Struct ExtendedPoint

pub struct ExtendedPoint { /* 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 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<'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, '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, '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, '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, 'b> Add<&'b SubgroupPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = ExtendedPoint

The resulting type after applying the + operator.

fn add(self, rhs: &'b SubgroupPoint) -> 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> 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> 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> 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<'a> Add<SubgroupPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<SubgroupPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

impl AddAssign<AffineNielsPoint> for ExtendedPoint

fn add_assign(&mut self, rhs: AffineNielsPoint)

Performs the += operation.

impl AddAssign<AffinePoint> for ExtendedPoint

fn add_assign(&mut self, rhs: AffinePoint)

Performs the += operation.

impl AddAssign<ExtendedNielsPoint> for ExtendedPoint

fn add_assign(&mut self, rhs: ExtendedNielsPoint)

Performs the += operation.

impl AddAssign<SubgroupPoint> for ExtendedPoint

fn add_assign(&mut self, rhs: SubgroupPoint)

Performs the += operation.

impl AddAssign for ExtendedPoint

fn add_assign(&mut self, rhs: ExtendedPoint)

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 CofactorCurve for ExtendedPoint

type Affine = AffinePoint

impl CofactorGroup for ExtendedPoint

type Subgroup = SubgroupPoint

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::Subgroup

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 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.

impl ConstantTimeEq for ExtendedPoint

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 ExtendedPoint

type AffineRepr = AffinePoint

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 Debug for ExtendedPoint

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

Formats the value using the given formatter.

impl Default for ExtendedPoint

fn default() -> ExtendedPoint

Returns the identity.

impl Display for ExtendedPoint

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

Formats the value using the given formatter.

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

fn from(extended: &'a 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> From<&'a SubgroupPoint> for &'a ExtendedPoint

fn from(val: &'a SubgroupPoint) -> &'a ExtendedPoint

Converts to this type from the input type.

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

Converts to this type from the input type.

impl From<SubgroupPoint> for ExtendedPoint

fn from(val: SubgroupPoint) -> ExtendedPoint

Converts to this type from the input type.

impl Group for ExtendedPoint

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 identity() -> Self

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

fn generator() -> Self

Returns a fixed generator of the prime-order subgroup.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> Self

Doubles this element.

impl GroupEncoding for ExtendedPoint

type Repr = [u8; 32]

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

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

Performs the *= operation.

impl MulAssign<Fr> for ExtendedPoint

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl Neg for ExtendedPoint

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.

type Output = ExtendedPoint

The resulting type after applying the - operator.

impl PartialEq for ExtendedPoint

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

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = ExtendedPoint

The resulting type after applying the - operator.

fn sub(self, rhs: &'b SubgroupPoint) -> 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> 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<'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> 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<'a> Sub<SubgroupPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<SubgroupPoint> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

impl SubAssign<AffineNielsPoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: AffineNielsPoint)

Performs the -= operation.

impl SubAssign<AffinePoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: AffinePoint)

Performs the -= operation.

impl SubAssign<ExtendedNielsPoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: ExtendedNielsPoint)

Performs the -= operation.

impl SubAssign<SubgroupPoint> for ExtendedPoint

fn sub_assign(&mut self, rhs: SubgroupPoint)

Performs the -= operation.

impl SubAssign for ExtendedPoint

fn sub_assign(&mut self, rhs: ExtendedPoint)

Performs the -= operation.

impl<T> Sum<T> for ExtendedPoint

where T: Borrow<ExtendedPoint>,

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 WnafGroup for ExtendedPoint

fn recommended_wnaf_for_num_scalars(num_scalars: usize) -> usize

Recommends a wNAF window size given the number of scalars you intend to multiply a base by. Always returns a number between 2 and 22, inclusive.

impl Copy for ExtendedPoint

impl Eq for ExtendedPoint