ProjectivePoint

primeorder

Struct ProjectivePoint 

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pub struct ProjectivePoint<C: PrimeCurveParams> { /* private fields */ }
Expand description

Point on a Weierstrass curve in projective coordinates.

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

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pub const IDENTITY: Self

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

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pub const GENERATOR: Self

Base point of the curve.

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

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

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pub fn neg(&self) -> Self

Returns -self.

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

Returns self + other.

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

Returns self - other.

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impl<C> Add<&AffinePoint<C>> for &ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the + operator.
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fn add(self, other: &AffinePoint<C>) -> ProjectivePoint<C>

Performs the + operation. Read more
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impl<C> Add<&AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the + operator.
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fn add(self, other: &AffinePoint<C>) -> ProjectivePoint<C>

Performs the + operation. Read more
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impl<C> Add<&ProjectivePoint<C>> for &ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the + operator.
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fn add(self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the + operation. Read more
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impl<C> Add<&ProjectivePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the + operator.
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fn add(self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the + operation. Read more
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impl<C> Add<AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the + operator.
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fn add(self, other: AffinePoint<C>) -> ProjectivePoint<C>

Performs the + operation. Read more
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impl<C> Add for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the + operator.
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fn add(self, other: ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the + operation. Read more
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impl<C> AddAssign<&AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the += operation. Read more
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impl<C> AddAssign<&ProjectivePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the += operation. Read more
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impl<C> AddAssign<AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the += operation. Read more
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impl<C> AddAssign for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the += operation. Read more
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impl<const N: usize, C> BatchNormalize<[ProjectivePoint<C>; N]> for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams, C::FieldElement: Invert<Output = CtOption<C::FieldElement>>,

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

The output of the batch normalization; a container of affine points.
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fn batch_normalize(points: &[Self; N]) -> [Self::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.
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impl<C: Clone + PrimeCurveParams> Clone for ProjectivePoint<C>
where C::FieldElement: Clone,

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

Returns a duplicate of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<C> CofactorGroup for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams, FieldBytes<C>: Copy, FieldBytesSize<C>: ModulusSize, CompressedPoint<C>: Copy, <UncompressedPointSize<C> as ArrayLength<u8>>::ArrayType: Copy,

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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.
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fn clear_cofactor(&self) -> Self::Subgroup

Maps self to the prime-order subgroup by multiplying this element by some k-multiple of the cofactor. Read more
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fn into_subgroup(self) -> CtOption<Self>

Returns self if it is contained in the prime-order subgroup. Read more
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fn is_torsion_free(&self) -> Choice

Determines if this element is “torsion free”, i.e., is contained in the prime-order subgroup. Read more
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fn is_small_order(&self) -> Choice

Determines if this element is of small order. Read more
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impl<C> ConditionallySelectable for ProjectivePoint<C>
where C: PrimeCurveParams,

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fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice. Read more
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fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice. Read more
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fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves. Read more
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impl<C> ConstantTimeEq for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Determine if two items are equal. Read more
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fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal. Read more
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impl<C> Curve for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams,

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type AffineRepr = AffinePoint<C>

The affine representation for this elliptic curve.
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fn to_affine(&self) -> AffinePoint<C>

Converts this element into its affine representation.
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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().
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impl<C: Debug + PrimeCurveParams> Debug for ProjectivePoint<C>
where C::FieldElement: Debug,

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

Formats the value using the given formatter. Read more
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impl<C> Default for ProjectivePoint<C>
where C: PrimeCurveParams,

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl<C: PrimeCurveParams> Double for ProjectivePoint<C>

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fn double(&self) -> Self

Double this point.
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impl<C> From<&AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Converts to this type from the input type.
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impl<C> From<&ProjectivePoint<C>> for AffinePoint<C>
where C: PrimeCurveParams,

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

Converts to this type from the input type.
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impl<C> From<&PublicKey<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Converts to this type from the input type.
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impl<C> From<AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Converts to this type from the input type.
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impl<C> From<ProjectivePoint<C>> for AffinePoint<C>
where C: PrimeCurveParams,

