When working with joint collections of confidential data from multiple
sources, e.g., in cloud-based multi-party computation scenarios, the ownership
relation between data providers and their inputs itself is confidential
information. Protecting data providers' privacy desires a function for secretly
shuffling the data collection. We present the first efficient secure
multi-party computation protocol for secret shuffling in scenarios with a
central server. Based on a novel approach to random index distribution, our
solution enables the randomization of the order of a sequence of encrypted data
such that no observer can map between elements of the original sequence and the
shuffled sequence with probability better than guessing. It allows for
shuffling data encrypted under an additively homomorphic cryptosystem with
constant round complexity and linear computational complexity. Being a
general-purpose protocol, it is of relevance for a variety of practical use
cases