摘 要：云计算是一种能为弱计算设备用户提供外包计算服务的新兴技术，为普通用户节省大量的计算资源。在外包计算中，科学计算是一类重要的应用，尤其以线性方程组外包求解为基本构造块。然而，在将方程组系数和常数项外包给云的过程中，不可避免的涉及隐私泄漏。该文给出具有隐私保护的基于 Gauss 迭代法的线性方程组外包计算算法，与已有文献中的基于 Jacobi迭代的方法相比，在相同精度下，能获得更快的计算速度，从而节省通信资源和计算资源。
关键词：隐私保护；线性方程组；Gauss 迭代法；Paillier 同态；外包计算
DOI:10.19850/j.cnki.2096-4706.2021.04.039
基金项目：广西科技基地和人才专项（桂科 AD18281024）；广西高校中青年教师基础能力提 升项目（2019KY0210）；国家级大学生创新训练 计划项目（202010595010）
中图分类号：TP333；O241.6 文献标识码：A 文章编号：2096-4706（2021）04-0149-04
Privacy Protection Outsourcing Computing of Linear System of Equations Based on Gauss Iterative Method
XI Yuxing，TANG Min，PANG Jianhu，ZHANG Yuhao
（School of Mathematics & Computing Science，Guilin University of Electronic Technology，Guilin 541004，China）
Abstract：Cloud computing is an emerging technology that can provide outsourcing computing services for users with weak computing devices，saving a lot of computing resources for ordinary users. In outsourcing computing，scientific computing is a kind of important application，especially taking the outsourcing solution of linear system of equations as the basic building block. However，in the process of outsourcing equation set coefficients and constant terms to the cloud，privacy leakage is inevitably involved. For this reason， outsourcing computing algorithm of linear system of equations based on Gauss iterative method，with privacy protection is proposed. Compared with the algorithm based on Jacobi iterative in existing literature，the algorithm proposed in this paper has high computing speed under the same precision，so as to save communication resources and computing resources.
Keywords：privacy protection；linear system of equations；Gauss iterative method；Paillier homomorphism；outsourcing computing
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作者简介：习宇兴（1998—），男，汉族，江西新余人，本 科在读，研究方向：信息与计算科学；唐敏（1980—），女，壮 族，广西桂林人，副教授，博士，研究方向：隐私保护；庞健虎 （1998—），男，汉族，广西南宁人，本科在读，研究方向：信息 与计算科学；张宇浩（1998—），男，汉族，安徽宿州人，硕士在读， 研究方向：机器学习、隐私保护。