Trait ark_ff::fields::CyclotomicMultSubgroup

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pub trait CyclotomicMultSubgroup: Field {
    const INVERSE_IS_FAST: bool = false;

    // Provided methods
    fn cyclotomic_square(&self) -> Self { ... }
    fn cyclotomic_square_in_place(&mut self) -> &mut Self { ... }
    fn cyclotomic_inverse(&self) -> Option<Self> { ... }
    fn cyclotomic_inverse_in_place(&mut self) -> Option<&mut Self> { ... }
    fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self { ... }
    fn cyclotomic_exp_in_place(&mut self, e: impl AsRef<[u64]>) { ... }
}

Expand description

Fields that have a cyclotomic multiplicative subgroup, and which can leverage efficient inversion and squaring algorithms for elements in this subgroup. If a field has multiplicative order p^d - 1, the cyclotomic subgroups refer to subgroups of order φ_n(p), for any n < d, where φ_n is the n-th cyclotomic polynomial.

§Note

Note that this trait is unrelated to the Group trait from the ark_ec crate. That trait denotes an additive group, while this trait denotes a multiplicative group.

Provided Associated Constants§

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const INVERSE_IS_FAST: bool = false

Is the inverse fast to compute? For example, in quadratic extensions, the inverse can be computed at the cost of negating one coordinate, which is much faster than standard inversion. By default this is false, but should be set to true for quadratic extensions.

Provided Methods§

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fn cyclotomic_square(&self) -> Self

Compute a square in the cyclotomic subgroup. By default this is computed using Field::square, but for degree 12 extensions, this can be computed faster than normal squaring.

§Warning

This method should be invoked only when self is in the cyclotomic subgroup.

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

Square self in place. By default this is computed using Field::square_in_place, but for degree 12 extensions, this can be computed faster than normal squaring.