# Improving Throughput of Mobile Sensors via Certificateless Signature Supporting Batch Verification
## 1 Introduction  
A smart grid is a new type of network based on multiple power devices, which integrates a power data transmission function and power transmission function. These terminal devices often have limited hardware resources while generating mass data. How to increase throughput while ensuring data validation with limited hardware resources is an urgent problem that smart grids face. The validation of power data ensures, on the one hand, the integrity of data. Integrity directly affects the statistical, regulatory, and distribution of the electricity resources. In addition, considering the uncertain work environment of these devices, it is inevitable that sensor equipment malfunctions lead to data anomalies. At this point, it is necessary to quickly locate the device sending the abnormal data. Therefore, tracing the source of the error data is also a function that needs to be implemented. Digital signature technology can protect data from tampering and repudiation, which is sufficient for the data requirements of smart grids. The earliest digital signature schemes mostly relied on the public-key infrastructure (PKI) setting, which bound user identity and public key information through the issuance of certificates by a CA (a certificate authority). However, this certificate can bring complex certificate management issues to the system and have high requirements for communicationbandwidth and storage resources for devices so that it is unsuitable for grid devices. To address this issue, cryptography researchers have proposed identity-based cryptosystems (IBCs) [1; 2] that directly use some identifiable information as public keys, such as phone numbers and email addresses. However, the private key comes entirely from the private key generator (PKG) in IBCs. This centralized trust dependency brings serious key escrow problems. Once the PKG center is attacked, it brings security issues to all subordinate devices. The certificateless public-key cryptosystem (CLPKC) inherits the advantages of the previous systems. In the CLPKC, there is neither certificates nor the problem of key escrow. Therefore, the CLPKC is more suitable for smart grid equipment in resource constrained scenarios. In detail, many smart grid sensors are embedded with sequential numbers in the equipment. The sequential numbers can be treated as identities of the users in the systems and can be used to verify signatures or trace the origin of the message. On the other hand, the identity-based setting is not enough for the smart grid environment since there are large numbers of nodes in the system and it is not easy to select a widely adopted and fully trusted third party as the PKG. Therefore, certificateless cryptography is a prominent candidate for such a system. As is known to all, the pairing operations are comparatively complex and take much more time for computation than other group structures like the elliptic curve setting. However, many certificateless cryptographic schemes share similar algebraic structures to the identity-based constructions and are built upon pairing-friendly groups. Pairing-free certificateless signature schemes have not been widely developed, especially the scheme derived from the national cryptographic standard. To sum up, signature schemes that satisfy the pairing-free, certificateless setting, based on the published standard have many applications in smart grid system. Unfortunately, few constructions have been studied in the literature. In addition, due to the high real-time requirements of data in the power system, the signature algorithm used must be able to calculate quickly [3]. The terminal node may generate electricity data at any time, and the server will receive multiple data streams from multiple nodes at the same time. The server must be able to quickly process signature verification, which requires the signature algorithm to preferably support batch verification. In these systems, both efficiency [4] and privacy-preserving properties [5] need to be taken into consideration.