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Chaos Cryptography with prescribed Entropy Production
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1  Complex Systems Analysis Laboratory. Mathematics Department. Aristotle University of Thessaloniki. Thessaloniki 54124, Greece


Cryptography with Chaos was proposed by Shannon in his classic 1949 paper, although the word chaos was not mentioned. This idea has been extended and realized by Chaotic i.e. Entropy producing Torus Automorphisms. The corresponding algorithms and the software have been developed for any Torus Automorphism, adapted to be applicable for encryption in real time. We may select and combine in an arbitrary way several chaotic maps, creating in this way an infinite number of keys. Decryption is simply the reverse application of the selected maps. Therefore, the cryptography is effectively symmetric. The novelties of our work are summarized as follows:

a) The possibility to design classes of chaotic torus maps with any desirable entropy production. The Torus parameters are computed as functions of the selected entropy production.

b) We demonstrate how to design Torus Automorphisms with integer parameters determined from the entropy production.

c) For Torus Automorphisms constructed from the Fibonacci sequence, the parameters are uniquely determined from the entropy production.

d) The Encryption Mechanisms are designed and implemented by selecting and combining the Torus Maps in an arbitrary way. These Encryptions are in fact new classes and examples of MonoBlock Ciphers.

e) The application of Cryptography with Chaos to content with texts and images.

Keywords: Cryptography, Chaos, Torus Automorphisms, Entropy production, Fibonacci sequence