Crate p3_binary_dft 

p3-binary-dft

An additive NTT over F_2-linear subspaces of the Plonky3 binary tower fields, the characteristic-2 analogue of a multiplicative-coset DFT. The domain S_ℓ is spanned by the first ℓ vectors of the Cantor basis added to p3-binary-field, and evaluation over it is computed by the Lin–Chung–Han (LCH) transform.

Part of Plonky3, dual-licensed under MIT and Apache 2.0.

Structs

AdditiveRsEncoder

Reed–Solomon over the additive NTT domain.

LchNtt

The Lin–Chung–Han additive NTT over the Cantor-basis domain.

NaiveAdditiveNtt

Reference additive NTT.

PolyBasisNtt

LchNtt over BinaryField128, with the data held in the polynomial basis throughout.

Traits

AdditiveNtt

An additive NTT: evaluation of the novel polynomial basis on an F_2-linear subspace.

ButterflyField

A field the additive transform has a butterfly kernel for.

EncodableLevel

A tower level this crate encodes over, together with the encoder it picks for that level.

Functions

domain_point

The index-th point of the additive NTT domain, Σ_r bit_r(index) · v_r.

domain_point_steps

The increments of domain_point(index << 1) as index runs upwards from zero.

interleaved_encode_batch

Reed–Solomon encode a message held one folding column at a time.

subfield_encode_batch

Reed–Solomon encode a subfield message over the additive NTT domain.

subfield_ntt_batch

Evaluate each column of a subfield message on the subspace of the wider level.

subspace_polynomial

The subspace polynomial W_j of S_j, defined by W_0(x) = x and W_j(x) = W_{j−1}(x)² + W_{j−1}(x).