Struct ProjectivePoint 

pub struct ProjectivePoint<C: PrimeCurveParams> {
    pub(crate) x: C::FieldElement,
    pub(crate) y: C::FieldElement,
    pub(crate) z: C::FieldElement,
}

Point on a Weierstrass curve in projective coordinates.

Fields

x: C::FieldElement

y: C::FieldElement

z: C::FieldElement

Implementations

impl<C> ProjectivePoint<C>

where C: PrimeCurveParams,

pub const IDENTITY: Self

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

pub const GENERATOR: Self

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(crate) fn to_affine_internal(self, zinv: C::FieldElement) -> AffinePoint<C>

pub fn neg(&self) -> Self

Returns -self.

pub fn add(&self, other: &Self) -> Self

Returns self + other.

fn add_mixed(&self, other: &AffinePoint<C>) -> Self

Returns self + other.

pub fn sub(&self, other: &Self) -> Self

Returns self - other.

fn sub_mixed(&self, other: &AffinePoint<C>) -> Self

Returns self - other.

pub fn mul(&self, k: &Scalar<C>) -> Self

Returns [k] self.

pub fn mul_vartime(&self, k: &Scalar<C>) -> Self

Returns [k] self computed in variable time.

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<&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<&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<C> BatchNormalize<[ProjectivePoint<C>]> for ProjectivePoint<C>

where C: PrimeCurveParams,

Available on crate feature alloc only.

type Output = Vec<<ProjectivePoint<C> as Curve>::Affine>

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

fn batch_normalize(points: &[Self]) -> Vec<<Self as CurveGroup>::Affine>

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.

fn batch_normalize_vartime(points: &Points) -> Self::Output

Perform a batched conversion to affine representation on a sequence of projective points in variable-time.

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

where C: PrimeCurveParams,

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

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

fn batch_normalize(points: &[Self; N]) -> [<Self as CurveGroup>::Affine; 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.

fn batch_normalize_vartime(points: &Points) -> Self::Output

Perform a batched conversion to affine representation on a sequence of projective points in variable-time.

impl<C: Clone + PrimeCurveParams> Clone for ProjectivePoint<C>

where C::FieldElement: Clone,

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<C> CofactorGroup for ProjectivePoint<C>

where C: PrimeCurveParams,

Prime order elliptic curves have a cofactor of 1.

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) -> 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<C> ConditionallySelectable for ProjectivePoint<C>

where C: PrimeCurveParams,

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<C> ConstantTimeEq for ProjectivePoint<C>

where C: PrimeCurveParams,

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<C> CtEq for ProjectivePoint<C>

where C: PrimeCurveParams,

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

Determine if self is equal to other in constant-time.

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

Determine if self is NOT equal to other in constant-time.

impl<C> CtSelect for ProjectivePoint<C>

where C: PrimeCurveParams,

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

Select between self and other based on choice, returning a copy of the value.

fn ct_swap(&mut self, other: &mut Self, choice: Choice)

Conditionally swap self and other if choice is Choice::TRUE.

impl<C> Curve for ProjectivePoint<C>

where C: PrimeCurveParams,

type Affine = 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(projective: &[Self], affine: &mut [Self::Affine])

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

impl<C: Debug + PrimeCurveParams> Debug for ProjectivePoint<C>

where C::FieldElement: Debug,

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

Formats the value using the given formatter.

impl<C> Default for ProjectivePoint<C>

where C: PrimeCurveParams,

fn default() -> Self

Returns the “default value” for a type.

impl<C: PrimeCurveParams> Double for ProjectivePoint<C>

fn double(&self) -> Self

Double this value, returning the doubled result.

fn double_in_place(&mut self)

Double this value in-place, assigning self + self to self.

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

where C: PrimeCurveParams,

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

Converts to this type from the input type.

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

where C: PrimeCurveParams,

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

Converts to this type from the input type.

impl<C> From<NonIdentity<ProjectivePoint<C>>> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn from(p: NonIdentity<ProjectivePoint<C>>) -> Self

Converts to this type from the input type.

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

where C: PrimeCurveParams,

fn from(p: ProjectivePoint<C>) -> AffinePoint<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> FromSec1Point<C> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn from_sec1_point(p: &Sec1Point<C>) -> CtOption<Self>

Decode curve point from a SEC1 Sec1Point.

fn from_sec1_bytes(bytes: &[u8]) -> Result<Self, Error>

Decode curve point from the provided SEC1 encoding (compressed, uncompressed, or identity) using the Octet-String-to-Elliptic-Curve-Point conversion.

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

👎Deprecated since 0.14.0: use FromSec1Point::from_sec1_point instead

DEPRECATED: legacy name for FromSec1Point::from_sec1_point.

impl<C> Generate for ProjectivePoint<C>

where C: PrimeCurveParams,

fn try_generate_from_rng<R: TryCryptoRng + ?Sized>( rng: &mut R, ) -> Result<Self, R::Error>

Generate random key using the provided TryCryptoRng.

fn generate_from_rng<R>(rng: &mut R) -> Self

where R: CryptoRng + ?Sized,

Generate random key using the provided CryptoRng.

fn try_generate() -> Result<Self, Error>

Randomly generate a value of this type using the system’s ambient cryptographically secure random number generator.

fn generate() -> Self

Randomly generate a value of this type using the system’s ambient cryptographically secure random number generator.

impl<C> Group for ProjectivePoint<C>

where C: PrimeCurveParams,

type Scalar = <C as CurveArithmetic>::Scalar

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

fn try_random<R: TryRng + ?Sized>(rng: &mut R) -> Result<Self, R::Error>

Returns an element chosen uniformly at random from the non-identity elements of this group using a user-provided fallible RNG.

