Paper 2026/1784

Faster Post-Quantum zkSNARK Provers Using the LCH Polynomial Basis

Abstract

Univariate-polynomial interactive oracle proofs (IOPs) over binary extension fields $\mathbb{F}_{2^m}$ underpin a class of plausibly post-quantum zkSNARKs, but rely heavily on polynomial arithmetic, where large-domain evaluation and division by subspace vanishing polynomials are the dominant prover costs. General-basis additive FFTs, such as Gao--Mateer and Lin-Chung-Han (LCH), accelerate the evaluation but impose a basis-conversion stage costing $O(n (\log n)^2)$ field additions and $O(n \log n)$ field multiplications that dominates in practice. To eliminate basis conversion entirely, we introduce a divide-and-conquer algorithm for polynomial division by vanishing polynomials that operates directly in the LCH polynomial basis, for arbitrary $\mathbb{F}_2$-basis elements, achieving optimal $O(n \log n)$ complexity. In the LCH polynomial basis, multiplying a vanishing polynomial by the random blinding polynomial reduces to appending random field elements, eliminating the multiplication entirely. We integrate native LCH-basis arithmetic and auxiliary optimizations across all phases of the Aurora IOP. Benchmarks on Preon (a NIST PQC Round-1 signature scheme candidate built on Aurora) show end-to-end signing speedups of $5.0\times$ for Preon-128A and $5.8\times$ for Preon-256C, with the polynomial transform alone $12.6$--$17.9\times$ faster.