Weakly Secure Coded Distributed Computing with Group-based Function Assignment.

This paper considers a distributed computing system where nodes are grouped such that nodes in the same group compute the same function. To complete a computing task distributedly, nodes need to exchange their local computation results with each other, which incurs communication cost and security concerns. The objective of this work is to study the tradeoff between computation and communication and avoid exchanged information leakage to eavesdroppers. Given a fixed computation load, we derive lower bounds on the communication load for 1-group and 2-group systems. New coding schemes are proposed and shown to be weakly secure and achieve the optimal tradeoffs for 1-group systems and for 2-group systems with large computation load.