In this paper, the impact of multiple eavesdroppers on cooperative single carrier systems with multiple relays and multiple destinations is examined. To achieve the secrecy diversity gains in the form of opportunistic selection, a two-stage scheme is proposed for joint relay and destination selection, in which, after the selection of the relay with the minimum effective maximum signal-to-noise ratio (SNR) to a cluster of eavesdroppers, the destination that has the maximum SNR from the chosen relay is selected. In order to accurately assess the secrecy performance, the exact and asymptotic expressions are obtained in closed-form for the ergodic secrecy rate in frequency selective fading. Based on the asymptotic analysis, key design parameters such as multiplexing gain, and power cost are characterized, from which new insights are drawn. Moreover, it is concluded that capacity ceiling occurs when the average received power at the eavesdropper is proportional to the counterpart at the destination.