Struct ProjectivePoint 

pub struct ProjectivePoint { /* private fields */ }

Available on crate feature arithmetic only.

A point on the secp256k1 curve in projective coordinates.

Implementations

impl ProjectivePoint

pub fn mul_by_generator(k: &Scalar) -> ProjectivePoint

Calculates k * G, where G is the generator.

pub fn mul_by_generator_vartime(k: &Scalar) -> ProjectivePoint

Calculates k * G in variable-time, where G is the generator.

impl ProjectivePoint

pub const IDENTITY: Self

Additive identity of the group: the point at infinity.

pub const GENERATOR: Self

Base point of secp256k1.

pub fn to_affine(&self) -> AffinePoint

Returns the affine representation of this point.

pub fn double(&self) -> ProjectivePoint

Doubles this point.

pub fn double_in_place(&mut self)

Doubles this point in-place.

pub fn endomorphism(&self) -> Self

Calculates SECP256k1 endomorphism: self * lambda.

pub fn eq_affine(&self, other: &AffinePoint) -> Choice

Check whether self is equal to an affine point.

This is a lot faster than first converting self to an AffinePoint and then doing the comparison. It is a little bit faster than converting other to a ProjectivePoint first.

Trait Implementations

impl Add for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<&AffinePoint> for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the + operator.

fn add(self, rhs: &AffinePoint) -> ProjectivePoint

Performs the + operation.

impl Add<&AffinePoint> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the + operator.

fn add(self, rhs: &AffinePoint) -> ProjectivePoint

Performs the + operation.

impl Add<&ProjectivePoint> for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the + operator.

fn add(self, rhs: &ProjectivePoint) -> ProjectivePoint

Performs the + operation.

impl Add<&ProjectivePoint> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the + operator.

fn add(self, rhs: &ProjectivePoint) -> ProjectivePoint

Performs the + operation.

impl Add<AffinePoint> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for ProjectivePoint

fn add_assign(&mut self, rhs: ProjectivePoint)

Performs the += operation.

impl AddAssign<&AffinePoint> for ProjectivePoint

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

Performs the += operation.

impl AddAssign<&ProjectivePoint> for ProjectivePoint

fn add_assign(&mut self, rhs: &ProjectivePoint)

Performs the += operation.

impl AddAssign<AffinePoint> for ProjectivePoint

fn add_assign(&mut self, rhs: AffinePoint)

Performs the += operation.

impl<U: ArraySize> BatchNormalize<Array<ProjectivePoint, U>> for ProjectivePoint

type Output = Array<AffinePoint, U>

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

fn batch_normalize(points: &Array<Self, U>) -> Array<AffinePoint, U>

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: &Array<Self, U>) -> Array<AffinePoint, U>

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

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

type Output = [AffinePoint; N]

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

fn batch_normalize(points: &[Self; N]) -> [AffinePoint; 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: &[Self; N]) -> [AffinePoint; N]

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

impl BatchNormalize<[ProjectivePoint]> for ProjectivePoint

Available on crate feature alloc only.

type Output = Vec<AffinePoint>

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

fn batch_normalize(points: &[Self]) -> Vec<AffinePoint>

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: &[Self]) -> Vec<AffinePoint>

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

impl Clone for ProjectivePoint

fn clone(&self) -> ProjectivePoint

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CofactorGroup for ProjectivePoint

secp256k1 has a cofactor of 1.

type Subgroup = ProjectivePoint

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 ProjectivePoint

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 ProjectivePoint

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 Copy for ProjectivePoint

impl CtEq for ProjectivePoint

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 CtSelect for ProjectivePoint

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 Curve for ProjectivePoint

type Affine = AffinePoint

The affine representation for this elliptic curve.

fn to_affine(&self) -> AffinePoint

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 Debug for ProjectivePoint

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

Formats the value using the given formatter.

impl Default for ProjectivePoint

fn default() -> Self

Returns the “default value” for a type.

impl DefaultIsZeroes for ProjectivePoint

impl Double for ProjectivePoint

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 Eq for ProjectivePoint

impl From<&AffinePoint> for ProjectivePoint

fn from(p: &AffinePoint) -> Self

Converts to this type from the input type.

impl From<&ProjectivePoint> for AffinePoint

fn from(p: &ProjectivePoint) -> AffinePoint

Converts to this type from the input type.

impl From<&PublicKey<Secp256k1>> for ProjectivePoint

fn from(public_key: &PublicKey) -> ProjectivePoint

Converts to this type from the input type.

