Struct ark_ec::models::short_weierstrass_jacobian::GroupProjective

#[must_use]
pub struct GroupProjective<P: Parameters> {
    pub x: P::BaseField,
    pub y: P::BaseField,
    pub z: P::BaseField,
    // some fields omitted
}

Jacobian coordinates for a point on an elliptic curve in short Weierstrass form, over the base field P::BaseField. This struct implements arithmetic via the Jacobian formulae

Fields

x: P::BaseField

y: P::BaseField

z: P::BaseField

Implementations

impl<P: Parameters> GroupProjective<P>

pub fn new(x: P::BaseField, y: P::BaseField, z: P::BaseField) -> Self

Trait Implementations

impl<'a, P: Parameters> Add<&'a GroupProjective<P>> for GroupProjective<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: Parameters> Add<&'a mut GroupProjective<P>> for GroupProjective<P>

type Output = Self

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<P: Parameters> Add<GroupProjective<P>> for GroupProjective<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: Parameters> AddAssign<&'a GroupProjective<P>> for GroupProjective<P>

fn add_assign(&mut self, other: &'a Self)

Performs the += operation.

impl<'a, P: Parameters> AddAssign<&'a mut GroupProjective<P>> for GroupProjective<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: Parameters> AddAssign<GroupProjective<P>> for GroupProjective<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: Parameters> CanonicalDeserialize for GroupProjective<P>

fn deserialize<R: Read>(reader: R) -> Result<Self, SerializationError>

Reads Self from reader.

fn deserialize_uncompressed<R: Read>(
    reader: R
) -> Result<Self, SerializationError>

Reads Self from reader without compression.

fn deserialize_unchecked<R: Read>(reader: R) -> Result<Self, SerializationError>

Reads self from reader without compression, and without performing validity checks. Should be used only when the input is trusted.

impl<P: Parameters> CanonicalSerialize for GroupProjective<P>

fn serialize<W: Write>(&self, writer: W) -> Result<(), SerializationError>

Serializes self into writer. It is left up to a particular type for how it strikes the serialization efficiency vs compression tradeoff. For standard types (e.g. bool, lengths, etc.) typically an uncompressed form is used, whereas for algebraic types compressed forms are used.

fn serialized_size(&self) -> usize

fn serialize_uncompressed<W: Write>(
    &self,
    writer: W
) -> Result<(), SerializationError>

Serializes self into writer without compression.

fn uncompressed_size(&self) -> usize

fn serialize_unchecked<W>(&self, writer: W) -> Result<(), SerializationError> where
    W: Write, 

Serializes self into writer without compression, and without performing validity checks. Should be used only when there is no danger of adversarial manipulation of the output.

impl<P: Parameters> Clone for GroupProjective<P> where
    P: Parameters, 

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: Parameters> Debug for GroupProjective<P> where
    P: Parameters, 

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

Formats the value using the given formatter.

impl<P: Parameters> Default for GroupProjective<P>

fn default() -> Self

Returns the “default value” for a type.

impl<P: Parameters> Display for GroupProjective<P>

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

Formats the value using the given formatter.

impl<P: Parameters> From<GroupAffine<P>> for GroupProjective<P>

fn from(p: GroupAffine<P>) -> GroupProjective<P>

Performs the conversion.

impl<P: Parameters> From<GroupProjective<P>> for GroupAffine<P>

fn from(p: GroupProjective<P>) -> GroupAffine<P>

Performs the conversion.

impl<P: Parameters> FromBytes for GroupProjective<P>

fn read<R: Read>(reader: R) -> IoResult<Self>

Reads Self from reader.

impl<P: Parameters> Hash for GroupProjective<P> where
    P: Parameters, 

fn hash<__HP>(&self, __state: &mut __HP) where
    __HP: Hasher, 

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<P: Parameters> MulAssign<<P as ModelParameters>::ScalarField> for GroupProjective<P>

fn mul_assign(&mut self, other: P::ScalarField)

Performs the *= operation.

