It is urgent to solve the contradiction between limited spectrum resources and the increasing demand from the ever-growing wireless networks. Spectrum redistribution is a powerful way to mitigate the situation of spectrum scarcity.In contrast to existing mechanisms for spectrum redistribution, which aim to maximize the spectrum utilization and social welfare, we propose DIARY in this paper, which not only achieves approximate revenue maximization, but also guarantees bid privacy via differential privacy. Furthermore, we present an effective method to address the fairness issue in spectrum auctions. Results from extensive evaluations show that DIARY has substantial competitive advantages over existing mechanisms. Keywords Mechanism design Á Differential privacy Á Fairness Á Resource allocation