Mix and Match: Secure Function Evaluation via Ciphertexts

We introduce a novel approach to general secure multiparty computation that avoids the intensive use of verifiable secret sharing characterizing nearly all previous protocols in the literature. Instead, our scheme involves manipulation of ciphertexts for which the underlying private key is shared by participants in the computation. The benefits of this protocol include a high degree of conceptual and structural simplicity, low message complexity, and substantial flexibility with respect to input and output value formats. We refer to this new approach as mix and match. While the atomic operations in mix and match are logical operations, rather than full field operations as in previous approaches, the techniques we introduce are nonetheless highly practical for computations involving intensive bitwise manipulation. One application for which mix and match is particularly well suited is that of sealed-bid auctions. Thus, as another contribution in this paper, we present a practical, mix-and-match-based auction protocol that is fully private and non-interactive and may be readily adapted to a wide range of auction strategies.