基于全同态加密保护医疗隐私的逻辑回归方案  

Fully homomorphic encryption-based logistic regression scheme for preserving medical privacy

作　　者：李杰[1,2] 马海英[3] 曹东杰[3] LI Jie;MA Haiying;CAO Dongjie(College of Education,Henan Normal University,Xinxiang 453007,China;School of Artificial Intelligence,Jiyuan Vocational and Technical College,Jiyuan 459000,China;School of Artificial Intelligence and Computer Science,Nantong University,Nantong 226019,China)

机构地区：[1]河南师范大学教育学部,河南新乡453007 [2]济源职业技术学院人工智能学院,河南济源459000 [3]南通大学人工智能与计算机学院,江苏南通226019

出　　处：《广西大学学报(自然科学版)》2025年第1期173-185,共13页Journal of Guangxi University(Natural Science Edition)

基　　金：河南省科技厅科技攻关项目(232102320089);南通市自然科学基金面上项目(JC2023069);河南省消防总队项目(2024XFLY02);河南省教研教改课题项目(2021SJGLX675,2024SJGLX0851)。

摘　　要：针对现有的医疗数据模型训练方案中存在隐私泄露和收敛速度慢的问题,提出基于全同态加密保护医疗隐私的逻辑回归方案。该方案首先利用Nesterov梯度下降法矫正逻辑回归算法中模型梯度的更新位置,加快其收敛速度,增大接近最优值的可能性,保证收敛精度;然后,利用全同态加密算法(CKKS)加密初始模型参数和医疗数据,使其在保护医疗数据隐私的前提下执行改进后的逻辑回归算法。为了提高模型训练中每轮迭代的效率,该方案通过减少2个向量的内积密文中的同态乘法计算次数,减小计算开销和噪声;利用极小极大近似多项式拟合Sigmoid函数,使医疗数据始终以密文的形式在不可信第三方服务器进行模型训练。通过合理的安全性假设,证明本方案在不可信的环境中进行模型训练时,能够确保医疗数据和模型参数的隐私安全。通过在真实数据集上测试本方案和相关方案的模型训练速度和精度,实验结果表明,本方案不仅具有较高的计算效率,而且提高了模型训练精度。In view of the problems of privacy leakage and slow convergence speed in the existing medical data model training schemes,a logistic regression scheme based on fully homomorphic encryption for protecting medical privacy was proposed.This scheme first used Nesterov gradient descent method to correct the update position of model gradient in the logistic regression algorithm,accelerating its convergence speed,increasing the possibility of approaching the optimal value,and ensuring the convergence accuracy.Then,it used the fully homomorphic encryption algorithm(CKKS)to encrypt the initial model parameters and medical data,enabling the execution of the improved logistic regression algorithm while protecting the privacy of medical data.To improve the efficiency of each round of iteration in model training,this scheme reduced the number of homomorphic multiplication operations in the inner product ciphertext of two vectors,thereby reducing the computational overhead and noise generated.Sigmoid function was approximated using a minimax polynomial to ensure that medical data remains in ciphertext form during model training on an untrusted third-party server.Through reasonable security assumptions,it was proved that this scheme can ensure the privacy and security of medical data and model parameters when training models in an untrusted environment.By testing the model training speed and accuracy of this scheme and related schemes on real datasets,the experimental results show that this scheme not only has high computational efficiency but also improves the model training accuracy.

关 键 词：全同态加密算法 梯度下降法 医疗隐私保护 逻辑回归 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]