## 4 Conclusions and Discussion on Future Directions of Smart Grids  
In the above, we have looked at the latest trends in smart grid and state-of-the-art research for secure data aggregation. The majority of countries around the world are implementing and realizing deployment policies for the popularization of the smart grid to meet the goals of low carbon emissions, efficient and reliable supply chains, and the liberalization of choices. At the same time, they are promoting interoperability in industry through standardization and regularization. There might arise various disputes over replacing existing power grid systems with intelligent smart grid counterparts in the present transition stage. However, considering current and future developments, it is necessary to recognize the tremendous advantages of the smart grid. The research on privacy-preserving data aggregation in smart grid environments is evolving in various aspects with respect to:  
* Privacy preservation: To achieve privacy protection during data transmission, semantically secure encryption algorithms are employed. Additionally, (additive) homomorphic encryption supporting evaluations on encrypted data such as ElGamal, Paillier, and lattice-based cryptosystems are being adopted in order to protect user privacy. Depending on the subject to be protected, all kinds of participating entities such as smart appliances, smart meters, (intermediate) gateways, and central controllers are taken into account. * Authentication: To produce accurate aggregate results, various kinds of authentication algorithms are being adopted. According to the situation, sender authentication that validates data origin is considered. Some algorithms are used in upstream directions to check forwarding entities during the process of transferring metering data to the central controller, while others are used to identify the central controller in downstream directions during delivery of decisions made from aggregate data. On the other hand, data authentication is combined with the above approaches to avoid false data injection attacks from malicious adversaries or unintended malfunctions. * Efficiency: In terms of computational efficiency, lightweight encryption algorithms are designed through modification of the existing homomorphic encryption schemes. Batch verification algorithms are also considered in the validation of received data authenticity. In terms of communication efficiency, data aggregation itself is devised to minimize the size of transmitted data with the modification of internal data structures. Furthermore, short signature schemes are also adopted in authentication mechanisms. In the metering data aggregation schemes presented so far, erroneous insertions by external intervention such as false data injection can be detected through authentication. However, not only the validation of smart meters participating in aggregation but also the validation of aggregated information should be considered at the same time for secure smart metering because metering data can be threatened by both the insider and outsider adversaries during the aggregation and transmission in the grid network. Although most of the state-of-the-art schemes adopted additive homomorphic encryption such as the Paillier cryptosystem, fully homomorphic encryption (FHE) would be more appropriate for complex statistical analysis at the central controller. However, since the current FHE requires computationally infeasible overheads for resource-limited smart meters in practice; designing more practical aggregation algorithms that satisfy both the security and scalability requirements will be an open problem in the smart grid system. Additionally when it comes to the authenticated aggregation, majority of state-of-the-art studies handle message authentication and data origin authentication assuming that smart meters are trustworthy. However, in practice, we need to consider more practical threat models.