Trait halo2_backend::arithmetic::CurveExt
pub trait CurveExt: PrimeCurve<Affine = Self::AffineExt, Scalar = Self::ScalarExt> + Group + Default + ConditionallySelectable + ConstantTimeEq + From<Self::Affine> {
type ScalarExt: WithSmallOrderMulGroup<3>;
type Base: WithSmallOrderMulGroup<3>;
type AffineExt: CurveAffine<CurveExt = Self, ScalarExt = Self::ScalarExt, Output = Self, Output = Self> + Mul<Self::ScalarExt> + for<'r> Mul<Self::ScalarExt>;
const CURVE_ID: &'static str;
// Required methods
fn endo(&self) -> Self;
fn jacobian_coordinates(&self) -> (Self::Base, Self::Base, Self::Base);
fn hash_to_curve<'a>(
domain_prefix: &'a str
) -> Box<dyn Fn(&[u8]) -> Self + 'a>;
fn is_on_curve(&self) -> Choice;
fn a() -> Self::Base;
fn b() -> Self::Base;
fn new_jacobian(
x: Self::Base,
y: Self::Base,
z: Self::Base
) -> CtOption<Self>;
}Expand description
This trait is a common interface for dealing with elements of an elliptic curve group in a “projective” form, where that arithmetic is usually more efficient.
Requires the alloc feature flag because of hash_to_curve.
Required Associated Types§
type ScalarExt: WithSmallOrderMulGroup<3>
type ScalarExt: WithSmallOrderMulGroup<3>
The scalar field of this elliptic curve.
type Base: WithSmallOrderMulGroup<3>
type Base: WithSmallOrderMulGroup<3>
The base field over which this elliptic curve is constructed.
Required Associated Constants§
Required Methods§
fn endo(&self) -> Self
fn endo(&self) -> Self
Apply the curve endomorphism by multiplying the x-coordinate by an element of multiplicative order 3.
fn jacobian_coordinates(&self) -> (Self::Base, Self::Base, Self::Base)
fn jacobian_coordinates(&self) -> (Self::Base, Self::Base, Self::Base)
Return the Jacobian coordinates of this point.
fn hash_to_curve<'a>(domain_prefix: &'a str) -> Box<dyn Fn(&[u8]) -> Self + 'a>
fn hash_to_curve<'a>(domain_prefix: &'a str) -> Box<dyn Fn(&[u8]) -> Self + 'a>
Requests a hasher that accepts messages and returns near-uniformly
distributed elements in the group, given domain prefix domain_prefix.
This method is suitable for use as a random oracle.
§Example
use pasta_curves::arithmetic::CurveExt;
fn pedersen_commitment<C: CurveExt>(
x: C::ScalarExt,
r: C::ScalarExt,
) -> C::Affine {
let hasher = C::hash_to_curve("z.cash:example_pedersen_commitment");
let g = hasher(b"g");
let h = hasher(b"h");
(g * x + &(h * r)).to_affine()
}fn is_on_curve(&self) -> Choice
fn is_on_curve(&self) -> Choice
Returns whether or not this element is on the curve; should always be true unless an “unchecked” API was used.
fn new_jacobian(x: Self::Base, y: Self::Base, z: Self::Base) -> CtOption<Self>
fn new_jacobian(x: Self::Base, y: Self::Base, z: Self::Base) -> CtOption<Self>
Obtains a point given Jacobian coordinates $X : Y : Z$, failing if the coordinates are not on the curve.
Object Safety§
This trait is not object safe.