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In this paper, we study the role of cooperative relays to provide and improve secure communication rates through decode-and-forward (DF) strategies in a full-duplex multiple relay network with an eavesdropper. We consider the DF scheme as a basis for cooperation and propose several strategies that implement different versions of this scheme suited for cooperation with multiple relays. Our goal is to give an efficient cooperation paradigm based on the DF scheme to provide and improve secrecy in a multiple relay network. We first study the DF strategy for secrecy in a single relay network. We propose a suboptimal DF with zero forcing (DF/ZF) strategy for which we obtain the optimal power control policy. Next, we consider the multiple relay problem. We propose three different strategies based on DF/ZF and obtain their achievable secrecy rates. The first strategy is a single hop strategy whereas the other two strategies are multiple hop strategies. In the first strategy, we show that it is possible to eliminate all the relays' signals from the eavesdropper's observation (full ZF), however, the achievable secrecy rate is limited by the worst source-relay channel. Our second strategy overcomes the drawback of the first strategy, however, with the disadvantage of enabling partial ZF only. Our third strategy provides a reasonable compromise between the first two strategies. That is, in this strategy, full ZF is possible and the rate achieved does not suffer from the drawback of the first strategy. We conclude our study by a set of numerical results to illustrate the performance of each of the proposed strategies in terms of the achievable rates in different practical scenarios.