Private Set Operations Over Encrypted Cloud Dataset and Applications

We introduce the notion of private set operations (PSO) as a symmetric-key primitive in the cloud scenario, where a client securely outsources his dataset to a cloud service provider and later privately issues queries in the form of common set operations. We define a syntax and security notion for PSO and propose a general construction that satisfies it. There are two main ingredients to our PSO scheme: an adjustable join (Adjoin) scheme (MIT-CSAIL-TR-2012-006 (2012) Cryptographic treatment of CryptDB's adjustable join. http://people.csail.mit.edu/nickolai/papers/popa-join-tr.pdf) and a tuple set (TSet) scheme (Cash, D., Jarecki, S., Jutla, C. S., Krawczyk, H., Rosu, M.-C., and Steiner, M. (2013) Highly-Scalable Searchable Symmetric Encryption With Support for Boolean Queries. 33rd Annual Cryptology Conf., Santa Barbara, CA, August 18-22, pp. 353-373. Springer, Berlin, Heidelberg). We also propose an Adjoin construction that is substantially more efficient (in computation and storage) than the previous ones (Mironov, I., Segev, G., and Shahaf, I. (2017) Strengthening the Security of Encrypted Databases: Non-Transitive Joins. 15th Int. Conf., TCC 2017, Baltimore, MD, USA, November 12-15, pp. 631-661. Springer, Cham) due to the hardness assumption that we rely on, while retaining the same security notion. The proposed PSO scheme can be used to perform join queries on encrypted databases without revealing the duplicate patterns in the unqueried columns, which is inherent to an Adjoin scheme. In addition, we also show that the PSO scheme can be used to perform Boolean search queries on a collection of encrypted documents. We also provide standard security proofs for our constructions and present detailed efficiency evaluation and compare them with well-known previous ones.