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One-Message Secure Reductions: On the Cost of Converting Correlations

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14081))

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Abstract

Correlated secret randomness is a useful resource for secure computation protocols, often enabling dramatic speedups compared to protocols in the plain model. This has motivated a line of work on identifying and securely generating useful correlations.

Different kinds of correlations can vary greatly in terms of usefulness and ease of generation. While there has been major progress on efficiently generating oblivious transfer (OT) correlations, other useful kinds of correlations are much more costly to generate. Thus, it is highly desirable to develop efficient techniques for securely converting copies of a given source correlation into copies of a given target correlation, especially when the former are cheaper to generate than the latter.

In this work, we initiate a systematic study of such conversions that only involve a single uni-directional message. We refer to such a conversion as a one-message secure reduction (OMSR). Recent works (Agarwal et al., Eurocrypt 2022; Khorasgani et al., Eurocrypt 2022) studied a similar problem when no communication is allowed; this setting is quite restrictive, however, with few non-trivial conversions being feasible. The OMSR setting substantially expands the scope of feasible results, allowing for direct applications to existing MPC protocols.

We obtain the following positive and negative results.

  • OMSR constructions. We present a general rejection-sampling based technique for OMSR with OT source correlations. We apply it to substantially improve in the communication complexity of optimized protocols for distributed symmetric cryptography (Dinur et al., Crypto 2021).

  • OMSR lower bounds. We develop general techniques for proving lower bounds on the communication complexity of OMSR, matching our positive results up to small constant factors.

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Acknowledgments

We thank the anonymous reviewers for helpful comments. M. Kelkar was partially supported by a Technion research scholarship. Y. Ishai and V. Narayanan were supported by ERC Project NTSC (742754), and ISF grant 2774/20. Y. Ishai was additionally supported by BSF grant 2018393.

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Authors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai, Varun Narayanan & Liav Zafar

  2. Cornell University, Ithaca, USA

    Mahimna Kelkar

  3. Cornell Tech, New York, USA

    Mahimna Kelkar

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  1. Yuval Ishai
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Correspondence to Mahimna Kelkar .

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  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Ishai, Y., Kelkar, M., Narayanan, V., Zafar, L. (2023). One-Message Secure Reductions: On the Cost of Converting Correlations. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_17

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  • DOI: https://doi.org/10.1007/978-3-031-38557-5_17

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