With the fast development of Internet of Things, huge volume of data is being collected from various sensors and devices, aggregated at gateways, and processed in the cloud. Due to privacy concern, data are usually encrypted before being outsourced to the cloud. However, encryption seriously impedes both computation over the data and sharing of the computation results. Computing maximum and minimum among a data set are two of the most basic operations in machine learning and data mining algorithms. In this paper, we study how to compute maximum and minimum over encrypted data and control the access to the computation result in a privacy-preserving manner. We present four schemes to realize privacy-preserving maximum and minimum computations with flexible access control that can adapt to various application scenarios. We further analyze their security and show their efficiency through extensive evaluations and comparisons with existing work. © 2019 IEEE.