TY - GEN
T1 - Succinct Arguments for RAM Programs via Projection Codes
AU - Ishai, Yuval
AU - Ostrovsky, Rafail
AU - Shah, Akash
N1 - Publisher Copyright:
© 2023, International Association for Cryptologic Research.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85173010102&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-38545-2_6
DO - 10.1007/978-3-031-38545-2_6
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AN - SCOPUS:85173010102
SN - 9783031385445
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 159
EP - 192
BT - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings, Part II
A2 - Handschuh, Helena
A2 - Lysyanskaya, Anna
T2 - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Y2 - 20 August 2023 through 24 August 2023
ER -