## 1 Introduction  
In the past few years, with the advances of information and communication technologies, users can easily access any service provided in various smart grid (SG) environments, including smart home, smart building, vehicle-to-grid (V2G) and advanced metering infrastructure (AMI) [1; 2; 3; 4]. In particular, smart grid using smart device has attracted growing attention from the academia, industries, and researchers. The SG device (sensing device, smart meter, etc.) is one of the core components, which collects various information (electricity consumption, payment, address, etc.) and transfers it to utility centers (power provider, power distributor, etc.) to provide secure, reliable, and efficient power distribution. According to the report of the U.S. Department of Energy (DoE), since 1988, electricity demand has risen by almost 30%. However, the transmission capacity of electricity has only increased by 15% [5]. Therefore, demand-response management has become an important issue to ensure reliable supply of electricity. In SG environments, the SG devices are deployed in industries, smart buildings, smart homes, etc. and collect many data in real-time, transferring electricity demands to energy generators. However, energy generators cannot efficiently handle these demands because the data collected by SG devices is very large and is difficult to handle it. To address these problems and maintain the efficient stability of supply, utility centers (UCs) analyze the data collected by SG devices and control fault detection, dynamic pricing, load balancing, leakage power, and demand-response [6]. However, the data transmitted between the UC and the SG devices can be tampered, injected, deleted, and forged by a malicious adversary because they are transmitted over an insecure channel [7]. The result of these situations can generate energy imbalances and gaps between energy demand and response. Therefore, authentication and key agreement mechanisms have become essential security requirements for smooth functioning of the SG operations with respect to demand response and data analytics. The security requirements for the SG system are summarized as follows:  
* Secure and efficient authentication and key agreement protocols are essential to ensure secure communication and privacy. * The proposed authentication and key agreement protocol must withstand various attacks such as replay, masquerade, and off-line identity guessing attacks. * Authentication and key agreement protocol should consider SG device limitations with respect to power consumption, communication bandwidth, and memory. In general, for power consumption feedback purposes, a SG relies heavily on the usage of a smart metering infrastructure. For instance, the data of SG device is useful for load forecasting, demand response management, and real-time pricing. However, the recording and transmission of power consumption data may cause serious privacy issues. If fine-grained power consumption data of the SG device is exposed, it can reveal the private information of consumers related to their daily routines or the appliances in the house. In addition, the computation and communication resources at the consumer's side in the SG environments are usually very limited. Therefore, secure and efficient authentication mechanisms for preserving user privacy with low computational costs are essential in resource-constrained SG environments. In 2019, [PERSON] et al. [6] proposed an elliptic curve cryptography (ECC)-based authentication protocol for demand response management in SG system. [PERSON] et al. claimed that their scheme can prevent various attacks. However, this paper shows that their scheme cannot withstand various attacks, including SG device stolen, session key disclosure, and masquerade attacks and cannot ensure secure mutual authentication. Furthermore, their scheme [6] is not suitable for resource-limited smart devices because it uses ECC with high computation and communication overheads.