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Adaptive Security of Practical Garbling Schemes

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Progress in Cryptology – INDOCRYPT 2020 (INDOCRYPT 2020)

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Abstract

A garbling scheme enables one to garble a circuit C and an input x in a way that C(x) can be evaluated, but nothing else is revealed. Since the first construction by Yao, tremendous practical efficiency improvements for selectively secure garbling schemes –where the adversary is forced to choose both input and circuit to be garbled at the same time– were proposed. However, in the more realistic setting of adaptive security where an adversary can choose the input adaptively based on the garbled circuit little is known about practical efficiency improvements. In this work, we initiate the study of practical garbling schemes that are both more efficient than Yao’s construction and adaptively secure. We provide insights into characteristics of these schemes and highlight the limitations of current techniques for proving adaptive security in this regime. Furthermore, we present an adaptively secure garbling scheme that garbles \(\mathsf {XOR}\) gates with 2 and \(\mathsf {AND}\) gates with 3 ciphertexts per gate, thus providing the first practical garbling scheme for NC1 circuits with adaptive security based on PRFs whose garbled circuit size is smaller than that of Yao’s construction.

Z. Jafargholi—Supported by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 669255 (MPCPRO).

S. Oechsner—Supported by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 669255 (MPCPRO), the Concordium Blockhain Research Center, Aarhus University, Denmark, and the Danish Independent Research Council under Grant-ID DFF-8021-00366B (BETHE).

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Notes

  1. 1.

    In considering the adaptive security of any selectively secure garbling scheme, we in fact consider a slightly modified variation of that scheme, where the output map is part of the garbled input.

  2. 2.

    Jafargholi et al. [15] circumvent this lower bound by considering indistinguishability-based instead of simulation-based security. Since the size of the garbled circuit increases by a factor of 2 (compared to YaoGC), it is out of scope of this work.

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Acknowledgments

The authors would like to thank Koutarou Suzuki and Ryo Kikuchi for helpful discussions.

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Authors and Affiliations

  1. Sepior, Aarhus, Denmark

    Zahra Jafargholi

  2. Aarhus University, Aarhus, Denmark

    Sabine Oechsner

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  1. Zahra Jafargholi
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  2. Sabine Oechsner
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Correspondence to Sabine Oechsner .

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  1. Inria Paris, Paris, France

    Karthikeyan Bhargavan

  2. University of Klagenfurt, Klagenfurt, Austria

    Elisabeth Oswald

  3. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Manoj Prabhakaran

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Jafargholi, Z., Oechsner, S. (2020). Adaptive Security of Practical Garbling Schemes. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_33

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