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Two-Round Concurrent 2PC from Sub-exponential LWE

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14438))

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Abstract

Secure computation is a cornerstone of modern cryptography and a rich body of research is devoted to understanding its round complexity. In this work, we consider two-party computation (2PC) protocols (where both parties receive output) that remain secure in the realistic setting where many instances of the protocol are executed in parallel (concurrent security). We obtain a two-round concurrent-secure 2PC protocol based on a single, standard, post-quantum assumption: The subexponential hardness of the learning-with-errors (LWE) problem. Our protocol is in the plain model, i.e., it has no trusted setup, and it is secure in the super-polynomial simulation framework of Pass (EUROCRYPT 2003). Since two rounds are minimal for (concurrent) 2PC, this work resolves the round complexity of concurrent 2PC from standard assumptions.

As immediate applications, our work establishes feasibility results for interesting cryptographic primitives, such as the first two-round password authentication key exchange (PAKE) protocol in the plain model and the first two-round concurrent secure computation protocol for quantum circuits (2PQC).

S. Badrinarayanan and R. Fernando—Part of the work was done while the author was affiliated with UCLA.

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Notes

  1. 1.

    It is also known how to achieve two-round MPC that satisfies a much weaker notion of semi-malicious security, where the adversary is assumed to follow the honest protocol specification. [36] Alternately, achieving full security in two rounds is possible if we allow for a trusted setup. In this paper, we focus on achieving full malicious security in the plain model, without setup.

  2. 2.

    The protocol of [2] is given in the form of a compiler that transforms a two-round semi-malicious-secure MPC protocol into a malicious-secure one.

  3. 3.

    See [31] for the exact definition of reusability obtained.

  4. 4.

    If we restrict ourselves to functionalities where only one party receives output, then it is known how to achieve two-round secure computation from much simpler assumptions [10], in the setting of standalone security.

  5. 5.

    See the full version of the paper [1].

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Acknowledgements

Giulio Malavolta was supported by the German Federal Ministry of Education and Research BMBF (grant 16KISK038, project 6GEM). Behzad Abdolmaleki was supported by the German Federal Ministry of Education and Research BMBF (grant 16KISK038, project 6GEM) and most of the work was done while he was affiliated with the Max Planck Institute for Security and Privacy. Rex Fernando was supported by the Algorand Centres of Excellence (ACE) Programme, the Defense Advanced Research Projects Agency under award number HR001120C0086, the Office of Naval Research under award number N000142212064, and the National Science Foundation under award numbers 2128519 and 2044679. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.

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Authors and Affiliations

  1. University of Sheffield, Sheffield, UK

    Behzad Abdolmaleki

  2. LinkedIn, Mountain View, USA

    Saikrishna Badrinarayanan

  3. Carnegie Mellon University, Pittsburgh, USA

    Rex Fernando

  4. Bocconi University, Milan, Italy

    Giulio Malavolta

  5. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta & Ahmadreza Rahimi

  6. UCLA, Los Angeles, USA

    Amit Sahai

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  1. Behzad Abdolmaleki
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  2. Saikrishna Badrinarayanan
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Correspondence to Behzad Abdolmaleki .

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  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Abdolmaleki, B., Badrinarayanan, S., Fernando, R., Malavolta, G., Rahimi, A., Sahai, A. (2023). Two-Round Concurrent 2PC from Sub-exponential LWE. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14438. Springer, Singapore. https://doi.org/10.1007/978-981-99-8721-4_3

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