Paper 2012/452

EPiC: Efficient Privacy-Preserving Counting for MapReduce

Erik-Oliver Blass and Guevara Noubir and Triet D. Vo-Huu

Abstract

In the face of an untrusted cloud infrastructure, outsourced data needs to be protected. We present EPiC, a practical protocol for the privacy-preserving evaluation of a fundamental operation on data sets: frequency counting. In an encrypted outsourced data set, a cloud user can specify a pattern, and the cloud will count the number of occurrences of this pattern in an oblivious manner. A pattern is expressed as a Boolean formula on the fields of data records and can specify values counting, range counting, and conjunctions/disjunctions of field values. We show how a general pattern, defined by a Boolean formula, is arithmetized into a multivariate polynomial and used in EPiC. To increase the performance of the system, we introduce a new somewhat homomorphic encryption scheme based on a previous work on the Hidden Modular Group assumption. 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.