Shuffle to Baffle: Towards Scalable Protocols for Secure Multi-party Shuffling

In secure multi-party shuffling, multiple parties, each holding an input, want to agree on a random permutation of their inputs while keeping the permutation secret. This problem is important as a primitive in many privacy-preserving applications such as anonymous communication, location-based services, and electronic voting. Known techniques for solving this problem suffer from poor scalability, load-balancing issues, trusted party assumptions, and/or weak security guarantees. In this paper, we propose an unconditionally-secure protocol for multi-party shuffling that scales well with the number of parties and is load-balanced. In particular, we require each party to send only a polylogarithmic number of bits and perform a polylogarithmic number of operations while incurring only a logarithmic round complexity. We show security under universal compos ability against up to about n/3 fully-malicious parties. We also provide simulation results in the full version of this paper showing that our protocol improves significantly over previous work. For example, for one million parties, when compared to the state of the art, our protocol reduces the communication and computation costs by at least three orders of magnitude and slightly decreases the number of communication rounds.