@inproceedings{543254b833114110acf6c633c2137054,
title = "Lower Bound on SNARGs in the Random Oracle Model",
abstract = "Succinct non-interactive arguments (SNARGs) have become a fundamental primitive in the cryptographic community. The focus of this work is constructions of SNARGs in the Random Oracle Model (ROM). Such SNARGs enjoy post-quantum security and can be deployed using lightweight cryptography to heuristically instantiate the random oracle. A ROM-SNARG is (t, ε) -sound if no t -query malicious prover can convince the verifier to accept a false statement with probability larger than ε. Recently, Chiesa-Yogev (CRYPTO {\textquoteright}21) presented a ROM-SNARG of length Θ(log (t/ ε) · log t) (ignoring log n factors, for n being the instance size). This improvement, however, is still far from the (folklore) lower bound of Ω(log (t/ ε) ). Assuming the randomized exponential-time hypothesis, we prove a tight lower bound of Ω(log (t/ ε) · log t) for the length of (t, ε) -sound ROM-SNARGs. Our lower bound holds for constructions with non-adaptive verifiers and strong soundness notion called salted soundness, restrictions that hold for all known constructions (ignoring contrived counterexamples). We prove our lower bound by transforming any short ROM-SNARG (of the considered family) into a same length ROM-SNARG in which the verifier asks only a few oracles queries, and then apply the recent lower bound of Chiesa-Yogev (TCC {\textquoteright}20) for such SNARGs.",
keywords = "Random oracle, SNARGs, high-entropy sets, lower bound",
author = "Iftach Haitner and Daniel Nukrai and Eylon Yogev",
note = "Publisher Copyright: {\textcopyright} 2022, International Association for Cryptologic Research.; 42nd Annual International Cryptology Conference, CRYPTO 2022 ; Conference date: 15-08-2022 Through 18-08-2022",
year = "2022",
doi = "https://doi.org/10.1007/978-3-031-15982-4_4",
language = "الإنجليزيّة",
isbn = "9783031159817",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "97--127",
editor = "Yevgeniy Dodis and Thomas Shrimpton",
booktitle = "Advances in Cryptology – CRYPTO 2022 - 42nd Annual International Cryptology Conference, CRYPTO 2022, Proceedings",
address = "ألمانيا",
}