The integration of information technologies into the current power grid has raised significant security concerns for the advanced metering infrastructure (AMI). Evidently, without employing proper security measures, illegal or malicious entities could launch miscellaneous attacks. Thus, scholars have presented several key agreement schemes, which can be used by different parties in the AMI guaranteeing their subsequent secure communications. However, after careful deliberation, we found that their efficiency could be still improved while keeping the desired security properties. Thus, in this paper, utilizing the Chebyshev chaotic maps, as one of the most efficient security methods, we first propose a novel certificateless anonymous authentication and key agreement scheme that both enhances the security and reduces the overhead on the computationally constrained measurement devices. To be more specific, we propose a novel signature scheme in the Chebyshev cryptosystem in order to make our protocol certificateless eliminating the key escrow issue and certificate management overhead. By the way, the proposed scheme is the first Chebyshev chaotic map-based key agreement protocol that is certificateless. Then, we validate the security of the proposed scheme using the random oracle model and ProVerif tool as two well-known and popular formal techniques. Our comprehensive functionality, communication cost, and execution time comparisons indicate the superiority of our scheme compared to the all related schemes in terms of both security and efficiency. For a key agreement, the execution time of the proposed scheme is just 539 microseconds, and its communication overhead is only 1088 bits, much better than the existing related ones.

将信息技术集成到当前的电网中已经引起了高级计量基础架构（AMI）的重大安全隐患。显然，如果不采取适当的安全措施，非法或恶意实体可能会发起其他攻击。因此，学者们提出了几种关键的协议方案，可以由AMI中的不同方使用，以保证其随后的安全通信。但是，经过深思熟虑，我们发现可以在保持所需安全性的同时提高效率。因此，在本文中，利用Chebyshev混沌图作为最有效的安全方法之一，我们首先提出了一种新颖的无证书匿名认证和密钥协商方案，该方案既可以提高安全性，又可以减少计算受限的测量设备的开销。更具体地说，我们在Chebyshev密码系统中提出了一种新颖的签名方案，以使我们的协议无证书，从而消除了密钥托管问题和证书管理开销。顺便说一下，提出的方案是第一个基于Chebyshev混沌图的无证书密钥协商协议。然后，我们使用随机预言模型和ProVerif工具作为两种众所周知且流行的形式化技术来验证所提出方案的安全性。我们全面的功能，通讯成本，执行时间的比较表明，在安全性和效率方面，我们的方案比所有其他方案都优越。对于一个关键协议，该方案的执行时间仅为539微秒，其通信开销仅为1088位，远优于现有的相关方案。