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Hospitals have to use a large amount of medical data from individuals while protecting their privacy to execute medical data mining. It is important to find `rare` cases among medical data of individuals in many healthcare applications. Therefore hospitals need privacy-preserving mining techniques to find rare cases among medical data of individuals. However, previous privacy-preserving data-mining techniques cannot be used to find rare cases. In this study, they suggest a privacy-preserving `range set union` protocol that can be used to find rare cases in the private medical datasets of individuals.