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What Security Can We Achieve Within 4 Rounds?

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Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

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Abstract

Katz and Ostrovsky (Crypto 2004) proved that five rounds are necessary for stand-alone general black-box constructions of secure two-party protocols and at least four rounds are necessary if only one party needs to receive the output. Recently, Ostrovsky, Richelson and Scafuro (Crypto 2015) proved optimality of this result by showing how to realize arbitrary functionalities in four rounds where only one party receives the output via a black-box construction (and an extension to five rounds where both parties receive the output). In this paper we study the question of what security is achievable for stand-alone two-party protocols within four rounds.

We first provide a four-round two-party protocol for coin-tossing that achieves 1 / p-simulation security (i.e. simulation fails with probability at most \(1/p+{\mathsf{negl}}\)), in the presence of malicious corruptions. Next, we provide a four-round two-party protocol for general functionalities, where both parties receive the output, that achieves 1 / p-security in the presence of malicious adversaries corrupting one of the parties, and full security in the presence of non-aborting malicious adversaries corrupting the other party.

Next, we provide a three-round oblivious-transfer protocol, that achieves 1 / p-simulation security against arbitrary malicious senders, while simultaneously guaranteeing a meaningful notion of privacy against malicious corruptions of either party.

Finally, we show that the simulation-based security guarantees for our three-round protocols are optimal by proving that 1 / p-simulation security is impossible to achieve against both parties in three rounds or less when requiring some minimal guarantees on the privacy of their inputs.

C. Hazay—Research partially supported by a grant from the Israel Ministry of Science and Technology (grant No. 3-10883), by the European Research Council under the ERC consolidators grant agreement n. 615172 (HIPS), and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office.

M. Venkitasubramaniam—Research supported by Google Faculty Research Grant and NSF Award CNS-1526377.

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Notes

  1. 1.

    Formally, they require an “implicit input” function that can, from a transcript of the interaction, specify the input of a particular party. Our protocols provide statistical privacy guarantees and such a security guarantee cannot be input-indistinguishable.

  2. 2.

    By fully secure, we mean standard simulation-based security.

  3. 3.

    We can consider some canonical representation of elements in \(D_i\) in \(\{0,1\}^*\).

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Authors and Affiliations

  1. Faculty of Engineering, Bar-Ilan University, Ramat Gan, Israel

    Carmit Hazay

  2. University of Rochester, Rochester, NY, 14611, USA

    Muthuramakrishnan Venkitasubramaniam

Authors
  1. Carmit Hazay
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  2. Muthuramakrishnan Venkitasubramaniam
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Correspondence to Carmit Hazay .

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Editors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Hazay, C., Venkitasubramaniam, M. (2016). What Security Can We Achieve Within 4 Rounds?. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_26

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_26

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  • Online ISBN: 978-3-319-44618-9

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