Efficient and Privacy-Preserving Min and $k$ th Min Computations in Mobile Sensing Systems

Protecting the privacy of mobile phone user participants is extremely important for mobile phone sensing applications. In this paper, we study how an aggregator can expeditiously compute the minimum value or the kth minimum value of all users' data without knowing them. We construct two secure protocols using probabilistic coding schemes and a cipher system that allows homomorphic bitwise XOR computations for our problems. Following the standard cryptographic security definition in the semi-honest model, we formally prove our protocols' security. The protocols proposed by us can support time-series data and need not to assume the aggregator is trusted. Moreover, different from existing protocols that are based on secure arithmetic sum computations, our protocols are based on secure bitwise XOR computations, thus are more efficient.