impl<P: Parameters> Neg for GroupProjective<P>

type Output = Self

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: Parameters> PartialEq<GroupAffine<P>> for GroupProjective<P>

fn eq(&self, other: &GroupAffine<P>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<P: Parameters> PartialEq<GroupProjective<P>> for GroupAffine<P>

fn eq(&self, other: &GroupProjective<P>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<P: Parameters> PartialEq<GroupProjective<P>> for GroupProjective<P>

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

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<P: Parameters> ProjectiveCurve for GroupProjective<P>

fn batch_normalization(v: &mut [Self])

Normalizes a slice of projective elements so that conversion to affine is cheap.

In more detail, this method converts a curve point in Jacobian coordinates (x, y, z) into an equivalent representation (x/z^2, y/z^3, 1).

For N = v.len(), this costs 1 inversion + 6N field multiplications + N field squarings.

(Where batch inversion comprises 3N field multiplications + 1 inversion of these operations)

fn double_in_place(&mut self) -> &mut Self

Sets self = 2 * self. Note that Jacobian formulae are incomplete, and so doubling cannot be computed as self + self. Instead, this implementation uses the following specialized doubling formulae:

• P::A is zero
• P::A is not zero

fn add_assign_mixed(&mut self, other: &GroupAffine<P>)

When other.is_normalized() (i.e., other.z == 1), we can use a more efficient formula to compute self + other.

const COFACTOR: &'static [u64]

type BaseField = P::BaseField

type ScalarField = P::ScalarField

type Affine = GroupAffine<P>

fn prime_subgroup_generator() -> Self

Returns a fixed generator of unknown exponent.

fn is_normalized(&self) -> bool

Checks if the point is already “normalized” so that cheap affine conversion is possible.

fn batch_normalization_into_affine(v: &[Self]) -> Vec<Self::Affine>

Normalizes a slice of projective elements and outputs a vector containing the affine equivalents.

#[must_use]

fn double(&self) -> Self

Doubles this element.

fn into_affine(&self) -> Self::Affine

Converts self into the affine representation.

fn add_mixed(self, other: &Self::Affine) -> Self

Set self to be self + other, where other: Self::Affine. This is usually faster than adding other in projective form.

fn mul<S: AsRef<[u64]>>(self, other: S) -> Self

Performs scalar multiplication of this element.

impl<'a, P: Parameters> Sub<&'a GroupProjective<P>> for GroupProjective<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: Parameters> Sub<&'a mut GroupProjective<P>> for GroupProjective<P>

type Output = Self

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<P: Parameters> Sub<GroupProjective<P>> for GroupProjective<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: Parameters> SubAssign<&'a GroupProjective<P>> for GroupProjective<P>

fn sub_assign(&mut self, other: &'a Self)

Performs the -= operation.

impl<'a, P: Parameters> SubAssign<&'a mut GroupProjective<P>> for GroupProjective<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: Parameters> SubAssign<GroupProjective<P>> for GroupProjective<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: Parameters> Sum<&'a GroupProjective<P>> for GroupProjective<P>

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Parameters> Sum<GroupProjective<P>> for GroupProjective<P>

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Parameters> ToBytes for GroupProjective<P>

fn write<W: Write>(&self, writer: W) -> IoResult<()>

Serializes self into writer.

impl<M: Parameters, ConstraintF: Field> ToConstraintField<ConstraintF> for GroupProjective<M> where
    M::BaseField: ToConstraintField<ConstraintF>, 

fn to_field_elements(&self) -> Option<Vec<ConstraintF>>

impl<P: Parameters> Zero for GroupProjective<P>

fn zero() -> Self

Returns the point at infinity, which always has Z = 0.

fn is_zero(&self) -> bool

Checks whether self.z.is_zero().

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<P: Parameters> Zeroize for GroupProjective<P>

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.

impl<P: Parameters> Copy for GroupProjective<P> where
    P: Parameters, 

impl<P: Parameters> Eq for GroupProjective<P>