Type Alias ProjectivePoint

pub type ProjectivePoint = ProjectivePoint<NistP256>;

Elliptic curve point in projective coordinates.

Aliased Type

struct ProjectivePoint { /* private fields */ }

Implementations

impl<C> ProjectivePoint<C>

where C: PrimeCurveParams,

pub const IDENTITY: ProjectivePoint<C>

Additive identity of the group a.k.a. the point at infinity.

pub const GENERATOR: ProjectivePoint<C>

Base point of the curve.

pub fn to_affine(&self) -> AffinePoint<C>

Returns the affine representation of this point, or None if it is the identity.

pub fn neg(&self) -> ProjectivePoint<C>

Returns -self.

pub fn add(&self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Returns self + other.

pub fn sub(&self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Returns self - other.

Trait Implementations

impl<C> Add<&AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the + operator.

fn add(self, other: &AffinePoint<C>) -> ProjectivePoint<C>

Performs the + operation.

impl<C> Add<&ProjectivePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the + operator.

fn add(self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the + operation.

impl<C> Add<AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the + operator.

fn add(self, other: AffinePoint<C>) -> ProjectivePoint<C>

Performs the + operation.

impl<C> Add for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the + operator.

fn add(self, other: ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the + operation.

impl<C> AddAssign<&AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn add_assign(&mut self, rhs: &AffinePoint<C>)

Performs the += operation.

impl<C> AddAssign<&ProjectivePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn add_assign(&mut self, rhs: &ProjectivePoint<C>)

Performs the += operation.

impl<C> AddAssign<AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn add_assign(&mut self, rhs: AffinePoint<C>)

Performs the += operation.

impl<C> AddAssign for ProjectivePoint<C>

where C: PrimeCurveParams,

fn add_assign(&mut self, rhs: ProjectivePoint<C>)

Performs the += operation.

impl<const N: usize, C> BatchNormalize<[ProjectivePoint<C>; N]> for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams, <C as PrimeCurveParams>::FieldElement: Invert<Output = CtOption<<C as PrimeCurveParams>::FieldElement>>,

type Output = [<ProjectivePoint<C> as Curve>::AffineRepr; N]

The output of the batch normalization; a container of affine points.

fn batch_normalize( points: &[ProjectivePoint<C>; N], ) -> [<ProjectivePoint<C> as Curve>::AffineRepr; N]

Perform a batched conversion to affine representation on a sequence of projective points at an amortized cost that should be practically as efficient as a single conversion. Internally, implementors should rely upon InvertBatch.

impl<C> Clone for ProjectivePoint<C>

where C: Clone + PrimeCurveParams, <C as PrimeCurveParams>::FieldElement: Clone,

fn clone(&self) -> ProjectivePoint<C>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<C> CofactorGroup for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams, GenericArray<u8, <C as Curve>::FieldBytesSize>: Copy, <C as Curve>::FieldBytesSize: ModulusSize, GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>: Copy, <<<C as Curve>::FieldBytesSize as ModulusSize>::UncompressedPointSize as ArrayLength<u8>>::ArrayType: Copy,

type Subgroup = ProjectivePoint<C>

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) -> <ProjectivePoint<C> 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<ProjectivePoint<C>>

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<C> ConditionallySelectable for ProjectivePoint<C>

where C: PrimeCurveParams,

fn conditional_select( a: &ProjectivePoint<C>, b: &ProjectivePoint<C>, choice: Choice, ) -> ProjectivePoint<C>

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<C> ConstantTimeEq for ProjectivePoint<C>

where C: PrimeCurveParams,

fn ct_eq(&self, other: &ProjectivePoint<C>) -> Choice

Determine if two items are equal.

impl<C> Curve for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams,

type AffineRepr = AffinePoint<C>

The affine representation for this elliptic curve.

fn to_affine(&self) -> AffinePoint<C>

Converts this element into its affine representation.

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().

impl<C> Debug for ProjectivePoint<C>

where C: Debug + PrimeCurveParams, <C as PrimeCurveParams>::FieldElement: Debug,

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

Formats the value using the given formatter.

impl<C> Default for ProjectivePoint<C>

where C: PrimeCurveParams,

fn default() -> ProjectivePoint<C>

Returns the “default value” for a type.

impl<C> Double for ProjectivePoint<C>

where C: PrimeCurveParams,

fn double(&self) -> ProjectivePoint<C>

Double this point.

impl<C> From<&AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn from(p: &AffinePoint<C>) -> ProjectivePoint<C>

Converts to this type from the input type.

impl<C> From<&PublicKey<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn from(public_key: &PublicKey<C>) -> ProjectivePoint<C>

Converts to this type from the input type.

impl<C> From<AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn from(p: AffinePoint<C>) -> ProjectivePoint<C>

Converts to this type from the input type.

impl<C> From<PublicKey<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn from(public_key: PublicKey<C>) -> ProjectivePoint<C>

Converts to this type from the input type.

impl<C> FromEncodedPoint<C> for ProjectivePoint<C>

where C: PrimeCurveParams, GenericArray<u8, <C as Curve>::FieldBytesSize>: Copy, <C as Curve>::FieldBytesSize: ModulusSize, GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>: Copy,

fn from_encoded_point( p: &EncodedPoint<<C as Curve>::FieldBytesSize>, ) -> CtOption<ProjectivePoint<C>>

Deserialize the type this trait is impl’d on from an EncodedPoint.

