Oblivious Transfer with Constant Computational Overhead

Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, Nicolas Resch, Peter Scholl

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

Abstract

The computational overhead of a cryptographic task is the asymptotic ratio between the computational cost of securely realizing the task and that of realizing the task with no security at all. Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2008) showed that secure two-party computation of Boolean circuits can be realized with constant computational overhead, independent of the desired level of security, assuming the existence of an oblivious transfer (OT) protocol and a local pseudorandom generator (PRG). However, this only applies to the case of semi-honest parties. A central open question in the area is the possibility of a similar result for malicious parties. This question is open even for the simpler task of securely realizing many instances of a constant-size function, such as OT of bits. We settle the question in the affirmative for the case of OT, assuming: (1) a standard OT protocol, (2) a slightly stronger “correlation-robust" variant of a local PRG, and (3) a standard sparse variant of the Learning Parity with Noise (LPN) assumption. An optimized version of our construction requires fewer than 100 bit operations per party per bit-OT. For 128-bit security, this improves over the best previous protocols by 1–2 orders of magnitude. We achieve this by constructing a constant-overhead pseudorandom correlation generator (PCG) for the bit-OT correlation. Such a PCG generates N pseudorandom instances of bit-OT by locally expanding short, correlated seeds. As a result, we get an end-to-end protocol for generating N pseudorandom instances of bit-OT with o(N) communication, O(N) computation, and security that scales sub-exponentially with N. Finally, we present applications of our main result to realizing other secure computation tasks with constant computational overhead. These include protocols for general circuits with a relaxed notion of security against malicious parties, protocols for realizing N instances of natural constant-size functions, and reducing the main open question to a potentially simpler question about fault-tolerant computation.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2023 - 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsCarmit Hazay, Martijn Stam
PublisherSpringer Science and Business Media Deutschland GmbH
Pages271-302
Number of pages32
ISBN (Print)9783031305443
DOIs
StatePublished - 1 Jan 2023
Event42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2023 - Lyon, France
Duration: 23 Apr 202327 Apr 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14004 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2023
Country/TerritoryFrance
CityLyon
Period23/04/2327/04/23

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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