Trait CofactorGroup 

pub trait CofactorGroup:
    Group
    + GroupEncoding
    + GroupOps<Self::Subgroup>
    + GroupOpsOwned<Self::Subgroup> {
    type Subgroup: PrimeGroup<Scalar = Self::Scalar> + Into<Self>;

    // Required methods
    fn clear_cofactor(&self) -> Self::Subgroup;
    fn into_subgroup(self) -> CtOption<Self::Subgroup>;
    fn is_torsion_free(&self) -> Choice;

    // Provided method
    fn is_small_order(&self) -> Choice { ... }
}

This trait represents an element of a cryptographic group with a large prime-order subgroup and a comparatively-small cofactor.

Required Associated Types

type Subgroup: PrimeGroup<Scalar = Self::Scalar> + Into<Self>

The large prime-order subgroup in which cryptographic operations are performed. If Self implements PrimeGroup, then Self::Subgroup may be Self.

Required Methods

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

Maps self to the prime-order subgroup by multiplying this element by some k-multiple of the cofactor.

The value k does not vary between inputs for a given implementation, but may vary between different implementations of CofactorGroup because some groups have more efficient methods of clearing the cofactor when k is allowed to be different than 1.

If Self implements [PrimeGroup], this returns self.

fn into_subgroup(self) -> CtOption<Self::Subgroup>

Returns self if it is contained in the prime-order subgroup.

If Self implements [PrimeGroup], this returns Some(self).

fn is_torsion_free(&self) -> Choice

Determines if this element is “torsion free”, i.e., is contained in the prime-order subgroup.

Returns:

• true if self has trivial torsion and is in the prime-order subgroup.
• false if self has non-zero torsion component and is not in the prime-order subgroup.

Provided Methods

fn is_small_order(&self) -> Choice

Determines if this element is of small order.

Returns:

• true if self is in the torsion subgroup.
• false if self is not in the torsion subgroup.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementations on Foreign Types

impl CofactorGroup for ProjectivePoint

secp256k1 has a cofactor of 1.

type Subgroup = ProjectivePoint

fn clear_cofactor(&self) -> <ProjectivePoint as CofactorGroup>::Subgroup

fn into_subgroup(self) -> CtOption<<ProjectivePoint as CofactorGroup>::Subgroup>

fn is_torsion_free(&self) -> Choice

impl CofactorGroup for ProjectivePoint

fn clear_cofactor(&self) -> <ProjectivePoint as CofactorGroup>::Subgroup

Maps any curve point onto the prime-order subgroup by multiplying it by the cofactor 8 (i.e. k = 1 times the cofactor).

BabyJubJub has cofactor 8, so every point splits uniquely as P = Q + T with Q in the prime-order subgroup and T a torsion point of order dividing 8. Because [8]T = O, the result [8]P = [8]Q always lies in the prime-order subgroup; it is the identity exactly when Q = O (i.e. when P is pure torsion).

Implemented as three doublings ([8]P = [2][2][2]P) on the backend’s complete (exception-free) doubling formula, which accepts torsion inputs (as do Group::double and the + operator). Like the rest of the crate this is almost — but not end-to-end — constant-time (see the crate-level Security notes). To clear the cofactor and multiply by a scalar in a single operation, use [ProjectivePoint::mul_with_cofactor_clear].

fn into_subgroup(self) -> CtOption<<ProjectivePoint as CofactorGroup>::Subgroup>

Returns self if it lies in the prime-order subgroup, otherwise CtOption::none().

Membership is decided by [ProjectivePoint::is_in_prime_order_subgroup], which normalizes to affine via a field inversion and is therefore not constant-time with respect to self.

fn is_torsion_free(&self) -> Choice

Returns true iff this element is torsion free, i.e. lies in the prime-order subgroup.

Delegates to [ProjectivePoint::is_in_prime_order_subgroup]. As noted there, this normalizes to affine coordinates and is not constant-time with respect to self.

type Subgroup = ProjectivePoint

impl<C> CofactorGroup for ProjectivePoint<C>

where C: PrimeCurveParams,

Prime order elliptic curves have a cofactor of 1.

type Subgroup = ProjectivePoint<C>

fn clear_cofactor(&self) -> <ProjectivePoint<C> as CofactorGroup>::Subgroup

fn into_subgroup( self, ) -> CtOption<<ProjectivePoint<C> as CofactorGroup>::Subgroup>

fn is_torsion_free(&self) -> Choice

Implementors