Distributed Secure Sparse Modeling Based on Random Unitary Transform

Data analysis on edge/cloud computing systems is becoming more important. However, if the information being analyzed may leak personal identification, the owners tend to withhold or partially block the data to ensure privacy protection. The resulting data is often insufficiently detailed to permit useful analysis. As a result, the desired analysis accuracy may not be achieved. To deal with this issue, several studies have examined encryption systems that support data analysis of encrypted data. Among the likely encryption systems, we focus on those based on the random unitary transform. This is because the random unitary transform offers lower computational complexity than other encryption approaches, and several signal processing algorithms have been proposed. However, analysis models for distributed encrypted data, have not been studied deeply enough. In this paper, we construct an analysis model for random unitary transform encrypted data by deriving a sparse model based on the elastic-net solution. The analytical model can derive the same elastic-net solution as that yielded by processing the original data (i.e. without encryption). The analytical model supports distributed encryption, where different parts of a data set are encrypted at different sites independently. Moreover, the proposed encryption model solves the problem that the security strength of random unitary transform decreases under certain conditions. Data aggregation after distributed encryption improves the accuracy of analyzing distributed privacy-sensitive information.