A Round and Communication Efficient Secure Ranking Protocol

In this work, we initiate the study of realizing a ranking functionality (m1, ⋯, mn)↦ (r1, ⋯, rn) in the non-adaptive malicious model, where $r_{i}=+ \sharp \{m_{j}:m_{j} < m_{i}\}$. Generically, it has been solved by a general multi-party computation technique (via a circuit formulation). However, such a solution is inefficient in either round complexity or communication complexity. In this work, we propose an efficient construction without a circuit. Our protocol is constant round and efficient in communication complexity as well. Furthermore, we show it is directly secure in the non-adaptive malicious model (i.e., without a compiler, as is used in many general constructions).