Secret-Key Exchange Through Synchronization of Randomized Chaotic Oscillators Aided by Logistic Hash Function

We have developed a method of secret-key exchange assisted by a secure hash algorithm for a stream cipher based on the augmented Lorenz map as a high-dimensional chaotic map. Two legitimate users are assumed to possess chaotic oscillators subject to the original Lorenz equations to exchange randomized chaotic signals. The oscillators achieve perfect synchronization and generate a sequence of binary numbers to be shared as the secret key. The users, as well as an eavesdropper, cannot estimate the synchronization error because of the randomization of chaotic signals. Nevertheless, only the legitimate users have high confidence in sharing the secret key because of the dynamical stability of the synchronization process. The users can confirm the sharing of the secret key by exchanging the hash values of the keys that are generated by a secure hash algorithm based on the logistic map. We discuss the performance of our method with reference to the results of numerical experiments.