SFPDML: Securer and Faster Privacy-Preserving Distributed Machine Learning Based on MKTFHE - Abstract - Attack, secret sharing, and activation function for logistic regression and neural networks

Aug 4, 2026

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Distributed machine learning attracts strong interest, yet privacy remains a major unresolved issue. Multi-key homomorphic encryption over the torus (MKTFHE) is a promising direction, but decryption can introduce security risks, and prior MKTFHE work often supports only Boolean and linear operations, making non-linear functions such as Sigmoid difficult to implement efficiently. The paper identifies a possible attack on an existing distributed MKTFHE decryption protocol and proposes a securer scheme using secret sharing. It further designs an MKTFHE-friendly activation function and instantiates logistic regression and neural-network training, showing about 10x efficiency improvement with comparable accuracy.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages20

Reading Time50 min

AccessFree to download

Introduction

Privacy computing with (MK)FHE

Limitations of non-linear operations in MKTFHE

SecureML-style piecewise activation and compare quads

Distributed decryption and discovered attacks

arXiv :2211 .09353v2 [ cs .CR] 19 Mar 2024 SFPDML: Securer and Faster Privacy-Preserving Distributed Machine Learning Based on MKTFHE Hongxiao Wang 1 , Zoe L. Jiang2 , 3 , Yanmin Zhao 1 , Siu-Ming Yiu 1(B) , Peng Yang2 , Man Chen4 , Zejiu Tan2 , and Bohan Jin2 1 University of Hong Kong, Hong Kong, China {hxwang, ymzhao, smyiu}@cs.hku.hk 2 Harbin Institute of Technology, Shenzhen, Shenzhen, China [zoeljiang@hit.edu.cn](zoeljiang@hit.edu.cn) {stuyangpeng, 23s151118, [23s051024](23s051024}@stu.hit.edu.cn)[}](23s051024}@stu.hit.edu.cn)[@stu.hit.edu.cn](23s051024}@stu.hit.edu.cn) 3 Peng Cheng Laboratory, Shenzhen, China 4 Shandong University, Jinan, China [chenman19961121@gamil.com](chenman19961121@gamil.com) Abstract In recent years, distributed machine learning has garnered significant attention. However, privacy continues to be an unresolved issue within this field. Multi-key homomorphic encryption over torus (MKTFHE) is one of the promising candidates for addressing this concern. Nevertheless, there may be security risks in the decryption of MKTFHE. Moreover, to our best known, the latest works about MKTFHE only support Boolean operation and linear operation which cannot directly compute the non-linear function like Sigmoid. Therefore, it is still hard to perform common machine learning such as logistic regression and neural networks in high performance. In this paper, we first discover a possible attack on the existing distributed decryption protocol for MKTFHE and subsequently introduce secret sharing to propose a securer one. Next, we design a new MKTFHE-friendly activation function via homogenizer and compare quads. Finally, we utilize them to implement logistic regression and neural network training in MKTFHE. Comparing the efficiency and accuracy between using Taylor polynomials of Sigmoid and our proposed function as an activation function, the experiments show that the efficiency of our function is 10 times higher than using 7-order Taylor polynomials straightly and the accuracy of the training model is similar to using a high-order polynomial as an activation function scheme. Keywords: privacy-preserving machine learning, multi-key fully homomorphic encryption, multi-key decryption, distributed machine learning. 1 Introduction In the big data era, it is necessary to transform centralized systems into distributed ones in machine learning tasks. However, these distributed systems lead to new challenges, and one of the most pressing is privacy [16, 30] . Privacy computing is a technique that enables data computation without any risk of information leakage. To outsource private computations, fully homomorphic encryption (FHE), a cryptographic tool, is employed. FHE is a unique form of encryption that allows users to perform computations on encrypted data without the need to first decrypt it. FHE can be divided into two categories: single-key fully homomorphic encryption and multi-key fully homomorphic encryption. Single-key FHE only allows a server to perform addition and multiplication on data encrypted by the same key. In contrast, multi-key FHE (MKFHE) proposed in [22] enables users to encrypt their own data under their own keys, but during the decryption of MKFHE, all secret keys of all participants are used. It prevents conspiracy between a user and a server to steal the data of other users. In recent years, multi-key fully homomorphic encryption over the torus (MKTFHE) has attracted significant attention from researchers, particularly in the areas of evaluation and decryption algorithms. Chen et al. [6] developed a library for implementing MKTFHE, focusing on an evaluation algorithm that takes a NAND gate as input. Subsequently, Jiang et al. [17] expanded the evaluation algorithm to include arithmetic operators such as adders, subtracters, multipliers, and dividers, enabling linear multi-key homomorphic arithmetic evaluation in MKTFHE. However, the inability to evaluate non-lin

FAQs

What problem does SFPDML address in MKTFHE-based distributed machine learning?

It addresses privacy issues in distributed learning and the difficulty of supporting non-linear functions needed for models like logistic regression and neural networks under MKTFHE, while also improving decryption security.

How does the paper improve the security of distributed MKTFHE decryption?

It discovers a possible attack on an existing distributed decryption protocol and introduces secret sharing to construct a securer distributed decryption approach.

How are non-linear activation functions such as Sigmoid implemented efficiently in MKTFHE?

The paper designs an MKTFHE-friendly activation function using homogenizer concepts and compare quads, enabling piecewise evaluation with only two compare quads instead of more complex interactive comparisons.

Aug 4, 2026

Upload by Violet