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Low-Communication Multiparty Triple Generation for SPDZ from Ring-LPN

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13177))

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Abstract

The SPDZ protocol for multi-party computation relies on a correlated randomness setup consisting of authenticated, multiplication triples. A recent line of work by Boyle et al. (Crypto 2019, Crypto 2020) has investigated the possibility of producing this correlated randomness in a silent preprocessing phase, which involves a “small” setup protocol with less communication than the total size of the triples being produced. These works do this using a tool called a pseudorandom correlation generator (PCG), which allows a large batch of correlated randomness to be compressed into a set of smaller, correlated seeds. However, existing methods for compressing SPDZ triples only apply to the 2-party setting.

In this work, we construct a PCG for producing SPDZ triples over large prime fields in the multi-party setting. The security of our PCG is based on the ring-LPN assumption over fields, similar to the work of Boyle et al. (Crypto 2020) in the 2-party setting. We also present a corresponding, actively secure setup protocol, which can be used to generate the PCG seeds and instantiate SPDZ with a silent preprocessing phase. As a building block, which may be of independent interest, we construct a new type of 3-party distributed point function supporting outputs over arbitrary groups (including large prime order), as well as an efficient protocol for setting up our DPF keys with active security.

Supported by the Aarhus University Research Foundation and Independent Research Fund Denmark (DFF) under project number 0165-00107B (C3PO).

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Notes

  1. 1.

    In the 2-party setting, there are efficient DPFs with logarithmic key size [BGI15, BGI16].

  2. 2.

    Tuples \(\bigl ((X_0, X_1), (b, X_b)\bigr )\) where \(X_0, X_1\overset{\$}{\leftarrow }\{0, 1\}^\lambda \) and \(b\overset{\$}{\leftarrow }\{0, 1\}\).

  3. 3.

    The protocol is more efficient when m is divisible by a power of 2.

  4. 4.

    Whether we need to add or subtract is specified by the sign multipliers \(u_i^b\).

  5. 5.

    The shares are elements of R and therefore polynomials.

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Acknowledgements

We thank the anonymous reviewers for their feedback, which helped to improve the paper.

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Authors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Damiano Abram & Peter Scholl

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  1. Damiano Abram
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  2. Peter Scholl
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Correspondence to Damiano Abram .

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Editors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

    Yohei Watanabe

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Abram, D., Scholl, P. (2022). Low-Communication Multiparty Triple Generation for SPDZ from Ring-LPN. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13177. Springer, Cham. https://doi.org/10.1007/978-3-030-97121-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-97121-2_9

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