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Adaptively Secure Computation for RAM Programs

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Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13276))

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Abstract

In this work, we study the communication complexity of secure multiparty computation under minimal assumptions in the presence of an adversary that can adaptively corrupt all parties eventually. Specifically, we are interested in understanding the complexity when modeling the underlying function as a RAM program. Under minimal assumptions, the work of Canetti et al. (STOC 2017) and Benhamouda et al. (TCC 2018) give protocols whose communication complexity grows quadratically in the circuit size when the computation is expressed as a Boolean circuit. In this work, we obtain the first two-round two-party computation protocol, which is secure against adaptive adversaries who can adaptively corrupt all parties where the communication complexity is proportional to the square of the RAM complexity of the function up to polylogarithmic factors assuming the existence of non-committing encryption.

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Notes

  1. 1.

    Indeed, in this case the static simulator obtains the inputs of all parties in the protocol and thus can simulate the execution by simply running the protocol.

  2. 2.

    We remark that to obtain our result, it sufficient to obtain a circuit-efficient adaptive zero-knowledge proof.

  3. 3.

    In a RAM program, a step circuit performs CPU computations at a particular time step.

  4. 4.

    We adopt the definition of ORAM from [10].

  5. 5.

    Note that for simplicity we only specify the leaf nodes accessed by \(P'^{D'}(x)\) instead of specifying each node accessed along the path from the root to the leaf.

  6. 6.

    We note that the PRF-based scheme \((r, F_k(r) \oplus m)\) satisfies both the properties.

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Acknowledgments

Work of Rafail Ostrovsky was supported by NSF award #2001096, US-Israel BSF grant 2015782, a Google Faculty Award, a JP Morgan Faculty Award, an IBM Faculty Research Award, a Xerox Faculty Research Award, an OKAWA Foundation Research Award, a B. John Garrick Foundation Award, a Teradata Research Award, a Lockheed-Martin Research Award, and the Sunday Group.

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Authors and Affiliations

  1. Georgetown University, Washington, USA

    Laasya Bangalore & Muthuramakrishnan Venkitasubramaniam

  2. UCLA, Los Angeles, USA

    Rafail Ostrovsky

  3. Ligero, Inc., Rochester, USA

    Oxana Poburinnaya

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  1. Laasya Bangalore
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  2. Rafail Ostrovsky
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  3. Oxana Poburinnaya
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  4. Muthuramakrishnan Venkitasubramaniam
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Corresponding author

Correspondence to Laasya Bangalore .

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Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Bangalore, L., Ostrovsky, R., Poburinnaya, O., Venkitasubramaniam, M. (2022). Adaptively Secure Computation for RAM Programs. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13276. Springer, Cham. https://doi.org/10.1007/978-3-031-07085-3_7

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