In this paper, we investigate the problem of secure communication between secondary users (SUs) and their serving base station in the presence of multiple eavesdroppers and multiple primary users. We analyze the interactions between the SUs and eavesdroppers using the framework of noncooperative game theory. To solve the formulated game, we propose a novel secure channel selection algorithm that enables the SUs and eavesdroppers to take distributed decisions so as to reach a Nash equilibrium point. We study and analyze several properties of the equilibrium resulting from the proposed algorithm. Simulation results show that the proposed approach yields significant improvements of at least 32.7%, in terms of the average secrecy rate per SU, relative to a classical spectrum sharing scheme. Moreover, the results show that the proposed scheme enables the SUs to reach Nash equilibrium with up to 86.5% less computation than standard learning algorithms.