

impl AddAssign<ExtendedNielsPoint> for JubjubExtended

fn add_assign(&mut self, rhs: ExtendedNielsPoint)

Performs the += operation.

impl AddAssign<JubjubAffine> for JubjubExtended

fn add_assign(&mut self, rhs: JubjubAffine)

Performs the += operation.

impl AddAssign<JubjubAffineNiels> for JubjubExtended

fn add_assign(&mut self, rhs: JubjubAffineNiels)

Performs the += operation.

impl AddAssign<JubjubSubgroup> for JubjubExtended

fn add_assign(&mut self, rhs: JubjubSubgroup)

Performs the += operation.

impl AddAssign for JubjubExtended

fn add_assign(&mut self, rhs: JubjubExtended)

Performs the += operation.

impl CircuitCurve for JubjubExtended

const COFACTOR: u128 = 8

Cofactor of the curve.

const NUM_BITS_SUBGROUP: u32 = 252

How many bits are needed to represent an element of the scalar field of the curve subgroup. This is the log2 rounded up of the curve order divided by the cofactor.

type Base = Fq

Base field over which the EC is defined.

type CryptographicGroup = JubjubSubgroup

Cryptographic group.

fn coordinates( &self, ) -> Option<(<JubjubExtended as CircuitCurve>::Base, <JubjubExtended as CircuitCurve>::Base)>

Returns the coordinates.

fn from_xy( x: <JubjubExtended as CircuitCurve>::Base, y: <JubjubExtended as CircuitCurve>::Base, ) -> Option<JubjubExtended>

Constructs a point in the curve from its coordinates

fn into_subgroup(self) -> <JubjubExtended as CircuitCurve>::CryptographicGroup

Checks that the point is part of the subgroup.

impl Clone for JubjubExtended

fn clone(&self) -> JubjubExtended

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CofactorCurve for JubjubExtended

type Affine = JubjubAffine

impl CofactorGroup for JubjubExtended

type Subgroup = JubjubSubgroup

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) -> <JubjubExtended as CofactorGroup>::Subgroup

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

fn into_subgroup(self) -> CtOption<<JubjubExtended as CofactorGroup>::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 JubjubExtended

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

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 JubjubExtended

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

Determine if two items are equal.

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

Determine if two items are NOT equal.

impl Curve for JubjubExtended

type AffineRepr = JubjubAffine

The affine representation for this elliptic curve.

fn batch_normalize( p: &[JubjubExtended], q: &mut [<JubjubExtended as Curve>::AffineRepr], )

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

fn to_affine(&self) -> <JubjubExtended as Curve>::AffineRepr

Converts this element into its affine representation.

impl Debug for JubjubExtended

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

Formats the value using the given formatter.

impl Default for JubjubExtended

fn default() -> JubjubExtended

Returns the identity.

impl Display for JubjubExtended

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

Formats the value using the given formatter.

impl EdwardsCurve for JubjubExtended

const A: <JubjubExtended as CircuitCurve>::Base

A parameter.

const D: <JubjubExtended as CircuitCurve>::Base

D parameter.

impl<'a> From<&'a JubjubExtended> for JubjubAffine

fn from(extended: &'a JubjubExtended) -> JubjubAffine

Constructs an affine point from an extended point using the map (U, V, Z, T1, T2) => (U/Z, V/Z) as Z is always nonzero. This requires a field inversion and so it is recommended to perform these in a batch using [batch_normalize] instead.

impl<'a> From<&'a JubjubSubgroup> for &'a JubjubExtended

fn from(val: &'a JubjubSubgroup) -> &'a JubjubExtended

Converts to this type from the input type.

impl From<JubjubAffine> for JubjubExtended

fn from(affine: JubjubAffine) -> JubjubExtended

Constructs an extended point (with Z = 1) from an affine point using the map (u, v) => (u, v, 1, u, v).

impl From<JubjubExtended> for JubjubAffine

fn from(extended: JubjubExtended) -> JubjubAffine

Converts to this type from the input type.

impl From<JubjubSubgroup> for JubjubExtended

fn from(val: JubjubSubgroup) -> JubjubExtended

Converts to this type from the input type.

impl Group for JubjubExtended

type Scalar = Fr

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

fn random(rng: impl RngCore) -> JubjubExtended

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

fn identity() -> JubjubExtended

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

fn generator() -> JubjubExtended

Returns a fixed generator of the prime-order subgroup.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> JubjubExtended

Doubles this element.

impl GroupEncoding for JubjubExtended

type Repr = [u8; 32]

The encoding of group elements.

fn from_bytes( bytes: &<JubjubExtended as GroupEncoding>::Repr, ) -> CtOption<JubjubExtended>

Attempts to deserialize a group element from its encoding.

