Succinct Arguments for RAM Programs via Projection Codes

Yuval Ishai, Rafail Ostrovsky, Akash Shah

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Motivated by the goal of proving statements that involve small subsets of a big database, we introduce and study the notion of projection codes. A standard error-correcting code allows one to encode a message x into a codeword X, such that even if a constant fraction of X is corrupted, the message x can still be recovered. A projection code extends this guarantee to any subset of the bits of x. Concretely, for every projection of x to a subset s of its coordinates, there is a subset S of comparable size such that the projected encoding X|S forms a robust encoding of the projected message x|s. Our first main result is a construction of projection codes with a near-optimal increase in the length of x and size of s. We then apply this to obtain our second main result: succinct arguments for the computation of a RAM program on a (big) committed database, where the communication and the run-time of both the prover and the verifier are close to optimal even when the RAM program run-time is much smaller than the database size. Our solution makes only a black-box use of a collision-resistant hash function, providing the first black-box alternative to previous non-black-box constructions with similar asymptotic efficiency.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings, Part II
EditorsHelena Handschuh, Anna Lysyanskaya
PublisherSpringer Science and Business Media Deutschland GmbH
Pages159-192
Number of pages34
ISBN (Print)9783031385445
DOIs
StatePublished - 2023
EventAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings - Santa Barbara, United States
Duration: 20 Aug 202324 Aug 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14082 LNCS

Conference

ConferenceAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Country/TerritoryUnited States
CitySanta Barbara
Period20/08/2324/08/23

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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