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Improvements of Homomorphic Secure Evaluation of Inverse Square Root

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Information and Communications Security (ICICS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14252))

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Abstract

Secure machine learning has attracted much attention recently. The celebrated CKKS homomorphic encryption scheme has played a key role in such an application. Inverse square root is widely used in machine learning, such as vector normalization, clustering, etc., but it is not a function that can be easily processed by CKKS. In 2022, Panda proposed a Newton iterative algorithm for homomorphic evaluation of inverse square root using CKKS scheme. The initial value of the iteration is selected as two straight lines intersecting at one point, which involves a very expensive homomorphic comparison operation. In this paper, we propose two novel methods for selecting the initial value of the inverse square root Newton iterative algorithm. Specifically, Taylor expansion and rational function are used as an initial value to avoid the homomorphic comparison operation and achieve a significant improvement of efficiency. The Taylor expansion method greatly reduces the initial value calculation consumption, but appropriately increases the number of Newton iterations. Compared with the Taylor expansion method, the rational function method is more costly in the initial value calculation stage but reduces the number of Newton iterations. Experiments are conducted on the SEAL open source library and we find that, while reaching the same accuracy, the total number of homomorphic levels consumed by the Taylor expansion method is about \(83.3\%\) of the best known results, and the rational function method is about \(56.9\%\).

This work was supported by the National Key Research and Development Program of China (2018YFA0704702) and National Natural Science Foundation of China (No. 12271306).

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Acknowledgements

The authors thank the anonymous reviewers for many helpful comments.

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Authors and Affiliations

  1. Key Laboratory of Cryptologic Technology and Information Security of Ministry of Education, Qingdao, 266237, China

    Hongyuan Qu & Guangwu Xu

  2. School of Cyber Science and Technology, Shandong University, Qingdao, 266237, China

    Hongyuan Qu & Guangwu Xu

  3. Shandong Institute of Blockchain, Jinan, 250101, China

    Guangwu Xu

  4. Quan Cheng Laboratory, Jinan, 250103, China

    Guangwu Xu

Authors
  1. Hongyuan Qu
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  2. Guangwu Xu
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Correspondence to Guangwu Xu .

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Editors and Affiliations

  1. Nankai University, Tianjin, China

    Ding Wang

  2. Columbia University, New York, NY, USA

    Moti Yung

  3. Nankai University, Tianjin, China

    Zheli Liu

  4. Xidian University, Xi’an, China

    Xiaofeng Chen

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Qu, H., Xu, G. (2023). Improvements of Homomorphic Secure Evaluation of Inverse Square Root. In: Wang, D., Yung, M., Liu, Z., Chen, X. (eds) Information and Communications Security. ICICS 2023. Lecture Notes in Computer Science, vol 14252. Springer, Singapore. https://doi.org/10.1007/978-981-99-7356-9_7

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  • DOI: https://doi.org/10.1007/978-981-99-7356-9_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-7355-2

  • Online ISBN: 978-981-99-7356-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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