LogStack: Stacked Garbling with O(b log b) Computation

David Heath, Vladimir Kolesnikov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Secure two party computation (2PC) of arbitrary programs can be efficiently achieved using garbled circuits (GC). Until recently, it was widely believed that a GC proportional to the entire program, including parts of the program that are entirely discarded due to conditional branching, must be transmitted over a network. Recent work shows that this belief is false, and that communication proportional only to the longest program execution path suffices (Heath and Kolesnikov, CRYPTO 20, [HK20a]). Although this recent work reduces needed communication, it increases computation. For a conditional with b branches, the players use O(b2) computation (traditional GC uses only O(b)). Our scheme LogStack reduces stacked garbling computation from O(b2) to O(blog b) with no increase in communication over [HK20a]. The cause of [HK20a]’s increased computation is the oblivious collection of garbage labels that emerge during the evaluation of inactive branches. Garbage is collected by a multiplexer that is costly to generate. At a high level, we redesign stacking and garbage collection to avoid quadratic scaling. Our construction is also more space efficient: [HK20a] algorithms require O(b) space, while ours use only O(log b) space. This space efficiency allows even modest setups to handle large numbers of branches. [HK20a] assumes a random oracle (RO). We track the source of this need, formalize a simple and natural added assumption on the base garbling scheme, and remove reliance on RO: LogStack is secure in the standard model. Nevertheless, LogStack can be instantiated with typical GC tricks based on non-standard assumptions, such as free XOR and half-gates, and hence can be implemented with high efficiency. We implemented LogStack (in the RO model, based on half-gates garbling) and report performance. In terms of wall-clock time and for fewer than 16 branches, our performance is comparable to [HK20a]’s; for larger branching factors, our approach clearly outperforms [HK20a]. For example, given 1024 branches, our approach is 31 × faster.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology – EUROCRYPT 2021 - 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsAnne Canteaut, François-Xavier Standaert
PublisherSpringer
Pages3-32
Number of pages30
ISBN (Print)9783030778828
DOIs
StatePublished - 2021
Externally publishedYes
Event40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2021 - Zagreb, Croatia
Duration: Oct 17 2021Oct 21 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12698 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2021
Country/TerritoryCroatia
CityZagreb
Period10/17/2110/21/21

Keywords

  • 2PC
  • Conditional branching
  • Garbled circuits
  • Stacked garbling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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