This paper studies the design of cooperative beamforming (CB) and cooperative jamming (CJ) for the physical layer security of an amplify-and-forward (AF) relay network in the presence of multiple multi-antenna eavesdroppers. The secrecy rate maximization (SRM) problem of such a network is to maximize the difference of two concave functions, a problem which is non-convex and has no efficient solution. Based on the inner convex approximation (ICA) and semidefinite relaxation (SDR) techniques, we propose two novel low-complexity schemes to design CB and CJ for SRM in the AF network. In the first strategy, relay nodes adopt the CB only to secure transmission. Based on ICA, this design guarantees convergence to a Karush-Kuhn-Tucker (KKT) solution of the SDR of the original problem. In the second strategy, the optimal joint CB and CJ design is studied and the proposed joint design can guarantee convergence to a KKT solution of the original problem. Moreover, in the second strategy, we prove that SDR always has a rank-1 solution for the SRM problem. Simulation results show the superiority of the proposed schemes.