The k th-Ranked Element

In this chapter we describe the construction of Aggarwal et al. [1] for securely computing the kth-ranked element of the union of two distributed and sorted data sets in the presence of semi-honest and malicious adversaries. An important special case of this problem is that of securely computing the median. The construction of [1] is based on the iterative protocol of [74] for computing the kth-ranked element with low communication complexity. The secure implementation of this fundamental problem has been looked at by researchers in the last few years, mostly due to its potential applications. One particular setting is where the data sets contain sensitive data, yet the particular kth element is of mutual interest. For instance, two health insurance companies may wish to compute the median life expectancy of their insured smokers, or two companies may wish to compute the median salary of their employees. By running secure protocols for these tasks, sensitive information is not unnecessarily revealed.