Privacy-preserving min and k-th min computations with fully homomorphic encryption

We design a secure protocol that a server can compute the minimum number of all participants´ data while kept unknown additional information about the users´ data in its execution. Ours protocol is based on fully homomorphic encryption and we utilize it to fix the problem of securely computing the minimum value. Besides, the used FHE scheme is a lattice-based cryptosystem that can resist some quantum adversaries who can carry out quantum computations on classical queries. We also expand the secure min computing protocol to the privacy-preserving the k-th min computing protocol, and present the security analysis of the two protocols on the assumption of the semi-honest model. In the previous literature, their solutions are based on secure arithmetic sum computations as well as secure bitwise XOR computations. Our protocols are more secure with the comparison to them.