We develop a new integrated communications and security (ICAS) design paradigm by leveraging the concept of reconfigurable intelligent surfaces (RISs). In particular, we propose RIS-assisted simultaneous transmission and secret key generation by sharing the RIS for these two tasks. Specifically, the legitimate transceivers intend to jointly optimize the data transmission rate and the key generation rate by configuring the phase-shift of the RIS in the presence of a smart attacker. We first derive the key generation rate of the RIS-assisted physical layer key generation (PLKG). Then, to obtain the optimal RIS configuration, we formulate the problem as a secure transmission (ST) game and prove the existence of the Nash equilibrium (NE), and then derive the NE point of the static game. For the dynamic ST game, we model the problem as a finite Markov decision process and propose a model-free reinforcement learning approach to obtain the NE point. Particularly, considering that the legitimate transceivers cannot obtain the channel state information (CSI) of the attacker in real-world conditions, we develop a deep recurrent Q-network (DRQN) based dynamic ST strategy to learn the optimal RIS configuration. The details of the algorithm are provided, and then, the system complexity is analyzed. Our simulation results show that the proposed DRQN based dynamic ST strategy has a better performance than the benchmarks even with a partial observation information, and achieves "one time pad" communication by allocating a suitable weight factor for data transmission and PLKG.