The emergence of new mobile and wireless networks, with novel capabilities, offers opportunities to widen classical Internet-based applications with new ways of use and possibilities. In this paper, we focus on a famous and widely used e-commerce application: auctions, and propose their deployment over ad hoc networks. We prove that such a novel mobile commerce application presents significant advantages with regard to conventional auction models. For the proposed auction model, we have particularly focused on crucial requirements generated by the ad hoc context. Actually, we have identified and then provided security and fairness requirements. Security is provided through threshold cryptography mechanisms, whereas fairness is provided on the basis of rounds duration calculation. Finally, a simulation model of our auctions scheme shows that the theoretical fair round duration can be optimized according to the number of bidders. Performances evaluation presents optimistic results promising a realistic and realizable deployment of this mobile auctions model.