Fast garbling of circuits over 3-valued logic

Yehuda Lindell, Avishay Yanai

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

3 Scopus citations


In the setting of secure computation, a set of parties wish to compute a joint function of their private inputs without revealing anything but the output. Garbled circuits, first introduced by Yao, are a central tool in the construction of protocols for secure two-party computation (and other tasks like secure outsourced computation), and are the fastest known method for constant-round protocols. In this paper, we initiate a study of garbling multivalent-logic circuits, which are circuits whose wires may carry values from some finite/infinite set of values (rather than only True and False). In particular, we focus on the threevalued logic system of Kleene, in which the admissible values are True, False, and Unknown. This logic system is used in practice in SQL where some of the values may be missing. Thus, efficient constant-round secure computation of SQL over a distributed database requires the ability to efficiently garble circuits over 3-valued logic. However, as we show, the two natural (naive) methods of garbling 3-valued logic are very expensive. In this paper, we present a general approach for garbling three-valued logic, which is based on first encoding the 3-value logic into Boolean logic, then using standard garbling techniques, and final decoding back into 3-value logic. Interestingly, we find that the specific encoding chosen can have a significant impact on efficiency. Accordingly, the aim is to find Boolean encodings of 3-value logic that enable efficient Boolean garbling (i.e., minimize the number of AND gates). We also show that Boolean AND gates can be garbled at the same cost of garbling XOR gates in the 3-value logic setting. Thus, it is unlikely that an analogue of free-XOR exists for 3-value logic garbling (since this would imply free-AND in the Boolean setting).

Original languageEnglish
Title of host publicationPublic-Key Cryptography - PKC 2018 - 21st IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings
EditorsMichel Abdalla, Ricardo Dahab
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages24
ISBN (Print)9783319765778
StatePublished - 2018
Event21st IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2018 - Rio de Janeiro, Brazil
Duration: 25 Mar 201829 Mar 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10769 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2018
CityRio de Janeiro

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2018.


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