Authenticated key exchange protocol using neural cryptography with secret boundaries

Key exchange is one of the major concerns in cryp-tology. Neural cryptography is a recent non-classical paradigm which achieves key exchange by mutual learning between two neural networks that receive the same input patterns and update their weights using specific rules. Each weight component of the network can be seen as a random walker in the weight space. The two walkers move in the weight space and reflect at two boundaries (left and right) which represent the network synaptic depth. The reflecting boundaries cause the distance between the two walkers decreases if one of them hits the boundary when a common direction is chosen at each step. Therefore, the mutual learning algorithm relies on this defined boundary condition to achieve synchronization between the two parties. In this paper, we aim to increase the security of the neural cryptography by authenticating the communication using preshared secrets. The mutual learning algorithm is modified so that the reflecting boundaries become hidden and only accessible by the two partners. New update rules are developed to exploit the secret information without adding any limitation to the initial configuration for the two parties. This is done by converting the two boundaries located at a straight line path to a one secret boundary located randomly at a circular path. Therefore, the mutual learning is impeded except this secret information is known. The proposed algorithm is called Neural Cryptography with Secret Boundaries (NCSB) and it is proved with information theory that the secret boundaries can not be revealed from the public information broadcast through the public channel.