Secure Determining of the k-th Greatest Element Among Distributed Private Values

One of the basic operations over distributed data is to find the k-th greatest value among union of these numerical data. The challenge arises when the datasets are private and their owners cannot trust any third party. In this paper, we propose a new secure protocol to find the k-th greatest value by means of secure summation sub-protocol. We compare our proposed protocol with other similar protocols. Specially, we will show that our scheme is more efficient than the well-known protocol of Aggarwal et.al. (2004) in terms of computation and communication complexity. Specifically, in the case of T
_i
= 1 secret value for any party P
_i
our protocol has log m computation overhead and δ log m communication overhead for party P
_i
, where m and δ are the maximum acceptable value and communication overhead of the secure summation sub-protocol, respectively. The overheads of our protocol is exactly half of the overheads of Aggarwal's protocol.