Binyi Chen: LatticeFold - A Lattice-based Folding Scheme and Applications to Succinct Proof Systems 

Abstract: Folding is a recent technique for building efficient recursive SNARKs. Several elegant folding protocols have been proposed, such as Nova, Supernova, Hypernova, Protostar, and others. However, all of them rely on an additively homomorphic commitment scheme based on discrete log, and are therefore not post-quantum secure.
In this work we present LatticeFold, the first lattice-based folding protocol based on the Module SIS problem. This folding protocol naturally leads to an efficient recursive lattice-based SNARK and an efficient PCD scheme. The key challenge is to construct a secure folding protocol that works with the Ajtai commitment scheme. The difficulty is ensuring that extracted witnesses are low norm through many rounds of folding. We present a novel technique using the sumcheck protocol to ensure that extracted witnesses are always low norm no matter how many rounds of folding are used. Our evaluation of the final proof system suggests that it is highly performant compared to existing folding schemes while providing plausible post-quantum security.
This is a joint work with Dan Boneh.