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Actively Secure Half-Gates with Minimum Overhead Under Duplex Networks

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Advances in Cryptology – EUROCRYPT 2023 (EUROCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14005))

Abstract

Actively secure two-party computation (2PC) is one of the canonical building blocks in modern cryptography. One main goal for designing actively secure 2PC protocols is to reduce the communication overhead, compared to semi-honest 2PC protocols. In this paper, we propose a new actively secure constant-round 2PC protocol with one-way communication of \(2\kappa +5\) bits per AND gate (for \(\kappa \)-bit computational security and any statistical security), essentially matching the one-way communication of semi-honest half-gates protocol. This is achieved by two new techniques:

  1. 1.

    The recent compression technique by Dittmer et al. (Crypto 2022) shows that a relaxed preprocessing is sufficient for authenticated garbling that does not reveal masked wire values to the garbler. We introduce a new form of authenticated bits and propose a new technique of generating authenticated AND triples to reduce the one-way communication of preprocessing from \(5\rho +1\) bits to 2 bits per AND gate for \(\rho \)-bit statistical security.

  2. 2.

    Unfortunately, the above compressing technique is only compatible with a less compact authenticated garbled circuit of size \(2\kappa +3\rho \) bits per AND gate. We designed a new authenticated garbling that does not use information theoretic MACs but rather dual execution without leakage to authenticate wire values in the circuit. This allows us to use a more compact half-gates based authenticated garbled circuit of size \(2\kappa +1\) bits per AND gate, and meanwhile keep compatible with the compression technique. Our new technique can achieve one-way communication of \(2\kappa +5\) bits per AND gate.

Our technique of yielding authenticated AND triples can also be used to optimize the two-way communication (i.e., the total communication) by combining it with the authenticated garbled circuits by Dittmer et al., which results in an actively secure 2PC protocol with two-way communication of \(2\kappa +3\rho +4\) bits per AND gate.

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Notes

  1. 1.

    VOLE is an arithmetic generalization of COT, and enables \(\mathsf P_{A}\) to obtain \((\varDelta , \textsf{K}[{\boldsymbol{u}}]) \in \mathbb F \times \mathbb F ^\ell \) and \(\mathsf P_{B}\) to get \(({\boldsymbol{u}}, \textsf{M}[{\boldsymbol{u}}]) \in \mathbb F ^\ell \times \mathbb F ^\ell \) such that \(\textsf{M}[{\boldsymbol{u}}]=\textsf{K}[{\boldsymbol{u}}]+{\boldsymbol{u}}\cdot \varDelta \), where \(\mathbb F \) is a large field such as \(\mathbb F =\mathbb F _{2^\rho }\).

  2. 2.

    An independent global key is necessary to perform the consistency check, and otherwise a malicious \(\mathsf P_{B}\) will always pass the check if is reused.

  3. 3.

    We define \(a_w, a_w', b_w, b_w'\) by the MAC tag and keys to implicitly authenticate them.

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Acknowledgements

Kang Yang is supported by the National Key Research and Development Program of China (Grant No. 2022YFB2702000), and by the National Natural Science Foundation of China (Grant Nos. 62102037, 61932019, 62022018). Yu Yu is supported by the National Natural Science Foundation of China (Grant Nos. 62125204 and 92270201), the National Key Research and Development Program of China (Grant No. 2018YFA0704701), and the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008). Yu Yu also acknowledges the support from the XPLORER PRIZE. Xiao Wang is supported by DARPA under Contract No. HR001120C0087, NSF award #2016240, #2236819, and research awards from Meta and Google. The views, opinions, and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. We thanks anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Hongrui Cui & Yu Yu

  2. Northwestern University, Evanston, USA

    Xiao Wang

  3. State Key Laboratory of Cryptology, Beijing, China

    Kang Yang

  4. Shanghai Qi Zhi Institute, Shanghai, China

    Yu Yu

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  1. Hongrui Cui
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  1. Bar-Ilan University, Ramat Gan, Israel

    Carmit Hazay

  2. Simula UiB, Bergen, Norway

    Martijn Stam

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Cui, H., Wang, X., Yang, K., Yu, Y. (2023). Actively Secure Half-Gates with Minimum Overhead Under Duplex Networks. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14005. Springer, Cham. https://doi.org/10.1007/978-3-031-30617-4_2

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