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.

fn mul_by_generator(scalar: &Self::Scalar) -> Self

Multiply by the generator of the prime-order subgroup.

fn random<R>(rng: &mut R) -> Self

where R: Rng + ?Sized,

Returns an element chosen uniformly at random from the non-identity elements of this group using a user-provided infallible RNG.

impl<C> GroupEncoding for ProjectivePoint<C>

where C: PrimeCurveParams,

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

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<C> LinearCombination<[(ProjectivePoint<C>, <C as CurveArithmetic>::Scalar)]> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn lincomb(points_and_scalars: &[(Self, Scalar<C>)]) -> Self

Calculates x1 * k1 + ... + xn * kn.

fn lincomb_vartime(points_and_scalars: &[(Self, Scalar<C>)]) -> Self

Calculates x1 * k1 + ... + xn * kn.

impl<C, const N: usize> LinearCombination<[(ProjectivePoint<C>, <C as CurveArithmetic>::Scalar); N]> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn lincomb(points_and_scalars: &[(Self, Scalar<C>); N]) -> Self

Calculates x1 * k1 + ... + xn * kn.

fn lincomb_vartime(points_and_scalars: &[(Self, Scalar<C>); N]) -> Self

Calculates x1 * k1 + ... + xn * kn.

impl<C> Mul<&<C as CurveArithmetic>::Scalar> for &ProjectivePoint<C>

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

type Output = ProjectivePoint<C>

The resulting type after applying the * operator.

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

Performs the * operation.

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

where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

type Output = ProjectivePoint<C>

The resulting type after applying the * operator.

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

Performs the * operation.

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

where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

type Output = ProjectivePoint<C>

The resulting type after applying the * operator.

fn mul(self, scalar: S) -> Self

Performs the * operation.

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

where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

fn mul_assign(&mut self, scalar: S)

Performs the *= operation.

impl<C> MulByGeneratorVartime for ProjectivePoint<C>

where C: PrimeCurveParams,

fn mul_by_generator_vartime(scalar: &Scalar<C>) -> Self

Multiply by the generator of the prime-order subgroup.

fn mul_by_generator_and_mul_add_vartime( a: &Self::Scalar, b_scalar: &Self::Scalar, b_point: &Self, ) -> Self

Multiply a by the generator of the prime-order subgroup, adding the result to the point P multiplied by the scalar b, i.e. compute aG + bP.

impl<C> MulVartime<&<C as CurveArithmetic>::Scalar> for &ProjectivePoint<C>

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

fn mul_vartime(self, scalar: &Scalar<C>) -> ProjectivePoint<C>

Multiply self by rhs in variable-time.

impl<C, S> MulVartime<S> for &ProjectivePoint<C>

where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

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

Multiply self by rhs in variable-time.

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

where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

fn mul_vartime(self, scalar: S) -> Self

Multiply self by rhs in variable-time.

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> 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: &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<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<&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<&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: Iterator<Item = &'a ProjectivePoint<C>>>(iter: I) -> Self

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: Iterator<Item = Self>>(iter: I) -> Self

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

impl<C> ToSec1Point<C> for ProjectivePoint<C>

where C: PrimeCurveParams,

fn to_sec1_point(&self, compress: bool) -> Sec1Point<C>

Serialize curve point as a SEC1 Sec1Point, optionally applying point compression according to the compress flag.

fn to_sec1_bytes(&self) -> Box<[u8]>

where C: PointCompression,

Encode curve point using the Elliptic-Curve-Point-to-Octet-String conversion and the point compression default for this curve as specified by the PointCompression trait.

fn to_compressed_point( &self, ) -> Array<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::CompressedPointSize>

Serialize curve point as a CompressedPoint.

fn to_uncompressed_point( &self, ) -> Array<u8, <<C as Curve>::FieldBytesSize as ModulusSize>::UncompressedPointSize>

Serialize curve point as a CompressedPoint.

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

👎Deprecated since 0.14.0: use ToSec1Point::to_sec1_point instead

DEPRECATED: legacy name for ToSec1Point::to_sec1_point.

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

where C: PrimeCurveParams,

type Error = Error

The type returned in the event of a conversion error.

fn try_from(point: &ProjectivePoint<C>) -> Result<PublicKey<C>>

Performs the conversion.

impl<C> TryFrom<ProjectivePoint<C>> for NonIdentity<ProjectivePoint<C>>

where C: PrimeCurveParams,

The constant-time alternative is available at NonIdentity::new().

type Error = Error

The type returned in the event of a conversion error.

fn try_from(point: ProjectivePoint<C>) -> Result<Self>

Performs the conversion.

impl<C> TryFrom<ProjectivePoint<C>> for PublicKey<C>

where C: PrimeCurveParams,

type Error = Error

The type returned in the event of a conversion error.

fn try_from(point: ProjectivePoint<C>) -> Result<PublicKey<C>>

Performs the conversion.

impl<C: Copy + PrimeCurveParams> Copy for ProjectivePoint<C>

where C::FieldElement: Copy,

impl<C> DefaultIsZeroes for ProjectivePoint<C>

where C: PrimeCurveParams,

impl<C> Eq for ProjectivePoint<C>

where C: PrimeCurveParams,

impl<C> PrimeCurve for ProjectivePoint<C>

where C: PrimeCurveParams,

impl<C> PrimeGroup for ProjectivePoint<C>

where C: PrimeCurveParams,