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Title:
Orbweaver: Succinct Linear Functional Commitments from Lattices
Authors: Ben Fisch, Zeyu Liu, Psi Vesely
Abstract: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.
ePrint: https://eprint.iacr.org/2024/2026
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