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2020 | OriginalPaper | Buchkapitel

Stacked Garbling

Garbled Circuit Proportional to Longest Execution Path

verfasst von : David Heath, Vladimir Kolesnikov

Erschienen in: Advances in Cryptology – CRYPTO 2020

Verlag: Springer International Publishing

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Abstract

Secure two party computation (2PC) of arbitrary programs can be efficiently achieved using garbled circuits (GC). The bottleneck of GC efficiency is communication. It is widely believed that it is necessary to transmit the entire GC during 2PC, even for conditional branches that are not taken.

This folklore belief is false.

We propose a novel GC technique, stacked garbling, that eliminates the communication cost of inactive conditional branches. We extend the ideas of conditional GC evaluation explored in (Kolesnikov, Asiacrypt 18) and (Heath and Kolesnikov, Eurocrypt 20). Unlike these works, ours is for general 2PC where no player knows which conditional branch is taken.

Our garbling scheme, \(\textsf {Stack}\), requires communication proportional to the longest execution path rather than to the entire circuit. \(\textsf {Stack}\) is compatible with state-of-the-art techniques, such as free XOR and half-gates.

\(\textsf {Stack}\) is a garbling scheme. As such, it can be plugged into a variety of existing protocols, and the resulting round complexity is the same as that of standard GC. The approach does incur computation cost quadratic in the conditional branching factor vs linear in standard schemes, but the tradeoff is beneficial for most programs: GC computation even on weak hardware is faster than GC transmission on fast channels.

We implemented \(\textsf {Stack}\) in C++. \(\textsf {Stack}\) reduces communication cost by approximately the branching factor: for 16 branches, communication is reduced by \(10.5{\times }\). In terms of wall-clock time for circuits with branching factor 16 over a 50 Mbps WAN on a laptop, \(\textsf {Stack}\) outperforms state-of-the-art half-gates-based 2PC by more than \(4{\times }\).

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Vorheriges Kapitel Reverse Firewalls for Actively Secure MPCs

Nächstes Kapitel Better Concrete Security for Half-Gates Garbling (in the Multi-instance Setting)

Nur mit Berechtigung zugänglich

Universal circuits provide an alternate method for implementing branching, but have impractical overhead, both in circuit size and in the cost of the gadgets required [KKW17].

The second secret allows \(\textsf {Eval}\) to prove that she did not retrieve one of the seeds and hence obtained the output label by GC evaluation of one branch. This prevents \(\textsf {Eval}\) from taking all n seeds and using them to forge a proof.

We use point-and-permute [BMR90] to encode a color bit in the least significant bit of each label. Color bits instruct \(\textsf {Eval}\) how to decrypt encrypted truth tables.

Formally, each garbled row is given a unique ID, and calls to H for that row take the ID as an extra argument. We omit this for simplicity of notation.

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Titel: Stacked Garbling
verfasst von: David Heath
Vladimir Kolesnikov
Verlag: Springer International Publishing
Buch: Advances in Cryptology – CRYPTO 2020
Print ISBN: 978-3-030-56879-5

Electronic ISBN: 978-3-030-56880-1

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-56880-1_27

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