Randomized average consensus based on additive privacy sharing

Distributed average consensus plays a crucial role in multi-agent systems. In data-sensitive applications, agents need to exchange state without disclosing true privacy. To address this issue, homomorphic encryption and random perturbations-based schemes are commonly adopted privacy-preserving approaches. However, homomorphic encryption is typically limited to scenarios where agents’ state values are non-negative integers with substantial computational overhead. On the other hand, random perturbation-based schemes often require prior knowledge of the total number of agents, rendering them ineffective in dynamic environments or vulnerable against external eavesdroppers. Motivated by this, we propose an additive secret-sharing method based on multiplication operations to achieve consensus among agents. Specifically, we first introduce random perturbations and exponentiation to true states. Based on this, each agent's true state is decomposed into secret shares, which are then transmitted over public channels. We design the scheme to enable fundamental operations to be executed in a distributed manner, thereby facilitating distributed average consensus. This solution resists attacks from both honest-but-curious and global eavesdropping agents, under the condition that each node is connected to at least one trusted node. In comparison with differential privacy solutions, our approach achieves consensus by an exact state value. Furthermore, it has a lighter resource consumption and broader applicability than homomorphic encryption schemes. Simulation results show the feasibility and security of our approach.