Outsourcing scalar products and matrix products on privacy-protected unencrypted data stored in untrusted clouds

Data controllers accumulate more and more data on people, of which a substantial proportion are personally identifiable and hence sensitive data. Storing and processing those data in local premises is increasingly inconvenient, but resorting to cloud storage and processing raises security and privacy issues. We show how to use untrusted clouds to compute scalar products and matrix products on privacy-protected data stored in them. These operations are useful in statistics, linear algebra, data analysis and engineering. In our solutions, the privacy-protected sensitive data stored in the clouds are not encrypted, but preserve some utility (that is, some statistical properties) of the original data. We consider two variants of honest-but-curious clouds: clouds that do not share information with each other and clouds that may collude by sharing information with each other. In addition to analyzing the security of the proposed protocols, we also evaluate their performance against a baseline consisting of downloading plus local computation.