Abstract

We present new constructions of succinct non-interactive functional commitments and arguments for circuits (i.e. P/poly), based on the SIS assumption without random oracles. For boolean circuits of depth d, we obtain

* a non-interactive functional commitment scheme with O(1)-sized transparent CRS, O(1)-sized commitment, and O(d)-sized openings;

* a non-interactive succinct argument (SNARG for P/poly) with O(1)-sized transparent CRS, and O(d)-sized unambiguous proofs.

Moreover, both schemes support fast online verification after a circuit-dependent pre-processing phase, and do not impose a bound on circuit parameters during set-up. Our constructions are simple, elementary and do not rely on correlation-intractable hashing.

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