fn from_bytes_unchecked( bytes: &<JubjubExtended as GroupEncoding>::Repr, ) -> CtOption<JubjubExtended>

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

fn to_bytes(&self) -> <JubjubExtended as GroupEncoding>::Repr

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

impl MapToCurveCPU<JubjubExtended> for JubjubExtended

fn map_to_curve(u: &<JubjubExtended as CircuitCurve>::Base) -> JubjubSubgroup

Map an element of the base field (a coordinate) to a pair of coordinates that satisfy the underlying curve equation.

impl MapToEdwardsParams<Fq> for JubjubExtended

const MONT_J: Fq

J constant of Montgomery curve: K * y^2 = x^3 + J * x^2 + x.

const MONT_K: Fq

K constant of Montgomery curve: K * y^2 = x^3 + J * x^2 + x.

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

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl MulAssign<Fr> for JubjubExtended

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl Neg for JubjubExtended

fn neg(self) -> JubjubExtended

Computes the negation of a point P = (U, V, Z, T) as -P = (-U, V, Z, -T1, T2). The choice of T1 is made without loss of generality.

type Output = JubjubExtended

The resulting type after applying the - operator.

impl PartialEq for JubjubExtended

fn eq(&self, other: &JubjubExtended) -> 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<'b> Sub<&'b ExtendedNielsPoint> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, other: &'b ExtendedNielsPoint) -> JubjubExtended

Performs the - operation.

impl<'b> Sub<&'b ExtendedNielsPoint> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b> Sub<&'b JubjubAffine> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, other: &'b JubjubAffine) -> JubjubExtended

Performs the - operation.

impl<'b> Sub<&'b JubjubAffine> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b> Sub<&'b JubjubAffineNiels> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, other: &'b JubjubAffineNiels) -> JubjubExtended

Performs the - operation.

impl<'b> Sub<&'b JubjubAffineNiels> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, other: &'b JubjubExtended) -> JubjubExtended

Performs the - operation.

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

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b> Sub<&'b JubjubSubgroup> for &JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, other: &'b JubjubSubgroup) -> JubjubExtended

Performs the - operation.

impl<'b> Sub<&'b JubjubSubgroup> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a> Sub<ExtendedNielsPoint> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: ExtendedNielsPoint) -> JubjubExtended

Performs the - operation.

impl Sub<ExtendedNielsPoint> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: ExtendedNielsPoint) -> JubjubExtended

Performs the - operation.

impl<'a> Sub<JubjubAffine> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: JubjubAffine) -> JubjubExtended

Performs the - operation.

impl Sub<JubjubAffine> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: JubjubAffine) -> JubjubExtended

Performs the - operation.

impl<'a> Sub<JubjubAffineNiels> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: JubjubAffineNiels) -> JubjubExtended

Performs the - operation.

impl Sub<JubjubAffineNiels> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: JubjubAffineNiels) -> JubjubExtended

Performs the - operation.

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

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a> Sub<JubjubSubgroup> for &'a JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: JubjubSubgroup) -> JubjubExtended

Performs the - operation.

impl Sub<JubjubSubgroup> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

fn sub(self, rhs: JubjubSubgroup) -> JubjubExtended

Performs the - operation.

impl Sub for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b> SubAssign<&'b ExtendedNielsPoint> for JubjubExtended

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

Performs the -= operation.

impl<'b> SubAssign<&'b JubjubAffine> for JubjubExtended

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

Performs the -= operation.

impl<'b> SubAssign<&'b JubjubAffineNiels> for JubjubExtended

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

Performs the -= operation.

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

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

Performs the -= operation.

impl<'b> SubAssign<&'b JubjubSubgroup> for JubjubExtended

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

Performs the -= operation.

impl SubAssign<ExtendedNielsPoint> for JubjubExtended

fn sub_assign(&mut self, rhs: ExtendedNielsPoint)

Performs the -= operation.

impl SubAssign<JubjubAffine> for JubjubExtended

fn sub_assign(&mut self, rhs: JubjubAffine)

Performs the -= operation.

impl SubAssign<JubjubAffineNiels> for JubjubExtended

fn sub_assign(&mut self, rhs: JubjubAffineNiels)

Performs the -= operation.

impl SubAssign<JubjubSubgroup> for JubjubExtended

fn sub_assign(&mut self, rhs: JubjubSubgroup)

Performs the -= operation.

impl SubAssign for JubjubExtended

fn sub_assign(&mut self, rhs: JubjubExtended)

Performs the -= operation.

impl<T> Sum<T> for JubjubExtended

where T: Borrow<JubjubExtended>,

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

where I: Iterator<Item = T>,

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

impl Copy for JubjubExtended

impl Eq for JubjubExtended