Secrecy: Secure collaborative analytics on secret-shared data

We study the problem of composing and optimizing relational query plans under secure multi-party computation (MPC). MPC enables mutually distrusting parties to jointly compute arbitrary functions over private data, while preserving data privacy from each other and from external entities. In this paper, we propose a relational MPC framework based on replicated secret sharing. We define a set of oblivious operators, explain the secure primitives they rely on, and provide an analysis of their costs in terms of operations and inter-party communication. We show how these operators can be composed to form end-to-end oblivious queries, and we introduce logical and physical optimizations that dramatically reduce the space and communication requirements during query execution, in some cases from quadratic to linear with respect to the cardinality of the input. We provide an efficient implementation of our framework, called Secrecy, and evaluate it using real queries from several MPC application areas. Our results demonstrate that the optimizations we propose can result in up to 1000x lower execution times compared to baseline approaches, enabling Secrecy to outperform state-of-the-art frameworks and compute MPC queries on millions of input rows with a single thread per party.