Research On Secure Matrix Multiplication Scheme Based On Coded Distributed Computing

In recent years,with the rapid development of Internet of things(IoT)and 5G technology,traditional centralized computing cannot handle the huge amount of data generated by network edge devices efficiently,and distributed computing that uses multiple computing devices to process data in parallel has come into being.Currently,distributed computing has received a lot of attention for its advantages such as reliability,high fault tolerance and openness.However,during data processing,there is a risk of data leakage due to malicious attacks(impersonation,eavesdropping,tampering,etc.),and how to ensure data security has become an urgent problem for distributed computing.It has been shown that linear network coding can effectively solve the data security problem.Therefore,in this paper,we take matrix multiplication as a representative computational task,and we comprehensive consideration of computational economy,and we propose a secure and efficient matrix multiplication scheme based on coded distributed computing using linear network coding techniques with the goal of ensuring data security.The details are as follows.In homogeneous distributed computing,we study the problem of secure matrix multiplication with the goal of minimizing communication cost.Firstly,we develop a codingbased model of homogeneous distributed computing,and we define decoding conditions and security condition.Then,we design a minimum communication cost task allocation scheme that satisfies the decoding condition and the security condition.Besides,we demonstrate that the minimum communication cost task allocation scheme achieves the minimum communication cost while ensuring data security.Finally,we conduct experiments and the experimental results show that the scheme effectively reduces the communication cost compared with other schemes.In this paper,we further extend the homogeneous distributed computing scenario to a heterogeneous distributed computing scenario and study the secure matrix multiplication problem under heterogeneous distributed computing,while extending the research objective to minimize the total cost(total cost of storage,computing and communication resources consumed by computing devices).Firstly,we develop a polynomial coding-based model for heterogeneous distributed computing,and we define the attack model and security requirements.Next,we design a secure polynomial codes,and we propose a task allocation scheme with the objective of minimizing the total cost.Then,we prove the optimality of the task allocation scheme.Finally,we experimentally illustrate the efficiency of the scheme.