Consider two, not necessarily identical, powerful computers or computer-grids connected by a unidirectional communication link that should transfer a long stream of information in the presence of a listening adversary that is slightly weaker. We present schemes that enhance the computation strength gap between the powerful computers and the adversary. In other words, the gap between the amount of information decrypted by the adversary and the information decrypted by the receiver grows with time. We also suggest schemes based on the shortest vector problem in which only the receivers are computationally powerful. The scheme is self-stabilizing in the sense that it can establish a security level without relying on (previously distributed private keys that are part of) the state. The iterative nested approach suggested, can be used for enhancing the security of the classical protocol of Ralph Merkle . Several applications for sensor networks and for secure communication with survivors are suggested.