MDA-FLH: Multidimensional Data Aggregation Scheme With Fine-Grained Linear Homomorphism for Smart Grid

Privacy-preserving multidimensional data aggregation (MDA) aggregates the data of all different users into a single value, preventing the leakage of personal data while ensuring its availability. However, most current MDA schemes only consider sum operations, i.e., the message of each dimension in the aggregation result is the sum of the corresponding dimensional messages of all individual message vectors. We propose an MDA scheme with fine-grained linear homomorphism, called MDA-FLH. First, we construct a fine-grained linear homomorphic encryption scheme which can assign different weights to each dimension of user's data and maintain the linear homomorphic property in each dimension. We combine the Chinese remainder theorem (CRT) and Paillier encryption to encode the multidimensional data with CRT and assign different weights to each dimension of user's data in the Paillier ciphertext. Second, our scheme has the property of fault tolerance. In conjunction with the extended Shamir's threshold secret-sharing scheme, a security-enhanced and fault-tolerant data aggregation method has been designed so that it is resistant to internal attacks such as the control center (CC) access to individual private data if given the corresponding ciphertext. Finally, two practical schemes are designed based on MDA-FLH: 1) fine-grained electricity price statistics scheme and 2) multistep electricity price statistics scheme. Security analysis shows that our scheme can achieve privacy, confidentiality, integrity, and source authentication. Performance analysis shows that our scheme is efficient, especially that smart meters (SMs) are computationally economic, which makes our scheme more suitable for resource-constrained SM. Also, our scheme can provide linear homomorphism operations on each dimension, which further expands its applications.