# A Lightweight Chaotic Map-Based Key Agreement Scheme for the Advanced Metering Infrastructure
## 1 Introduction  
The advanced metering infrastructure (AMI) is a complete network processing system for collecting, storing and analyzing user electricity data, which is mainly composed of smart meters (SMs), data concentrators (DCs), the measurement data management system (MDMS), the local communication network, and the communication network connecting power company data center [1]. Among them, the communication network in the AMI includes uplink and downlink networks. The smart meter collects electricity consumption information from the user side and uploads the message to the MDMS through the DC, which belongs to the uplink network, and the process of MDMS transmitting command information from DC to SM belongs to the downlink network [2]. Eavesdropping, tampering and other attacks on the uplink network will lead to the exposure of electricity data and billing fraud, resulting in privacy leakage (such as whether the user is at home, whether the house is idle) and economic losses. Attacks on the downlink network will lead to errors in the command information, which will destroy the normal operation of the power system and can even lead to the paralysis of the whole power system [3, 4]. For example, in 2014, Spanish hackers used meter vulnerabilities to conduct billing fraud and even shut down the entire circuit system, causing a large-scale power outage. In 2019, hackers used a firewall vulnerability to launch a denial-of-service attack against the American electrical company, resulting in equipment communication interruption. In [5], the security vulnerabilities in the AMI were analyzed, and authentication and encryption were pointed out to be effective means to ensure the secure communication ofthe AMI. The secure communication scheme based on asymmetric cryptography has problems such as high communication overheads and multiple interactions during asymmetric encryption and decryption, making it unsuitable for smart meters with limited computing and communication resources. The key agreement mechanism allows both parties to negotiate the same session key before communication and uses symmetric encryption to communicate, which has less computation power and a faster speed. The certificateless key agreement scheme can not only avoid the complex certificate management in public key infrastructure (PKI), but also avoid the key escrow in identity-based cryptography (IBC). It is very suitable for entities in AMI with limited computation and communication resources such as smart meters [6]. In certificateless key agreement schemes, the scheme based on the hash algorithm [7] uses ultra-lightweight hash functions to achieve key agreements, which is suitable for scenarios with very limited communication resources, but cannot meet the security requirements well. In order to enhance security, many key agreement schemes based on bilinear pairing and an elliptic curve have been proposed. Bilinear mapping is simply a mapping \(e\), which can map two elements in the cyclic group \(G_{1}\) and \(G_{2}\) of order \(n\) to one element in \(G_{3}\), and the mapping satisfies bilinearity. The elliptic curve cryptosystem is based on the generalized discrete logarithm problem, and the use of shorter operands can provide the same security level as RSA. In [8], anonymous communication between edge computing infrastructures in smart grid was realized, but the complexity of pairing operation increases the computational overhead. In addition, [9] proved that the scheme struggles to resist impersonation and transient key exposure attacks. In [10], a key exchange scheme named AAS-IoTaSG was proposed for the smart grid environment in the Internet of Things. This scheme is based on the anonymous signature, which allows the dynamic addition of nodes. However, it is proved by [9] that the scheme struggles to resist man-in-the-middle attacks and impersonation attacks.