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Revisiting the Efficiency of Perfectly Secure Asynchronous Multi-party Computation Against General Adversaries

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Progress in Cryptology – INDOCRYPT 2022 (INDOCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13774))

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Abstract

In this paper, we present a perfectly-secure multi-party computation (MPC) protocol in the asynchronous communication setting with optimal resilience. Our protocol is secure against a computationally-unbounded malicious adversary characterized by an adversary structure \(\mathcal {Z}\), which enumerates all possible subsets of potentially corrupt parties. The protocol incurs an amortized communication of \(\mathcal {O}(|\mathcal {Z}|^2)\) bits per multiplication. This improves upon the previous best protocol of Choudhury and Pappu (INDOCRYPT 2020), which requires an amortized communication of \(\mathcal {O}(|\mathcal {Z}|^3)\) bits per multiplication. Previously, perfectly-secure MPC with amortized communication of \(\mathcal {O}(|\mathcal {Z}|^2)\) bits per multiplication was known only in the relatively simpler synchronous communication setting (Hirt and Tschudi, ASIACRYPT 2013).

A. Appan and A. Chandramouli—Work done when the author was a student at International Institute of Information Technology, Bangalore

The full version of the article is available at [1]

A. Choudhury—This research is an outcome of the R &D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation (formerly Media Lab Asia). The author is also thankful to the Electronics, IT & BT Government of Karnataka for supporting this work under the CIET project.

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Notes

  1. 1.

    \(\mathcal {Z}\) satisfies the \(\mathbb {Q}^{(k)}(\mathcal {P}, \mathcal {Z})\) condition [18], if the union of no k sets from \(\mathcal {Z}\) covers \(\mathcal {P}\).

  2. 2.

    A secret-sharing scheme is called linear, if the shares are computed as a linear function of the secret and the underlying randomness used in the scheme.

  3. 3.

    From [14], every deterministic ABA protocol must have non-terminating runs, where the parties may run the protocol forever, without obtaining any output. To circumvent this result, randomized ABA protocols are considered and the best we can hope for from such protocols is that the parties eventually obtain an output, asymptotically with probability 1 (this property is called almost-surely termination property).

  4. 4.

    The reason for two different discarded sets is that the various instances of cheater-identification are executed asynchronously, thus resulting in a corrupt party to be identified by different honest parties during different iterations.

  5. 5.

    Here, the summand-list of a selected party refers to the summands it was supposed to share during the respective \(\varPi _{\textsf{OptMult}}\) instance of that iteration.

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Authors and Affiliations

  1. International Institute of Information Technology, Bangalore, India

    Ananya Appan, Anirudh Chandramouli & Ashish Choudhury

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  1. Ananya Appan
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  2. Anirudh Chandramouli
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  3. Ashish Choudhury
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Correspondence to Ashish Choudhury .

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  1. University of Hyogo, Hyogo, Japan

    Takanori Isobe

  2. Indian Institute of Technology Madras, Chennai, India

    Santanu Sarkar

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Appan, A., Chandramouli, A., Choudhury, A. (2022). Revisiting the Efficiency of Perfectly Secure Asynchronous Multi-party Computation Against General Adversaries. In: Isobe, T., Sarkar, S. (eds) Progress in Cryptology – INDOCRYPT 2022. INDOCRYPT 2022. Lecture Notes in Computer Science, vol 13774. Springer, Cham. https://doi.org/10.1007/978-3-031-22912-1_10

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