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

Converts to this type from the input type.
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impl<C> From<PublicKey<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Converts to this type from the input type.
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impl<C> FromEncodedPoint<C> for ProjectivePoint<C>
where C: PrimeCurveParams, FieldBytes<C>: Copy, FieldBytesSize<C>: ModulusSize, CompressedPoint<C>: Copy,

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fn from_encoded_point(p: &EncodedPoint<C>) -> CtOption<Self>

Deserialize the type this trait is impl’d on from an EncodedPoint.
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impl<C> Group for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams,

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type Scalar = <C as CurveArithmetic>::Scalar

Scalars modulo the order of this group’s scalar field.
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fn random(rng: impl RngCore) -> Self

Returns an element chosen uniformly at random from the non-identity elements of this group. Read more
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fn identity() -> Self

Returns the additive identity, also known as the “neutral element”.
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fn generator() -> Self

Returns a fixed generator of the prime-order subgroup.
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fn is_identity(&self) -> Choice

Determines if this point is the identity.
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fn double(&self) -> Self

Doubles this element.
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impl<C> GroupEncoding for ProjectivePoint<C>
where C: PrimeCurveParams, FieldBytes<C>: Copy, FieldBytesSize<C>: ModulusSize, CompressedPoint<C>: Copy, <UncompressedPointSize<C> as ArrayLength<u8>>::ArrayType: Copy,

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

The encoding of group elements. Read more
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fn from_bytes(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element from its encoding.
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fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element, not checking if the element is valid. Read more
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fn to_bytes(&self) -> Self::Repr

Converts this element into its byte encoding. This may or may not support encoding the identity.
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impl<C> LinearCombination for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams,

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

Calculates x * k + y * l.
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impl<C> Mul<&<C as CurveArithmetic>::Scalar> for &ProjectivePoint<C>
where C: PrimeCurveParams, ProjectivePoint<C>: Double,

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type Output = ProjectivePoint<C>

The resulting type after applying the * operator.
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fn mul(self, scalar: &Scalar<C>) -> ProjectivePoint<C>

Performs the * operation. Read more
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impl<C, S> Mul<S> for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

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type Output = ProjectivePoint<C>

The resulting type after applying the * operator.
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fn mul(self, scalar: S) -> Self

Performs the * operation. Read more
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impl<C, S> MulAssign<S> for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams, S: Borrow<Scalar<C>>,

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fn mul_assign(&mut self, scalar: S)

Performs the *= operation. Read more
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impl<C> MulByGenerator for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams,

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

Multiply by the generator of the prime-order subgroup.
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impl<'a, C> Neg for &'a ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn neg(self) -> ProjectivePoint<C>

Performs the unary - operation. Read more
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impl<C> Neg for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn neg(self) -> ProjectivePoint<C>

Performs the unary - operation. Read more
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impl<C> PartialEq for ProjectivePoint<C>
where C: PrimeCurveParams,

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fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<C> PrimeCurve for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams, FieldBytes<C>: Copy, FieldBytesSize<C>: ModulusSize, CompressedPoint<C>: Copy, <UncompressedPointSize<C> as ArrayLength<u8>>::ArrayType: Copy,

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type Affine = AffinePoint<C>

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impl<C> Sub<&AffinePoint<C>> for &ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn sub(self, other: &AffinePoint<C>) -> ProjectivePoint<C>

Performs the - operation. Read more
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impl<C> Sub<&AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn sub(self, other: &AffinePoint<C>) -> ProjectivePoint<C>

Performs the - operation. Read more
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impl<C> Sub<&ProjectivePoint<C>> for &ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn sub(self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the - operation. Read more
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impl<C> Sub<&ProjectivePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn sub(self, other: &ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the - operation. Read more
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impl<C> Sub<AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn sub(self, other: AffinePoint<C>) -> ProjectivePoint<C>

Performs the - operation. Read more
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impl<C> Sub for ProjectivePoint<C>
where C: PrimeCurveParams,

