EPiC: Efficient Privacy-Preserving Counting for MapReduce

In the face of an untrusted cloud infrastructure, outsourced data needs to be protected. Fully homomorphic encryption is one solution that also allows performing operations on outsourced data. However, the involved high overhead of today’s fully homomorphic encryption techniques outweigh cloud cost saving advantages, rendering it impractical. We present EPiC, a practical, efficient protocol for the privacy-preserving evaluation of a fundamental operation on data sets: frequency counting. In an IND-CPA encrypted outsourced data set, a cloud user can specify a pattern, and the cloud will count the number of occurrences of this pattern in a completely oblivious manner. A pattern is expressed as a boolean formula on the fields of the records and can specify values counting, range counting, and conjunctions/disjunctions of field values. EPiC’s main idea is, first, to reduce the problem of counting to a summation of polynomial evaluations. Second, to efficiently evaluate the summation of polynomial evaluations in a privacy-preserving manner, we extend previous work on the Hidden Modular Group Order assumption and design a new somewhat homomorphic encryption scheme. We show how a general pattern, defined by a boolean formula, is arithmetized into a multivariate polynomial over GF (2) and used in EPiC. This scheme is highly efficient in our particular counting scenario. Besides a formal analysis where we prove EPiC’s privacy, we also present implementation and evaluation results. We specifically target Google’s prominent MapReduce paradigm as offered by major cloud providers. Our evaluation performed both locally and in Amazon’s public cloud with data sets sizes of up to 1 TByte shows only modest overhead compared to non-private counting, attesting to EPiC’s efficiency.