Struct jubjub::ExtendedPoint

pub struct ExtendedPoint { /* fields omitted */ }

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().

Methods

impl ExtendedPoint

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_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) -> ExtendedPoint

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) -> ExtendedPoint

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

Trait Implementations

impl Copy for ExtendedPoint

impl Debug for ExtendedPoint

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

Formats the value using the given formatter.

impl<'a, 'b> Sub<&'b ExtendedNielsPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<ExtendedNielsPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, 'b> Sub<&'b AffineNielsPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b> Sub<&'b AffineNielsPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a> Sub<AffineNielsPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

fn sub(self, rhs: AffineNielsPoint) -> ExtendedPoint

Performs the - operation.

impl Sub<AffineNielsPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

fn sub(self, rhs: AffineNielsPoint) -> ExtendedPoint

Performs the - operation.

impl<'a, 'b> Sub<&'b ExtendedPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<ExtendedPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, 'b> Sub<&'b AffinePoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b> Sub<&'b AffinePoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a> Sub<AffinePoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

fn sub(self, rhs: AffinePoint) -> ExtendedPoint

Performs the - operation.

impl Sub<AffinePoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

fn sub(self, rhs: AffinePoint) -> ExtendedPoint

Performs the - operation.

impl PartialEq<ExtendedPoint> for ExtendedPoint

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

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

#[must_use]

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

This method tests for !=.

impl From<AffinePoint> for ExtendedPoint

fn from(affine: AffinePoint) -> ExtendedPoint

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

impl From<ExtendedPoint> for AffinePoint

fn from(extended: ExtendedPoint) -> AffinePoint

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, 'b> Add<&'b ExtendedNielsPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<ExtendedNielsPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, 'b> Add<&'b AffineNielsPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b> Add<&'b AffineNielsPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a> Add<AffineNielsPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

fn add(self, rhs: AffineNielsPoint) -> ExtendedPoint

Performs the + operation.

impl Add<AffineNielsPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

fn add(self, rhs: AffineNielsPoint) -> ExtendedPoint

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<ExtendedPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, 'b> Add<&'b AffinePoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b> Add<&'b AffinePoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a> Add<AffinePoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

fn add(self, rhs: AffinePoint) -> ExtendedPoint

Performs the + operation.

impl Add<AffinePoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

fn add(self, rhs: AffinePoint) -> ExtendedPoint

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Neg for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

fn neg(self) -> ExtendedPoint

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.

impl AddAssign<ExtendedNielsPoint> for ExtendedPoint

fn add_assign(&mut self, rhs: ExtendedNielsPoint)

Performs the += operation.

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

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

Performs the += operation.

impl AddAssign<AffineNielsPoint> for ExtendedPoint

fn add_assign(&mut self, rhs: AffineNielsPoint)

Performs the += operation.

impl<'b> AddAssign<&'b AffineNielsPoint> for ExtendedPoint

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

Performs the += operation.

impl AddAssign<ExtendedPoint> for ExtendedPoint

fn add_assign(&mut self, rhs: ExtendedPoint)

Performs the += operation.

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

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

Performs the += operation.

impl AddAssign<AffinePoint> for ExtendedPoint

fn add_assign(&mut self, rhs: AffinePoint)

Performs the += operation.

impl<'b> AddAssign<&'b AffinePoint> for ExtendedPoint

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

Performs the += operation.

impl SubAssign<ExtendedNielsPoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: ExtendedNielsPoint)

Performs the -= operation.

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

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

Performs the -= operation.

impl SubAssign<AffineNielsPoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: AffineNielsPoint)

Performs the -= operation.

impl<'b> SubAssign<&'b AffineNielsPoint> for ExtendedPoint

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

Performs the -= operation.

impl SubAssign<ExtendedPoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: ExtendedPoint)

Performs the -= operation.

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

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

Performs the -= operation.

impl SubAssign<AffinePoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: AffinePoint)

Performs the -= operation.

impl<'b> SubAssign<&'b AffinePoint> for ExtendedPoint

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

Performs the -= operation.

impl MulAssign<Fr> for ExtendedPoint

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

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

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

Performs the *= operation.

impl Clone for ExtendedPoint

fn clone(&self) -> ExtendedPoint

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Default for ExtendedPoint

fn default() -> ExtendedPoint

Returns the identity.

impl ConstantTimeEq for ExtendedPoint

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

Determine if two items are equal.

impl ConditionallySelectable for ExtendedPoint

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.