Asymptotically Quasi-Optimal Cryptography

Leo de Castro, Carmit Hazay, Yuval Ishai, Vinod Vaikuntanathan, Muthu Venkitasubramaniam

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


The question of minimizing the computational overhead of cryptography was put forward by the work of Ishai, Kushilevitz, Ostrovsky and Sahai (STOC 2008). The main conclusion was that, under plausible assumptions, most cryptographic primitives can be realized with constant computational overhead. However, this ignores an additive term that may depend polynomially on the (concrete) computational security parameter λ. In this work, we study the question of obtaining optimal efficiency, up to polylogarithmic factors, for all choices of n and λ, where n is the size of the given task. In particular, when n= λ, we would like the computational cost to be only O~ (λ). We refer to this goal as asymptotically quasi-optimal (AQO) cryptography. We start by realizing the first AQO semi-honest batch oblivious linear evaluation (BOLE) protocol. Our protocol applies to OLE over small fields and relies on the near-exponential security of the ring learning with errors (RLWE) assumption. Building on the above and on known constructions of AQO PCPs, we design the first AQO zero-knowledge (ZK) argument system for Boolean circuit satisfiability. Our construction combines a new AQO ZK-PCP construction that respects the AQO property of the underlying PCP along with a technique for converting statistical secrecy into soundness via OLE reversal. Finally, combining the above results, we get AQO secure computation protocols for Boolean circuits with security against malicious parties under RLWE.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings
EditorsOrr Dunkelman, Stefan Dziembowski
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages32
ISBN (Print)9783031069437
StatePublished - 2022
Event41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022 - Trondheim, Norway
Duration: 30 May 20223 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13275 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022

Bibliographical note

Funding Information:
We thank Henry Corrigan-Gibbs for helpful comments and Hemanta Maji for answering our questions on [BGMN18]. C. Hazay was supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by ISF grant No. 1316/18. Y. Ishai was supported in part by ERC Project NTSC (742754), BSF grant 2018393, and ISF grant 2774/20. L. de Castro and V. Vaikuntanathan were supported by grants from MIT-IBM Watson AI Labs and Analog Devices, by a Microsoft Trustworthy AI grant, and by DARPA under Agreement No. HR00112020023.

Publisher Copyright:
© 2022, International Association for Cryptologic Research.


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