Independent research on lattice-based proof systems.
Espalier is a succinct argument system over cyclotomic rings. Soundness reduces to Module-SIS, so the system is post-quantum secure. It uses no pairings, no discrete-log assumption, and no trusted setup.
Post-quantum proof systems are, as a rule, expensive to prove. Proofs are small and verification is cheap; the cost sits with the prover. In privacy applications this matters more than it first appears, because the prover is the end user. The witness is the user's secret, so it cannot be shipped to a server, and the proving work lands on whatever device the user happens to hold. Espalier targets client-side proving on commodity mobile hardware, and the design is organised around that constraint rather than around verifier cost.
Two techniques do most of the work. Cordon reduction controls norm growth. The witness is split into balanced strata, and a single aggregated norm bound is proved over a shared Johnson-Lindenstrauss projection instead of one bound per stratum. Norm slack then grows additively with recursion depth rather than multiplicatively, which keeps the ring modulus from inflating as folding proceeds. Lateral amortization handles repetition. Many instances of the same circuit are batched under one commitment and reduced by a random linear combination over the ring, so the committed data and the bulk of the prover's ring arithmetic are paid for once rather than per instance. Together they are what brings the prover inside a mobile memory budget.
These numbers come from an internal prototype. They have not been independently reproduced. There is no public implementation, and the prototype is not available, so nobody outside the group has checked them. They should be read as claims rather than as measurements.
Espalier: Succinct Lattice Arguments for Client-Side Proving (v0.9 preprint, May 2026)