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type Output = ProjectivePoint<C>

The resulting type after applying the - operator.
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fn sub(self, other: ProjectivePoint<C>) -> ProjectivePoint<C>

Performs the - operation. Read more
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impl<C> SubAssign<&AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the -= operation. Read more
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impl<C> SubAssign<&ProjectivePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the -= operation. Read more
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impl<C> SubAssign<AffinePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the -= operation. Read more
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impl<C> SubAssign for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Performs the -= operation. Read more
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impl<'a, C> Sum<&'a ProjectivePoint<C>> for ProjectivePoint<C>
where C: PrimeCurveParams,

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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.
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impl<C> Sum for ProjectivePoint<C>
where C: PrimeCurveParams,

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

Takes an iterator and generates Self from the elements by “summing up” the items.
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impl<C> ToEncodedPoint<C> for ProjectivePoint<C>
where C: PrimeCurveParams, FieldBytesSize<C>: ModulusSize, CompressedPoint<C>: Copy, <UncompressedPointSize<C> as ArrayLength<u8>>::ArrayType: Copy,

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

Serialize this value as a SEC1 EncodedPoint, optionally applying point compression.
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impl<C> TryFrom<&ProjectivePoint<C>> for PublicKey<C>
where C: PrimeCurveParams,

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type Error = Error

The type returned in the event of a conversion error.
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fn try_from(point: &ProjectivePoint<C>) -> Result<PublicKey<C>>

Performs the conversion.
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impl<C> TryFrom<ProjectivePoint<C>> for PublicKey<C>
where C: PrimeCurveParams,

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type Error = Error

The type returned in the event of a conversion error.
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fn try_from(point: ProjectivePoint<C>) -> Result<PublicKey<C>>

Performs the conversion.
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impl<C: Copy + PrimeCurveParams> Copy for ProjectivePoint<C>
where C::FieldElement: Copy,

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impl<C> DefaultIsZeroes for ProjectivePoint<C>
where C: PrimeCurveParams,

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impl<C> Eq for ProjectivePoint<C>
where C: PrimeCurveParams,

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impl<C> PrimeGroup for ProjectivePoint<C>
where Self: Double, C: PrimeCurveParams, FieldBytes<C>: Copy, FieldBytesSize<C>: ModulusSize, CompressedPoint<C>: Copy, <UncompressedPointSize<C> as ArrayLength<u8>>::ArrayType: Copy,

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impl<T> ConditionallyNegatable for T
where T: ConditionallySelectable, &'a T: for<'a> Neg<Output = T>,

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fn conditional_negate(&mut self, choice: Choice)

Negate self if choice == Choice(1); otherwise, leave it unchanged. Read more
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Calls .tap_deref() only in debug builds, and is erased in release builds.
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fn tap_deref_mut_dbg<T>(self, func: impl FnOnce(&mut T)) -> Self
where Self: DerefMut<Target = T> + Deref, T: ?Sized,

Calls .tap_deref_mut() only in debug builds, and is erased in release builds.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> TryConv for T

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fn try_conv<T>(self) -> Result<T, Self::Error>
where Self: TryInto<T>,

Attempts to convert self into T using TryInto<T>. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<Z> Zeroize for Z
where Z: DefaultIsZeroes,

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fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.
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impl<T, Rhs, Output> GroupOps<Rhs, Output> for T
where T: Add<Rhs, Output = Output> + Sub<Rhs, Output = Output> + AddAssign<Rhs> + SubAssign<Rhs>,

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impl<T, Rhs, Output> GroupOpsOwned<Rhs, Output> for T
where T: for<'r> GroupOps<&'r Rhs, Output>,

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impl<T, Rhs, Output> ScalarMul<Rhs, Output> for T
where T: Mul<Rhs, Output = Output> + MulAssign<Rhs>,

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impl<T, Rhs, Output> ScalarMulOwned<Rhs, Output> for T
where T: for<'r> ScalarMul<&'r Rhs, Output>,