Outsourcing analyses on privacy-protected multivariate categorical data stored in untrusted clouds

Outsourcing data storage and computation to the cloud is appealing due to the cost savings it entails. However, when the data to be outsourced contain private information, appropriate protection mechanisms should be implemented by the data controller. Data splitting, which consists of fragmenting the data and storing them in separate clouds for the sake of privacy preservation, is an interesting alternative to encryption in terms of flexibility and efficiency. However, multivariate analyses on data split among various clouds are challenging, and they are even harder when data are nominal categorical (i.e., textual, non-ordinal), because the standard arithmetic operators cannot be used. In this article, we tackle the problem of outsourcing multivariate analyses on nominal data split over several honest-but-curious clouds. Specifically, we propose several secure protocols to outsource to multiple clouds the computation of a variety of multivariate analyses on nominal categorical data (frequency-based and semantic-based). Our protocols have been designed to outsource as much workload as possible to the clouds, in order to retain the cost-saving benefits of cloud computing while ensuring that the outsourced stay split and hence privacy-protected versus the clouds. The experiments we report on the Amazon cloud service show that by using our protocols the controller can save nearly all the runtime because it can integrate partial results received from the clouds with very little computation.