Struct AffinePoint 

pub struct AffinePoint<C: PrimeCurveParams> {
    pub(crate) x: C::FieldElement,
    pub(crate) y: C::FieldElement,
    pub(crate) infinity: u8,
}

Point on a Weierstrass curve in affine coordinates.

Fields

x: C::FieldElement

x-coordinate

y: C::FieldElement

y-coordinate

infinity: u8

Is this point the point at infinity? 0 = no, 1 = yes

This is a proxy for Choice, but uses u8 instead to permit const constructors for IDENTITY and GENERATOR.

Implementations

impl<C> AffinePoint<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 is_identity(&self) -> Choice

Is this point the point at infinity?

fn to_compact(self) -> Self

Conditionally negate AffinePoint for use with point compaction.

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

Internal RNG that avoids a TryCryptoRng bound so we can use it with group.

TODO(tarcieri): find some way to avoid this?

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

where C: PrimeCurveParams,

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

where C: PrimeCurveParams,

type FieldRepr = Array<u8, <C as Curve>::FieldBytesSize>

Field element representation with curve-specific serialization/endianness.

fn from_coordinates(x: &Self::FieldRepr, y: &Self::FieldRepr) -> CtOption<Self>

Creates an affine point from its coordinates.

fn x(&self) -> FieldBytes<C>

Get the affine x-coordinate as a serialized field element.

fn y(&self) -> FieldBytes<C>

Get the affine y-coordinate as a serialized field element.

fn x_is_odd(&self) -> Choice

Is the affine x-coordinate odd?

fn y_is_odd(&self) -> Choice

Is the affine y-coordinate odd?

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

where C::FieldElement: Clone,

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<C> ConditionallySelectable for AffinePoint<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 AffinePoint<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 AffinePoint<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 AffinePoint<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> CurveAffine for AffinePoint<C>

where C: PrimeCurveParams,

type Curve = ProjectivePoint<C>

The efficient representation for this elliptic curve.

type Scalar = <C as CurveArithmetic>::Scalar

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

fn identity() -> AffinePoint<C>

Returns the additive identity.

fn generator() -> AffinePoint<C>

Returns a fixed generator of unknown exponent.

fn is_identity(&self) -> Choice

Determines if this point represents the additive identity.

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

Converts this affine point to its efficient representation.

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

where C::FieldElement: Debug,

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

Formats the value using the given formatter.

impl<C> DecompactPoint<C> for AffinePoint<C>

where C: PrimeCurveParams,

fn decompact(x_bytes: &FieldBytes<C>) -> CtOption<Self>

Attempt to decompact an elliptic curve point

impl<C> DecompressPoint<C> for AffinePoint<C>

where C: PrimeCurveParams,

fn decompress(x_bytes: &FieldBytes<C>, y_is_odd: Choice) -> CtOption<Self>

Attempt to decompress an elliptic curve point.

impl<C> Default for AffinePoint<C>

where C: PrimeCurveParams,

fn default() -> Self

Returns the “default value” for a 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<&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 AffinePoint<C>

where C: PrimeCurveParams,

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

Converts to this type from the input type.

impl<C> From<AffinePoint<C>> for Sec1Point<C>

where C: PrimeCurveParams,

fn from(affine: AffinePoint<C>) -> Sec1Point<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<AffinePoint<C>>> for AffinePoint<C>

where C: PrimeCurveParams,

fn from(affine: NonIdentity<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 AffinePoint<C>

where C: PrimeCurveParams,

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

Converts to this type from the input type.

impl<C> FromSec1Point<C> for AffinePoint<C>

where C: PrimeCurveParams,

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

Attempts to parse the given Sec1Point as an SEC1-encoded AffinePoint.

Returns

None value if encoded_point is not on the secp384r1 curve.

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 AffinePoint<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> GroupEncoding for AffinePoint<C>

where C: PrimeCurveParams,

fn from_bytes(bytes: &Self::Repr) -> CtOption<Self>

NOTE: not constant-time with respect to identity point

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

The encoding of group elements.

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, S> Mul<S> for &AffinePoint<C>

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

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 AffinePoint<C>

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

type Output = ProjectivePoint<C>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

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

Multiply self by rhs in variable-time.

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

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

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

Multiply self by rhs in variable-time.

impl<C> Neg for &AffinePoint<C>

where C: PrimeCurveParams,

type Output = AffinePoint<C>

The resulting type after applying the - operator.

fn neg(self) -> AffinePoint<C>

Performs the unary - operation.

impl<C> Neg for AffinePoint<C>

where C: PrimeCurveParams,

type Output = AffinePoint<C>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

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

where C: PrimeCurveParams,

fn sub_assign(&mut self, rhs: &AffinePoint<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> ToCompactSec1Point<C> for AffinePoint<C>

where C: PrimeCurveParams,

fn to_compact_encoded_point(&self) -> CtOption<Sec1Point<C>>

Serialize this value as a SEC1 compact Sec1Point

impl<C> ToSec1Point<C> for AffinePoint<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<&AffinePoint<C>> for PublicKey<C>

where C: PrimeCurveParams,

type Error = Error

The type returned in the event of a conversion error.

fn try_from(affine_point: &AffinePoint<C>) -> Result<PublicKey<C>>

Performs the conversion.

impl<C> TryFrom<&EncodedPoint<<C as Curve>::FieldBytesSize>> for AffinePoint<C>

where C: PrimeCurveParams,

type Error = Error

The type returned in the event of a conversion error.

fn try_from(point: &Sec1Point<C>) -> Result<AffinePoint<C>>

Performs the conversion.

impl<C> TryFrom<AffinePoint<C>> for NonIdentity<AffinePoint<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(affine_point: AffinePoint<C>) -> Result<Self>

Performs the conversion.

impl<C> TryFrom<AffinePoint<C>> for PublicKey<C>

where C: PrimeCurveParams,

type Error = Error

The type returned in the event of a conversion error.

fn try_from(affine_point: AffinePoint<C>) -> Result<PublicKey<C>>

Performs the conversion.

impl<C> TryFrom<EncodedPoint<<C as Curve>::FieldBytesSize>> for AffinePoint<C>

where C: PrimeCurveParams,

type Error = Error

The type returned in the event of a conversion error.

fn try_from(point: Sec1Point<C>) -> Result<AffinePoint<C>>

Performs the conversion.

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

where C::FieldElement: Copy,

impl<C> DefaultIsZeroes for AffinePoint<C>

where C: PrimeCurveParams,

impl<C> Eq for AffinePoint<C>

where C: PrimeCurveParams,