Edge computing brings computation and storage resources to the edge of the mobile network to solve the problems of low latency and high real-time demand. However, edge computing is more vulnerable to malicious attacks due to its open and dynamic environments. In this article, we investigate security defense strategies in edge computing systems, focusing on scenarios with one attacker and multiple defenders to determine optimal defense strategies with minimal resource allocation. Firstly, we formulate the interactions between the defenders and the attackers as the mean-field Stackelberg game model, where the state and the objective functions of the defenders are coupled through the mean-field term, and are strongly influenced by the strategy of the attacker. Then, we analyze the local optimal strategies of the defenders given an arbitrary strategy of the attackers. We demonstrate the Nash equilibrium and the mean-field equilibrium for both the defenders and the attackers. Finally, simulation analysis will illustrate the dynamic evolution of the defense strategy of the defenders and the trajectory of the attackers based on the proposed Stackelberg game model.

An important feature of Nyberg-Rueppel type digital signature algorithms is message recovery, this signature algorithm can recover the original information from the signature directly by the verifier in the verification phase after signing the message. However, this algorithm is currently vulnerable to quantum attacks and its security cannot be guaranteed. Number Theory Research Unit (NTRU) is an efficient public-key cryptosystem and is considered to be one of the best quantum-resistant encryption schemes. This paper proposes an NTRU-like message recoverable signature algorithm to meet the key agreement requirements in the post-quantum world. This algorithm, designed for the Internet of Things (IoT), constructs a secure system using the Group-Based Message Recoverable Signature Algorithm (NR-GTRU), by integrating a Group-Based NTRU-Like Public-Key Cryptosystem (GTRU) with an efficient Nyberg-Rueppel type of NTRU digital signature algorithm (NR-NTRU). This signature algorithm, resistant to quantum algorithm attacks, offers higher security at the cost of a slight efficiency reduction compared to traditional NTRU signature algorithms, and features Nyberg-Rueppel message recovery, making it well-suited for IoT applications.