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SNARGs for P/poly from SIS

Talkat Proofs (Simons Institute) · 2025-07-11..07-17· [cryptography]
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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.

AI-written summary · about

  1. 0:00SNARGs for P/poly intro
  2. 1:23SNARGs for deterministic computation
  3. 8:23Functional commitments core
  4. 15:49SIS assumption variants
  5. 20:03Warm-up functional commitments
  6. 31:09Relaxing SIS verification
  7. 36:30Homomorphic multiplication with relaxations
  8. 41:39Chainable commitments for circuits
  9. 47:19Merkle recursion for openings
  10. 51:57Summary of results
  11. 53:47Related works and future
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