Orbweaver: Succinct Linear Functional Commitments from Lattices

We present Orbweaver, a plausibly post-quantum functional commitment for linear relations that achieves quasilinear prover time together with $O(\log n)$ proof size and polylogarithmic verifier time. Orbweaver enables evaluation of linear functions on committed vectors over cyclotomic rings and the integers. It is extractable, preprocessing, non-interactive, structure-preserving, and supports compact public proof aggregation. The security of our scheme is based on the $k$-$R$-ISIS assumption (and its knowledge counterpart), whereby we require a trusted setup to generate a universal structured reference string. We use Orbweaver to construct succinct univariate and multilinear polynomial commitments.

 Concretely, our scheme has smaller proofs than most other succinct post-quantum arguments for large statements. For binary vectors of length $2^{30}$ we achieve $302$KiB linear map evaluation proofs with evaluation binding, and $1$MiB proofs when extractability is required; for $32$-bit integers these sizes are $494$KiB and $1.6$MiB, respectively.