Secure Computation of the Median (and Other Elements of Specified Ranks)
 Gagan Aggarwal,
 Nina Mishra,
 Benny Pinkas
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Abstract
We consider the problem of securely computing the kthranked element of the union of two or more large, confidential data sets. This is a fundamental question motivated by many practical contexts. For example, two competitive companies may wish to compute the median salary of their combined employee populations without revealing to each other the exact salaries of their employees. While protocols do exist for computing the kthranked element, they require time that is at least linear in the sum of the sizes of their combined inputs. This paper investigates twoparty and multiparty protocols for both the semihonest and malicious cases. In the twoparty setting, we prove that the problem can be solved in a number of rounds that is logarithmic in k, where each round requires communication and computation cost that is linear in b, the number of bits needed to describe each element of the input data. In the multiparty setting, we prove that the number of rounds is linear in b, where each round has overhead proportional to b multiplied by the number of parties. The multiparty protocol can be used in the twoparty case. The overhead introduced by our protocols closely match the communication complexity lower bound. Our protocols can handle a malicious adversary via simple consistency checks.
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 Title
 Secure Computation of the Median (and Other Elements of Specified Ranks)
 Journal

Journal of Cryptology
Volume 23, Issue 3 , pp 373401
 Cover Date
 20100701
 DOI
 10.1007/s0014501090599
 Print ISSN
 09332790
 Online ISSN
 14321378
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Secure function evaluation
 Secure multiparty computation
 kthranked element
 Median
 Semihonest adversary
 Malicious adversary
 Industry Sectors
 Authors

 Gagan Aggarwal ^{(1)}
 Nina Mishra ^{(2)}
 Benny Pinkas ^{(3)}
 Author Affiliations

 1. Google Research, Mountain View, CA, USA
 2. Search Labs, Microsoft Research, Mountain View, CA, USA
 3. Department of Computer Science, University of Haifa, Haifa, Israel