With the increasingly pervasive deployment of fog servers, fog computing extends data processing and analysis to network edges. At the same time, as the next-generation power grid, the smart grid should meet the requirements of security, efficiency, and real-time monitoring of user energy consumption. By utilizing the low-latency and distributed properties of fog computing, it can improve communication efficiency and user service satisfaction in smart grids. For the sake of providing adequate functionality for the power grid, various schemes have been proposed. Whereas, many methods are vulnerable to privacy leakage since the existence of trusted authority may increase the exposure to threats. In this paper, we propose the EPri-MDAS: an Efficient Privacy-preserving Multiple Data Aggregation Scheme without trusted authority based on the ElGamal homomorphic cryptosystem, which achieves both data integrity verification and data source authentication with the most efficient block cipher-based authenticated encryption algorithm. It performs well in energy efficiency with strong security. Especially, the proposed multidimensional aggregation statistics scheme can perform the fine-grained data analyses; it also allows for fault tolerance while protecting personal privacy. The security analysis and simulation experiments show that EPri-MDAS can satisfy the security requirements and work efficiently in the smart grid.

CRAFT is an substitution-permutation network tweakable block cipher proposed at fast software encryption 2019 by Beierle et al., which is designed to optimize the efficient protection against differential fault analysis (DFA) attacks. In this paper, the full round differential characteristics for CRAFT block cipher are given. A new method on counting the number of differentials by using correlation matrix is given. We can compute the number of all optimal characteristics or suboptimum differentials with the same input difference and output difference by hand. We explore the multiple differential trails and compute the probability of differential characteristic by using the multiplication of correlation matrices. Our work complements automatic search methods for the best differential with a careful manual analysis. Since the automatic search method is stranded by storage and search space limitations, which will cause a computer to crash as the number of search rounds increases. Thanks to the correlation matrix technique, we are able to find differential distinguishers for 9-round of the cipher with the probability of at least 2 − 40.68 + 2 − 48.60 ${2}^{-40.68}+{2}^{-48.60}$ . Moreover, we can construct differential distinguisher covers more rounds based on the 9-round differential distinguishers. As one of its typical application, we propose the differential characteristics for the full-round CRAFT which ensure that the probability of each round is optimal. Besides, we explore the clustering effect on the full round by exhibiting a class of high probability characteristics for 9-round. In general, we obtain a good understanding of the propagation of differences for CRAFT due to its algebraic structure.