# Light-Weighted Password-Based Multi-Group Authenticated Key Agreement for Wireless Sensor Networks
## 1 Introduction
Although these approaches do not require the maintenance of public key systems, all communicating users share the same password so these protocols do not protect the privacy of users. In 2013, [PERSON] et al. [14] proposed a password-based group-authenticated key agreement protocol for the integrated electronic patient record (EPR) information system, which enabled users to have their own passwords. A multi-server authentication protocol based on dynamic identity is proposed by [PERSON] et al. [15]. [PERSON] et al. [16] demonstrated that [PERSON] et al. 's protocol [17] is not protected against the user anonymity problem and cannot resist user impersonation and session key discloser attack. In 2017, [PERSON] et al. [18] applied an extended chaotic map to present password-less group authentication key agreement which improves the computation efficiency for the simple group password-based authenticated key agreement (SGPAKE) proposed by [PERSON] et al [19]. Although most limitations in the field of security have been overcome, the above protocols require many time-consuming modular exponential computations or scalar multiplications on elliptic curves and so are inefficient  
Figure 1: In a key hypergraph, one sensor node is allowed to belong to multiple independent groups. and unsuitable for use in many practical scenarios. Moreover, most of them are difficult to extend to multiple groups. Recently, a number of key agreement protocols based on chaotic maps were proposed, which have improved computational efficiency. Using Chebyshev chaotic maps has been shown to be more efficient than cryptography using modular exponential computations and scalar multiplications on elliptic curves [20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. However, Chebyshev chaotic maps and their enhancement are affected by the discrete logarithm problem and the Diffie-Hellman problem [30; 31; 32; 33]. In addition, most of them were developed for two communication entities (two-party) or three communication entities (three-party), and can only be extend to group key agreement protocol with difficulty. In our analysis, we present a novel password-based multi-group authenticated key agreement protocol for WSNs that was based on the extended chaotic map-based Diffie-Hellman problem. The main contributions of this paper are:  
(1). The proposed protocol enables one sensor node to belong to several mutually independent groups and ensures group key security. Additionally, the real identities of group members cannot be revealed. (2). Accordingly, the proposed protocol is suitable for multiple groups and ensures users' anonymity. It overcomes not only the limitations of previously proposed protocols and has a lower computational cost, but also offers greater security and is suitable for WSNs. The remainder of this paper is organized as follows. The primitives used are described in Section 2. The proposed extended chaotic map-based multi-group authenticated key agreement protocol is illustrated in Section 3. In Section 4, we presented the security analysis and overall comparison. The conclusions are drawn in Section 5.