SNARGs for P/poly from SIS
summary
New lattice construction gives SNARGs for P/poly from SIS (no random oracles) by building functional commitments that compress GSW-style encryptions into a small CRS and then open to f(x) via low-norm SIS preimages. Concrete guarantees: constant-sized transparent CRS, constant-sized commitments, O(d)-sized openings and proofs (d = circuit depth), online verification after circuit-dependent preprocessing runs in time linear in |x|, and proofs are computationally unique; security reduces to standard SIS via an algebraic relaxation and Merkle-style recursion.
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chapters (11)
- 0:00SNARGs for P/poly intro
- 1:23SNARGs for deterministic computation
- 8:23Functional commitments core
- 15:49SIS assumption variants
- 20:03Warm-up functional commitments
- 31:09Relaxing SIS verification
- 36:30Homomorphic multiplication with relaxations
- 41:39Chainable commitments for circuits
- 47:19Merkle recursion for openings
- 51:57Summary of results
- 53:47Related works and future
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