Paper 2025/2124 Original: eprint.iacr.org/2025/2124 ↗

SALSAA – Sumcheck-Aided Lattice-based Succinct Arguments and Applications

Abstract

We present SALSAA, a more efficient and more versatile extension of the state-of-the-art lattice-based fully-succinct argument frameworks, ``RoK, paper, SISsors (RPS)'' and ``RoK and Roll (RnR)'' [Klooß, Lai, Nguyen, and Osadnik; ASIACRYPT'24, '25], integrating the sumcheck technique as a main component. This integration enables us to design an efficient norm-check protocol (controlling the norm during witness extraction) with a strictly linear-time prover while reducing proof sizes by 2-3$\times$ compared to the previous quasi-linear-time norm-check in RPS/RnR, eliminating a central performance bottleneck. The sumcheck integration also allows us to natively support a wider class of relations, including rank-1 constraint systems (R1CS), which are widely used to express real-world computations. To demonstrate the versatility and efficiency of our framework, we showcase three impactful applications achieved by different RoKs (Reductions of Knowledge) compositions: (i) a lattice-based succinct argument of knowledge with a linear-time prover, achieving a verifier time of $41$ ms, prover runtime of $10.61$ s, and proof size of $979$ KB for a witness of $2^{28}$ $\mathbb{Z}_q$ elements; (ii) a polynomial commitment scheme with matching performance; and (iii) the first lattice-based folding scheme natively operating on $\ell_2$-norm-bounded witnesses, achieving highly efficient verification in $2.28$ ms and producing a proof of just $73$ KB for a witness of $2^{28}$ $\mathbf{Z}_q$ elements, outperforming prior works for the family of linear relations. We provide a modular, concretely efficient Rust implementation of our framework, benchmarked over cyclotomic rings with AVX-512-accelerated NTT-based arithmetic, demonstrating the practical efficiency of our approach.