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Fregata: Faster Homomorphic Evaluation of AES via TFHE

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Information Security (ISC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14411))

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Abstract

Gentry et al. [26] first presented a homomorphic evaluation of the AES-128 based on the BGV scheme, however, it suffered from high evaluation latency. Despite considerable efforts have been directed towards designing FHE-friendly symmetric encryption algorithms, the efficient homomorphic evaluation of the well-studied and standardized AES remains an attractive challenge for researchers in the transciphering community.

In this paper, we present a novel homomorphic evaluation framework based on the TFHE scheme, demonstrating the optimal latency for AES-128 evaluation. Specifically, we propose mixed packing to achieve efficient S-box evaluation and an optimized circuit bootstrapping as a bridge to connect the whole evaluation framework. Furthermore, we show the versatility of our evaluation framework by extending it to other ciphers, such as SM4. To validate the effectiveness of our proposed framework, we conduct implementation experiments, which indicate that the evaluation of AES takes 86 s on a single core, a 3\(\times \) improvement over the state-of-the-art [39]. Moreover, with a 16-thread parallel implementation, it takes about 9 s. For SM4 evaluation, it takes only 78 s on a single core, about 73\(\times \) improvement compared to publicly available BGV-based solution [40].

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Notes

  1. 1.

    We called our framework “Fregata”, which cleverly reads like “Free Gate”, emphasizing the fact that it eliminates the cost for XOR gate due to message encoding. Its speed reflects our efficient homomorphic evaluation of S-box.

  2. 2.

    https://github.com/tfhe/experimental-tfhe.

  3. 3.

    https://github.com/tfhe/tfhe.

  4. 4.

    https://bitbucket.org/malb/lwe-estimator.

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Acknowledgement

We thank the anonymous ISC2023 reviewers for their helpful comments. This work was supported by the Huawei Technologies Co., Ltd. and CAS Project for Young Scientists in Basic Research Grant No. YSBR-035.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Benqiang Wei, Ruida Wang, Zhihao Li, Qinju Liu & Xianhui Lu

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Benqiang Wei, Ruida Wang, Zhihao Li, Qinju Liu & Xianhui Lu

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  1. Benqiang Wei
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  2. Ruida Wang
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  3. Zhihao Li
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Correspondence to Xianhui Lu .

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Editors and Affiliations

  1. University of Cyprus, Nicosia, Cyprus

    Elias Athanasopoulos

  2. Radboud University, Nijmegen, The Netherlands

    Bart Mennink

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Wei, B., Wang, R., Li, Z., Liu, Q., Lu, X. (2023). Fregata: Faster Homomorphic Evaluation of AES via TFHE. In: Athanasopoulos, E., Mennink, B. (eds) Information Security. ISC 2023. Lecture Notes in Computer Science, vol 14411. Springer, Cham. https://doi.org/10.1007/978-3-031-49187-0_20

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