Comparison-based MPC in Star Topology

Abstract

With the large amount of data generated nowadays, analysis of this data has become eminent. Since a vast amount of this data is private, it is also important that the analysis is done in a secure manner. Comparison-based functions are commonly used in data analysis. These functions use the comparison operation as the basis. Secure computation of such functions have been discussed for median by Aggarwal et al. (EUROCRYPT’04) and for convex hull by Shelat and Venkitasubramaniam (ASIACRYPT’15). In this paper, we present a generic protocol for the secure computation of comparison-based functions. In order to scale to a large number of participants, we propose this protocol in a star topology with an aim to reduce the communication complexity. We also present a protocol for one specific comparison-based function, the kt h ranked element. The construction of one of our protocols leaks some intermediate values but does not reveal information about an individual party’s inputs. We demonstrate that our protocol offers better performance than the protocol for kt h ranked element by Tueno et. al. (FC’20) by providing an implementation.