  Many spectrum auction mechanisms have been proposed for spectrum allocation
problem, and unfortunately, few of them protect the bid privacy of bidders and
achieve good social efficiency. In this paper, we propose PPS, a Privacy
Preserving Strategyproof spectrum auction framework. Then, we design two
schemes based on PPS separately for 1) the Single-Unit Auction model (SUA),
where only single channel to be sold in the spectrum market; and 2) the
Multi-Unit Auction model (MUA), where the primary user subleases multi-unit
channels to the secondary users and each of the secondary users wants to access
multi-unit channels either. Since the social efficiency maximization problem is
NP-hard in both auction models, we present allocation mechanisms with
approximation factors of $(1+\epsilon)$ and 32 separately for SUA and MUA, and
further judiciously design strategyproof auction mechanisms with privacy
preserving based on them. Our extensive evaluations show that our mechanisms
achieve good social efficiency and with low computation and communication
overhead.
