## 1 Introduction  
With the development of Advanced Metering Infrastructure (AMI), Smart Metering as an important research subject in Smart Grid (SG) plays an increasingly important role and is closely associated with people's daily life [1, 2]. Aggregating fine-grained metering data attracts householders and power suppliers. Power suppliers can calculate, forecast, and regulate accurately power distribution/price of the next period in real time while detecting fraud reports. Based on billing details and current power price, householders can adjust its appliance consumption module to reduce the power billing at the peak time; however, accessing householder's information on metering may cause security and privacy concerns, such as daily routines, the type of applications, etc. [1, 2]. For this, in SG systems, one of the challenges faced by power big data is how to design one aggregation mechanism to balance the use of power data and individual privacy protection [2]. Protecting such sensitive private data from individual privacy threats needs to limit the authority of the utility company employee [2]. Namely, Supplier Billing System (SBS, sub-suppliers) will know only the total amount of the consumption for each customer, while the Energy Management System (EMS, demand prediction division) should know only the total consumption of customers in a certain region for each time period. To achieving the goals, smart metering systems often introduce the MeterData Management System (MDMS), which stores the measured values of smart meters (SMs), and aggregates it before sending the aggregation to the SBS and EMS [2]. With the appearance of MDMS, another concern is upgrading, namely the malicious action of householders and regional MDMS employees. Unfortunately, a malicious householder may collude with the regional MDMS employee to report a false consumption to the SBS department; attackers may steal or forge power usage and consumption information. In addition, a regional MDMS employee may submit a fraudulent aggregation in a neighborhood. A World Bank report finds that each year over 6 billion dollars cannot post due to the energy theft and fraud report in the United States, in 2009, the FBI reported a wide and organized attempt that may have cost up to $400 million loss annually and power supplier suffered a great monetary loss [3]. To fend off this type of attack, it is desirable that suppliers or the public should detect the fraud profile from malicious aggregators or dishonest householders [4]. Privacy-preserving metering protocols have been discussed in lots of literatures [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. They mainly focused on the studies of homomorphic aggregation [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 20; 23; 24], by which, aggregators can only obtain the fine-grained aggregation data within a certain region or householders' billing in a serial period while protecting individual privacy. However, most of them can only resist against single external or semi-trustable attack [11; 13; 14; 19], and how to fend off internal attackers (e.g. aggregators or householders) is an open problem. Internal attackers can legally collect and store power consumption information of users; therefore, they pose a higher threat than external attackers [18]. Most of existing works [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 23; 24] about additively homomorphic, multiplicative homomorphic, and their combination with other cryptography endeavored to address the problem. Most of them improved Paillier encryption [6; 7; 8; 9] by their combination with other cryptography, such as stream ciphers [5; 19; 23] and modular addition [7; 24], to prevent power suppliers/operators from intercepting individual user data, and to detect fraudulent from dishonest users. To ensure the integrity of transmitted messages and fend off attacks such as man-in the middle attack and denial-of-service attack against SG, signature and authentication methods are proposed in References [8; 15; 16; 17].