Proceedings of the 2025 3rd International Conference on Image, Algorithms, and Artificial Intelligence (ICIAAI 2025)

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Research on Paillier Decryption Acceleration and Security Enhancement Based on CRT and Montgomery Algorithm

Authors
Hui Lian1, *
1School of Economics and Management, Tongji University, Shanghai, China
*Corresponding author. Email: lianhui@tongji.edu.cn
Corresponding Author
Hui Lian
Available Online 31 August 2025.
DOI
10.2991/978-94-6463-823-3_13How to use a DOI?
Keywords
Paillier; Decryption; CRT; Montgomery algorithm
Abstract

Facing the need for privacy protection in federated learning, this paper conducts a systematic review of the Paillier based on OpenMP parallel acceleration using the Chinese remainder theorem and Montgomery algorithm (CM-Paillier-OMP) encryption scheme that uses OpenMP (OMP) parallel computing and is based on the Chinese Remainder Theorem (CRT) and the Montgomery algorithm. It reveals that it faces a triple limitation: the increase in key length leads to a decline in computational efficiency, the Montgomery algorithm introduces the risk of side-channel attacks and lacks the ability to resist quantum attacks. In order to solve these problems, this paper proposes a multi-dimensional optimization scheme. At the algorithm level, the Karatsuba algorithm is integrated to reduce the complexity of large-number multiplication. The sliding window algorithm is adopted to optimize the pre-computation process of modular exponentiation. The overall complexity is reduced to at least O ( n log 2 3 ) and a positive correlation with n 0.415 can theoretically be achieved; At the security level, the side-channel defense technology and post-quantum cryptography algorithm are integrated to build a dual protection system against physical attacks and quantum computing.

Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 2025 3rd International Conference on Image, Algorithms, and Artificial Intelligence (ICIAAI 2025)
Series
Advances in Computer Science Research
Publication Date
31 August 2025
ISBN
978-94-6463-823-3
ISSN
2352-538X
DOI
10.2991/978-94-6463-823-3_13How to use a DOI?
Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Hui Lian
PY  - 2025
DA  - 2025/08/31
TI  - Research on Paillier Decryption Acceleration and Security Enhancement Based on CRT and Montgomery Algorithm
BT  - Proceedings of the 2025 3rd International Conference on Image, Algorithms, and Artificial Intelligence (ICIAAI 2025)
PB  - Atlantis Press
SP  - 135
EP  - 147
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-823-3_13
DO  - 10.2991/978-94-6463-823-3_13
ID  - Lian2025
ER  -