Size-hiding computation for multiple parties

Lindell, Nissim, and Orlandi (ASIACRYPT 2013) studied feasibility and infeasibility of general two-party protocols that hide not only the contents of the inputs of parties, but also some sizes of the inputs and/or the output. In this paper, we extend their results to n-party protocols for n ≥ 2, and prove that it is infeasible to securely compute every function while hiding two or more (input or output) sizes. Then, to circumvent the infeasibility, we naturally extend the communication model in a way that any adversary can learn neither the contents of the messages nor the numbers of bits exchanged among honest parties. We note that such “size-hiding”computation is never a trivial problem even by using our “size-hiding”channel, since size-hiding computation of some function remains infeasible as we show in the text. Then, as our main result, we give a necessary and sufficient condition for feasibility of size-hiding computation of an arbitrary function, in terms of which of the input and output sizes must be hidden from which of the n parties. In particular, it is now possible to let each input/output size be hidden from some parties, while the previous model only allows the size of at most one input to be hidden. Our results are based on a security model slightly stronger than the honest-but-curious model.