impl<C> Group for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams,

type Scalar = <C as CurveArithmetic>::Scalar

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

fn random(rng: impl RngCore) -> ProjectivePoint<C>

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

fn identity() -> ProjectivePoint<C>

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

fn generator() -> ProjectivePoint<C>

Returns a fixed generator of the prime-order subgroup.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> ProjectivePoint<C>

Doubles this element.

impl<C> GroupEncoding for ProjectivePoint<C>

where C: PrimeCurveParams, GenericArray<u8, <C as Curve>::FieldBytesSize>: Copy, <C as Curve>::FieldBytesSize: ModulusSize, GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>: Copy, <<<C as Curve>::FieldBytesSize as ModulusSize>::UncompressedPointSize as ArrayLength<u8>>::ArrayType: Copy,

type Repr = GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>

The encoding of group elements.

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

Attempts to deserialize a group element from its encoding.

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

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

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

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

impl<C> LinearCombination for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams,

fn lincomb(x: &Self, k: &Self::Scalar, y: &Self, l: &Self::Scalar) -> Self

Calculates x * k + y * l.

impl<C, S> Mul<S> for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams, S: Borrow<<C as CurveArithmetic>::Scalar>,

type Output = ProjectivePoint<C>

The resulting type after applying the * operator.

fn mul(self, scalar: S) -> ProjectivePoint<C>

Performs the * operation.

impl<C, S> MulAssign<S> for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams, S: Borrow<<C as CurveArithmetic>::Scalar>,

fn mul_assign(&mut self, scalar: S)

Performs the *= operation.

impl<C> MulByGenerator for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams,

fn mul_by_generator( scalar: &<ProjectivePoint<C> as Group>::Scalar, ) -> ProjectivePoint<C>

Multiply by the generator of the prime-order subgroup.

impl<C> Neg for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the - operator.

fn neg(self) -> ProjectivePoint<C>

Performs the unary - operation.

impl<C> PartialEq for ProjectivePoint<C>

where C: PrimeCurveParams,

fn eq(&self, other: &ProjectivePoint<C>) -> 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<C> PrimeCurve for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams, GenericArray<u8, <C as Curve>::FieldBytesSize>: Copy, <C as Curve>::FieldBytesSize: ModulusSize, GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>: Copy, <<<C as Curve>::FieldBytesSize as ModulusSize>::UncompressedPointSize as ArrayLength<u8>>::ArrayType: Copy,

type Affine = AffinePoint<C>

impl<C> Sub<&AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the - operator.

fn sub(self, other: &AffinePoint<C>) -> ProjectivePoint<C>

Performs the - operation.

impl<C> Sub<&ProjectivePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the - operator.

fn sub(self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the - operation.

impl<C> Sub<AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the - operator.

fn sub(self, other: AffinePoint<C>) -> ProjectivePoint<C>

Performs the - operation.

impl<C> Sub for ProjectivePoint<C>

where C: PrimeCurveParams,

type Output = ProjectivePoint<C>

The resulting type after applying the - operator.

fn sub(self, other: ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the - operation.

impl<C> SubAssign<&AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn sub_assign(&mut self, rhs: &AffinePoint<C>)

Performs the -= operation.

impl<C> SubAssign<&ProjectivePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn sub_assign(&mut self, rhs: &ProjectivePoint<C>)

Performs the -= operation.

impl<C> SubAssign<AffinePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn sub_assign(&mut self, rhs: AffinePoint<C>)

Performs the -= operation.

impl<C> SubAssign for ProjectivePoint<C>

where C: PrimeCurveParams,

fn sub_assign(&mut self, rhs: ProjectivePoint<C>)

Performs the -= operation.

impl<'a, C> Sum<&'a ProjectivePoint<C>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn sum<I>(iter: I) -> ProjectivePoint<C>

where I: Iterator<Item = &'a ProjectivePoint<C>>,

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

impl<C> Sum for ProjectivePoint<C>

where C: PrimeCurveParams,

fn sum<I>(iter: I) -> ProjectivePoint<C>

where I: Iterator<Item = ProjectivePoint<C>>,

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

impl<C> ToEncodedPoint<C> for ProjectivePoint<C>

where C: PrimeCurveParams, <C as Curve>::FieldBytesSize: ModulusSize, GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>: Copy, <<<C as Curve>::FieldBytesSize as ModulusSize>::UncompressedPointSize as ArrayLength<u8>>::ArrayType: Copy,

fn to_encoded_point( &self, compress: bool, ) -> EncodedPoint<<C as Curve>::FieldBytesSize>

Serialize this value as a SEC1 EncodedPoint, optionally applying point compression.

impl<C> Copy for ProjectivePoint<C>

where C: Copy + PrimeCurveParams, <C as PrimeCurveParams>::FieldElement: Copy,

impl<C> DefaultIsZeroes for ProjectivePoint<C>

where C: PrimeCurveParams,

impl<C> Eq for ProjectivePoint<C>

where C: PrimeCurveParams,

impl<C> PrimeGroup for ProjectivePoint<C>

where ProjectivePoint<C>: Double, C: PrimeCurveParams, GenericArray<u8, <C as Curve>::FieldBytesSize>: Copy, <C as Curve>::FieldBytesSize: ModulusSize, GenericArray<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>: Copy, <<<C as Curve>::FieldBytesSize as ModulusSize>::UncompressedPointSize as ArrayLength<u8>>::ArrayType: Copy,