This paper investigates a multi-user uplink mobile edge computing (MEC) network, where the users offload partial tasks securely to an access point under the non-orthogonal multiple access policy with the aid of a reconfigurable intelligent surface (RIS) against a multi-antenna eavesdropper. We formulate a non-convex optimization problem of minimizing the total energy consumption subject to secure offloading requirement, and we build an efficient block coordinate descent framework to iteratively optimize the number of local computation bits and transmit power at the users, the RIS phase shifts, and the multi-user detection matrix at the access point. Specifically, we successively adopt successive convex approximation, semi-definite programming, and semidefinite relaxation to solve the problem with perfect eavesdropper's channel state information (CSI), and we then employ S-procedure and penalty convex-concave to achieve robust design for the imperfect CSI case. We provide extensive numerical results to validate the convergence and effectiveness of the proposed algorithms. We demonstrate that RIS plays a significant role in realizing a secure and energy-efficient MEC network, and deploying a well-designed RIS can save energy consumption by up to 60\% compared to that without RIS. We further reveal impacts of various key factors on the secrecy energy efficiency, including RIS element number and deployment position, user number, task scale and duration, and CSI imperfection.

翻译：本文研究了一种多用户上行移动边缘计算网络，其中用户在可重构智能表面的辅助下，通过非正交多址策略将部分任务安全卸载至接入点，以对抗多天线窃听者。我们构建了一个非凸优化问题，旨在最小化总能量消耗，同时满足安全卸载要求，并建立了一个高效的块坐标下降框架，迭代优化用户本地计算比特数与发射功率、可重构智能表面相移以及接入点多用户检测矩阵。具体而言，我们依次采用逐次凸逼近、半定规划和半定松弛方法求解窃听者信道状态信息完美已知情况下的问题，随后利用S-过程和惩罚凸凹方法实现信道状态信息不完美情况下的鲁棒设计。我们提供了大量数值结果以验证所提算法的收敛性和有效性。结果表明，可重构智能表面在实现安全节能的移动边缘计算网络中发挥着重要作用，部署设计良好的可重构智能表面相比无表面情况可节省高达60%的能耗。我们进一步揭示了多种关键因素对保密能效的影响，包括可重构智能表面单元数量与部署位置、用户数量、任务规模与持续时间以及信道状态信息的不完美性。