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MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security

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Progress in Cryptology – INDOCRYPT 2019 (INDOCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11898))

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Abstract

Most modern actively-secure multiparty computation (MPC) protocols involve generating random data that is secret-shared and authenticated, and using it to evaluate arithmetic or Boolean circuits in different ways. In this work we present a generic method for converting authenticated secret-shared data between different fields, and show how to use it to evaluate so-called “mixed” circuits with active security and in the full-threshold setting. A mixed circuit is one in which parties switch between different subprotocols dynamically as computation proceeds, the idea being that some protocols are more efficient for evaluating arithmetic circuits, and others for Boolean circuits.

One use case of our switching mechanism is for converting between secret-sharing-based MPC and garbled circuits (GCs). The former is more suited to the evaluation of arithmetic circuits and can easily be used to emulate arithmetic over the integers, whereas the latter is better for Boolean circuits and has constant round complexity. Much work already exists in the two-party semi-honest setting, but the n-party dishonest majority case was hitherto neglected.

We call the actively-secure mixed arithmetic/Boolean circuit a marbled circuit. Our implementation showed that mixing protocols in this way allows us to evaluate a linear Support Vector Machine with 400 times fewer AND gates than a solution using GC alone albeit with twice the preprocessing required using only SPDZ (Damgård et al., CRYPTO’12), and thus our solution offers a tradeoff between online and preprocessing complexity. When evaluating over a WAN network, our online phase is 10 times faster than the plain SPDZ protocol.

This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. N66001-15-C-4070, and by the FWO under an Odysseus project GOH9718N.

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Authors and Affiliations

  1. University of Bristol, Bristol, UK

    Dragos Rotaru & Tim Wood

  2. imec-COSIC KU Leuven, Leuven, Belgium

    Dragos Rotaru & Tim Wood

Authors
  1. Dragos Rotaru
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Correspondence to Dragos Rotaru .

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Editors and Affiliations

  1. University of Warwick, Warwick, UK

    Feng Hao

  2. CSIRO Data61, Marsfield, NSW, Australia

    Sushmita Ruj

  3. Nanyang Technological University, Singapore, Singapore

    Sourav Sen Gupta

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Rotaru, D., Wood, T. (2019). MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security. In: Hao, F., Ruj, S., Sen Gupta, S. (eds) Progress in Cryptology – INDOCRYPT 2019. INDOCRYPT 2019. Lecture Notes in Computer Science(), vol 11898. Springer, Cham. https://doi.org/10.1007/978-3-030-35423-7_12

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  • DOI: https://doi.org/10.1007/978-3-030-35423-7_12

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