# A Lightweight Chaotic Map-Based Key Agreement Scheme for the Advanced Metering Infrastructure
## 1 Introduction
In [11], a key agreement scheme based on the elliptic curve was designed for the smart grid, but it was proved by [12] that the scheme cannot complete the authentication process in practical application scenarios. In [13], an authentication and key agreement scheme based on elliptic curves was proposed for smart grid environments that can satisfy forward confidentiality. In [14], a DRMAS scheme for identity authentication in demand response management in smart grid environment was proposed, which is based on the elliptic curve and the certificate. The use of the certificate and elliptic curve cryptosystem results in higher overheads. In [15], a lightweight authentication protocol was proposed for the smart metering infrastructure. The protocol is based on one-way hash and an elliptic curve, which can meet the security characteristics such as anonymity and mutual authentication. However, the scheme proved to be fragile in the face of impersonation attacks and key leakage attacks, and could not provide forward secrecy. In [16], in order to protect the secure communication between users and substations, an authentication scheme was designed using the elliptic curve cryptosystem. It was proved in [2] that the scheme could not provide anonymous and forward secrecy security features and could not resist ESL (Ephemeral Secret Leakage) attacks. In [17], a privacy protection and lightweight authentication scheme based on elliptic curves was proposed to achieve secure communication between SMs and neighbor area network gateways. In [18], [PERSON] et al. 's scheme [19] was proven to fail to satisfy security characteristics such as anonymity, and a lightweight key agreement scheme based on elliptic curves was proposed to establish a secure channel for data transmission in the smart grid environment. In [20], a blockchain-based privacy preserving authentication scheme was proposed for demand response management in the smart grid environment, establishing a secure channel between smart meters and service providers. However, the above schemes still have deficiencies in security, and still need more computational and communication overheads compared with other non-bilinear mapping and non-elliptic curve schemes. In recent years, many scholars have proposed key agreement schemes based on chaotic maps. The chaotic map is a kind of random nonlinear process with high initial value sensitivity, high complexity and good confidentiality. The chaotic map based on the Chebyshev polynomial originates from the expansion of a multi-angle cosine function and sine function, which is very suitable for the design of cryptography and secure communication schemes. The definition and properties are shown in Section 2. According to relevant research, the cost of chaotic mapping is only about one-third of the elliptic curve point multiplication operation, which can greatly reduce the operation cost. Compared with bilinear pairing and elliptic curves, chaotic maps have lower computational complexity and higher security. [PERSON] et al. [21] proposed a lightweight authentication scheme for electric vehicle charging, but it was proved that the scheme had errors in the registration and key agreement stages, and could not achieve secure communication [22]. In [23], for the Internet of Vehicles environment, a group key agreement scheme based on chaotic map and bilinear pairing was designed which can support batch authentication. In [24; 25], an efficient authentication and group authentication protocol based on chaotic mapping was designed for the Internet of Vehicles. In [26], a three-factor authentication scheme based on the chaotic map was designed for mobile devices, which can meet the corresponding security evaluation criteria. However, the above schemes do not conform to the architecture and message transmission mode of the AMI and cannot be directly applied to the advanced metering infrastructure.