MCSEC: Secure Coded Matrix Multiplication Scheme for Edge Computing with Minimum Communication Cost

Edge computing is an emerging technology that enables real-time and high-efficiency data processing by utilizing the storage, computing and communication capabilities of edge devices. Data security of computing tasks is the most important consideration in edge computing. Ensuring data security will bring additional communication load. Many researchers have proposed effective solutions to reduce the communication load. However, they did not further consider the communication cost in edge computing, i.e., the sum of the cost of each data transmission over the network, which includes communication load (the total amount of data transmission over the network). In this paper, we use communication cost instead of communication load and take matrix multiplication as the computing tasks to study the problem of secure matrix multiplication in edge computing with minimum communication cost (SMC). Specifically, we first theoretically analyze the security and decodability conditions of SMC to get the maximum number of matrix multiplication tasks stored on each edge device. Then we propose a scheme, i.e., Minimum Communication cost Secure coded Edge Computing (MCSEC), which adopts dynamic allocation and linear coding methods to allocate the matrix multiplication tasks to multiple edge devices and complete the coding design to satisfy the requirement of information-theoretic security (ITS), respectively. Moreover, we prove that the MCSEC achieves minimum communication cost by using constructive and logical analysis methods. Finally, we conduct extensive simulation experiments to evaluate the efficiency of MCSEC. The experiment results demonstrate that the MCSEC effectively reduces the communication cost (up to 71%) compared with other schemes.