Batch Identification Game Model for Invalid Signatures in Wireless Mobile Networks

Secure access is one of the fundamental problems in wireless mobile networks. Digital signature is a widely used technique to protect messages' authenticity and nodes' identities. From the practical perspective, to ensure the quality of services in wireless mobile networks, ideally the process of signature verification should introduce minimum delay. Batch cryptography technique is a powerful tool to reduce verification time. However, most of the existing works focus on designing batch verification algorithms for wireless mobile networks without sufficiently considering the impact of invalid signatures, which can lead to verification failures and performance degradation. In this paper, we propose a Batch Identification Game Model (BIGM) in wireless mobile networks, enabling nodes to find invalid signatures with reasonable delay no matter whether the game scenario is complete information or incomplete information. Specifically, we analyze and prove the existence of Nash Equilibriums (NEs) in both scenarios, to select the dominant algorithm for identifying invalid signatures. To optimize the identification algorithm selection, we propose a self-adaptive auto-match protocol which estimates the strategies and states of attackers based on historical information. Comprehensive simulation results in terms of NE reasonability, algorithm selection accuracy, and identification delay are provided to demonstrate that BIGM can identify invalid signatures more efficiently than existing algorithms.