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ASIACRYPT 2021: Advances in Cryptology – ASIACRYPT 2021 pp 305–334Cite as

Two-Round Adaptively Secure MPC from Isogenies, LPN, or CDH

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13091))

Abstract

We present a new framework for building round-optimal (two-round) adaptively secure MPC. We show that a relatively weak notion of OT that we call indistinguishability OT with receiver oblivious sampleability (\(\mathsf {r\hbox {-}iOT}\)) is enough to build two-round, adaptively secure MPC against malicious adversaries in the CRS model. We then show how to construct \(\mathsf {r\hbox {-}iOT}\) from CDH, LPN, or isogeny-based assumptions that can be viewed as group actions (such as CSIDH and CSI-FiSh). This yields the first constructions of two-round adaptively secure MPC against malicious adversaries from CDH, LPN, or isogeny-based assumptions. We further extend our non-isogeny results to the plain model, achieving (to our knowledge) the first construction of two-round adaptively secure MPC against semi-honest adversaries in the plain model from LPN.

Our results allow us to build two-round adaptively secure MPC against malicious adversaries from essentially all of the well-studied assumptions in cryptography. In addition, our constructions from isogenies or LPN provide the first post-quantum alternatives to LWE-based constructions for round-optimal adaptively secure MPC. Along the way, we show that \(\mathsf {r\hbox {-}iOT} \) also implies non-committing encryption (NCE), thereby yielding the first constructions of NCE from isogenies or LPN.

N. Alamati—Most of the work was done while the author was affiliated with UC Berkeley.

S. Patranabis—Most of the work was done while the author was affiliated with ETH Zürich.

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Notes

  1. 1.

    Note that constant round maliciously secure MPC against adaptive corruptions can only be achieved in the CRS model; see [GS12] for results establishing the impossibility of maliciously secure adaptive MPC in the plain model from black-box simulation.

  2. 2.

    The secure erasures model allows erasing the internal state of an honest party when its gets adaptively corrupted by the adversary. It is a strictly weaker model than the one we consider, where erasing the party’s state is not allowed.

  3. 3.

    Unlike CDH or LPN, we do not achieve a construction of \(\mathsf {r\hbox {-}iOT} \) from isogeny-based assumptions in the plain model. Achieving this seemingly requires new techniques for sampling obliviously from the “set” of an effective group action beyond those used in state-of-the-art isogeny-based cryptography.

  4. 4.

    For standard two-message OT protocols, the setup algorithm need not output a trapdoor \(\textsf {td}\), but we include it for certain security properties described subsequently.

  5. 5.

    This is slightly different from the traditional notion of sender’s indistinguishability security for two-message OT; we refer to [DGH+20] for more details.

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Acknowledgements

The work of Pratik Sarkar is supported by the DARPA SIEVE project and NSF awards 1931714, 1414119.

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Authors and Affiliations

  1. UC Berkeley and Visa Research, Berkeley, USA

    Navid Alamati

  2. Fujitsu Research of America, Sunnyvale, USA

    Hart Montgomery

  3. ETH Zürich and Visa Research, Zürich, Switzerland

    Sikhar Patranabis

  4. Boston University, Boston, USA

    Pratik Sarkar

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  1. Navid Alamati
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  2. Hart Montgomery
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  3. Sikhar Patranabis
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  4. Pratik Sarkar
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Correspondence to Navid Alamati , Hart Montgomery , Sikhar Patranabis or Pratik Sarkar .

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Editors and Affiliations

  1. NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Alamati, N., Montgomery, H., Patranabis, S., Sarkar, P. (2021). Two-Round Adaptively Secure MPC from Isogenies, LPN, or CDH. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13091. Springer, Cham. https://doi.org/10.1007/978-3-030-92075-3_11

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