# PUF and Chaotic Map-Based Authentication Protocol for Underwater Acoustic Networks
## 1 Introduction
### Related Work  
In 2019, [PERSON] et al. [3] proposed a security-enhanced authentication and key agreement scheme for WSN, but their scheme cannot resist offline password guessing attacks, impersonation attacks, and does not achieve session key secrecy, identity unlinkability, and perfect forward secrecy. In 2020, [PERSON] et al. [4] proposed an authentication scheme for WSN in IoT environments, but their scheme is vulnerable to offline password guessing attacks, impersonation attacks, and fails to achieve perfect forward secrecy, user anonymity, and unlinkability. In 2021, [PERSON] et al. [5] presented a lightweight authentication protocol for WSN environments using ECC to prevent various security issues. However, their scheme does not provide perfect forward security and suffers from desynchronization attacks and stolen-verifier attacks. Later, [PERSON] et al. [6] presented a two-factor user authentication protocol for smart homes using ECC. [PERSON] et al. [7] presented that [PERSON] et al. 's scheme cannot resist impersonation attacks, session key disclosure attacks, and secure user authentication. They proposed a lightweight authentication scheme to overcome the security problems of [PERSON] et al. 's protocol. In 2021, [PERSON] et al. [8] proposed a user authentication protocol using fuzzy extractor and hash-chain in the IIoT environment. In 2023, [PERSON] et al. [9] proposed a three-factor-based authentication scheme of 5G WSN for IoT systems and claimed that their scheme is secure. However, [PERSON] et al. [10] pointed out that their scheme is vulnerable to user impersonation attacks, sensor node impersonation attacks, and capture attacks, and lacks user unlinkability and three-factor secrecy. Recently, chaotic map has been widely concerned since it has better security and performance than traditional cryptography. The difficulty of the chaotic map's Diffie-Hellman problem and its semi-group property make it feasible to establish secure session keys. In addition, the computation overhead of a Chebyshev polynomial is approximately \(1/3\) of the scalar multiplication on elliptic curves [11]. It significantly reduces the computing overhead and energy consumption of resource-constrained sensor nodes, which is more suitable for devices with a limited battery life and smaller computation power. In 2015, [PERSON] et al. [12] proposed a three-party authenticated key agreement scheme based on chaotic maps without a password table. [PERSON] et al. [13] showed that the scheme of [PERSON] et al. fails to guarantee user anonymity and put forward an improved scheme. In 2016, [PERSON] et al. [14] introduced a two-factor authentication scheme for WSN using the chaotic map. However, the protocol of [PERSON] et al. suffers from sensor node impersonation attacks [15]. In 2018, [PERSON] et al. [16] proposed an efficient three-factor authentication scheme for WSN using the hash function. However, [PERSON] et al. [17] showed that the scheme does not provide security against session key disclosure attacks, desynchronization attacks, sensor node impersonation attacks, and session-specific temporary information attacks. Besides, they presented an improvement protocol for WSN using chaotic maps. In 2019, [PERSON] et al. [18] introduced a multi-server authentication protocol using extended chaotic maps. However, [PERSON] et al. [19] found that their protocol is insecure against user impersonation attacks,session-specific temporary information attacks, and time synchronization problems, and proposed another protocol based on extended chaotic maps. In 2021, [PERSON] et al. [20] proposed a chaotic map-based authentication protocol for an industrial medical cyber-physical system. However, [PERSON] et al. [21] showed that their protocol is vulnerable to identity guessing attacks, user impersonation attacks, trace attacks, desynchronization attacks, and lacks perfect forward secrecy, and they proposed a security-enhanced one.