Caulk: Lookup Arguments in Sublinear Time

Arantxa Zapico; Vitalik Buterin; Dmitry Khovratovich; Mary Maller; Anca Nitulescu; Mark Simkin

Paper 2022/621

Caulk: Lookup Arguments in Sublinear Time

Arantxa Zapico

Vitalik Buterin

Dmitry Khovratovich

Mary Maller

Anca Nitulescu

Mark Simkin

Abstract

We present position-hiding linkability for vector commitment schemes: one can prove in zero knowledge that one or values that comprise commitment cm all belong to the vector of size committed to in C. Our construction Caulk can be used for membership proofs and lookup arguments and outperforms all existing alternatives in prover time by orders of magnitude. For both single- and multi-membership proofs Caulk beats SNARKed Merkle proofs by the factor of 100 even if the latter instantiated with Poseidon hash. Asymptotically our prover needs time to prove a batch of openings, whereas proof size is and verifier time is . As a lookup argument, Caulk is the first scheme with prover time sublinear in the table size, assuming preprocessing time and storage. It can be used as a subprimitive in verifiable computation schemes in order to drastically decrease the lookup overhead. Our scheme comes with a reference implementation and benchmarks.

Metadata

Available format(s): PDF
Publication info: Preprint.
Contact author(s): arantxa zapico @ upf edu
khovratovich @ gmail com
mary maller @ ethereum org
History: 2022-08-17: revised; 2022-05-23: received; See all versions
Short URL: https://ia.cr/2022/621
License: CC BY

BibTeX

@misc{cryptoeprint:2022/621,
      author = {Arantxa Zapico and Vitalik Buterin and Dmitry Khovratovich and Mary Maller and Anca Nitulescu and Mark Simkin},
      title = {Caulk: Lookup Arguments in Sublinear Time},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/621},
      year = {2022},
      url = {https://eprint.iacr.org/2022/621}
}