Oblivious stable sorting protocol and oblivious binary search protocol for secure multi-party computation

Multi-party computation (MPC) sorting and searching protocols are frequently used in different databases with varied applications, as in cooperative intrusion detection systems, private computation of set intersection and oblivious RAM. Ivan Damgard et al. have proposed two techniques i.e., bit-decomposition protocol and bit-wise less than protocol for MPC. These two protocols are used as building blocks and have proposed two oblivious MPC protocols. The proposed protocols are based on data-dependent algorithms such as insertion sort and binary search. The proposed multi-party sorting protocol takes the shares of the elements as input and outputs the shares of the elements in sorted order. The proposed protocol exhibits O ( 1 ) constant round complexity and O ( n log n ) communication complexity. The proposed multi-party binary search protocol takes two inputs. One is the shares of the elements in sorted order and the other one is the shares of the element to be searched. If the position of the search element exists, the protocol returns the corresponding shares, otherwise it returns shares of zero. The proposed multi-party binary search protocol exhibits O ( 1 ) round complexity and O ( n log n ) communication complexity. The proposed multi-party sorting protocol works better than the existing quicksort protocol when the input is in almost sorted order. The proposed multi-party searching protocol gives almost the same results, when compared to the general binary search algorithm.