impl From<AffinePoint> for ProjectivePoint

fn from(p: AffinePoint) -> Self

Converts to this type from the input type.

impl From<NonIdentity<ProjectivePoint>> for ProjectivePoint

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

Converts to this type from the input type.

impl From<ProjectivePoint> for AffinePoint

fn from(p: ProjectivePoint) -> AffinePoint

Converts to this type from the input type.

impl From<PublicKey<Secp256k1>> for ProjectivePoint

fn from(public_key: PublicKey) -> ProjectivePoint

Converts to this type from the input type.

impl FromSec1Point<Secp256k1> for ProjectivePoint

fn from_sec1_point(p: &Sec1Point) -> 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 Generate for ProjectivePoint

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>

Available on crate feature getrandom only.

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

fn generate() -> Self

Available on crate feature getrandom only.

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

impl Group for ProjectivePoint

type Scalar = 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(k: &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 GroupEncoding for ProjectivePoint

type Repr = Array<u8, UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B1>>

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

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

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

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

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

impl LinearCombination<[(ProjectivePoint, Scalar)]> for ProjectivePoint

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

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

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

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

impl Mul<&Scalar> for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, other: &Scalar) -> ProjectivePoint

Performs the * operation.

impl Mul<&Scalar> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, other: &Scalar) -> ProjectivePoint

Performs the * operation.

impl Mul<Scalar> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, other: Scalar) -> ProjectivePoint

Performs the * operation.

impl MulAssign<&Scalar> for ProjectivePoint

fn mul_assign(&mut self, rhs: &Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for ProjectivePoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MulByGeneratorVartime for ProjectivePoint

fn mul_by_generator_vartime(k: &Scalar) -> ProjectivePoint

Multiply by the generator of the prime-order subgroup.

fn mul_by_generator_and_mul_add_vartime( a: &Self::Scalar, b: &Self::Scalar, p: &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 MulVartime<&Scalar> for &ProjectivePoint

fn mul_vartime(self, other: &Scalar) -> ProjectivePoint

Multiply self by rhs in variable-time.

impl MulVartime<&Scalar> for ProjectivePoint

fn mul_vartime(self, other: &Scalar) -> ProjectivePoint

Multiply self by rhs in variable-time.

impl MulVartime<Scalar> for ProjectivePoint

fn mul_vartime(self, other: Scalar) -> ProjectivePoint

Multiply self by rhs in variable-time.

impl Neg for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

fn neg(self) -> ProjectivePoint

Performs the unary - operation.

impl Neg for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

fn neg(self) -> ProjectivePoint

Performs the unary - operation.

impl PartialEq for ProjectivePoint

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 PartialEq<AffinePoint> for ProjectivePoint

fn eq(&self, other: &AffinePoint) -> 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 PartialEq<ProjectivePoint> for AffinePoint

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

impl PrimeGroup for ProjectivePoint

impl Sub for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<&AffinePoint> for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

fn sub(self, rhs: &AffinePoint) -> ProjectivePoint

Performs the - operation.

impl Sub<&AffinePoint> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

fn sub(self, rhs: &AffinePoint) -> ProjectivePoint

Performs the - operation.

impl Sub<&ProjectivePoint> for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

fn sub(self, rhs: &ProjectivePoint) -> ProjectivePoint

Performs the - operation.

impl Sub<&ProjectivePoint> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

fn sub(self, rhs: &ProjectivePoint) -> ProjectivePoint

Performs the - operation.

impl Sub<AffinePoint> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for ProjectivePoint

fn sub_assign(&mut self, rhs: ProjectivePoint)

Performs the -= operation.

impl SubAssign<&AffinePoint> for ProjectivePoint

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

Performs the -= operation.

impl SubAssign<&ProjectivePoint> for ProjectivePoint

fn sub_assign(&mut self, rhs: &ProjectivePoint)

Performs the -= operation.

impl SubAssign<AffinePoint> for ProjectivePoint

fn sub_assign(&mut self, rhs: AffinePoint)

Performs the -= operation.

impl Sum for ProjectivePoint

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

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

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

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

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

impl ToSec1Point<Secp256k1> for ProjectivePoint

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

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,

Available on crate feature alloc only.

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 TryFrom<&ProjectivePoint> for PublicKey

type Error = Error

The type returned in the event of a conversion error.

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

Performs the conversion.

impl TryFrom<ProjectivePoint> for NonIdentity<ProjectivePoint>

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) -> Result<Self>

Performs the conversion.

impl TryFrom<ProjectivePoint> for PublicKey

type Error = Error

The type returned in the event of a conversion error.

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

Performs the conversion.