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A connection between the theory of neural networks and cryptography is presented. A new phenomenon, namely synchronization of neural networks is leading to a new method of exchange of secret messages. Numerical simulations show that two artificial networks being trained by Hebbian learning rule on their mutual outputs develop an antiparallel state of their synaptic weights. The synchronized weights are used to construct an ephemeral key exchange protocol for a secure transmission of secret data. It is shown that an opponent who knows the protocol and all details of any transmission of the data has no chance to decrypt the secret message, since tracking the weights is a hard problem compared to synchronization. The complexity of the generation of the secure channel is linear with the size of the network.PACS numbers: 87.18.Sn,89.70.+cThe ability to build a secure channel is one of the most challenging fields of research in modern communication. Since the secure channel has many applications, in particular for mobile phone, satellite and internet-based communications, there is a need for fast, effective and secure transmission protocols [1]. Here we present a novel principle of a cryptosystem based on a new phenomenon which we observe for artificial neural networks.The goal of cryptography is to enable two partners to communicate over an insecure channel in such a way that an opponent cannot understand and 1

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In simulations of laser models and experiments with electronic circuits, we identify transitions from weak to strong and back to weak chaos upon monotonically increasing the coupling strength.

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