Digital chaotic ciphers have been investigated for more than a decade. However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed. We propose a chaotic Feistel cipher and a chaotic uniform cipher. Our plan is to examine crypto components from both dynamical-system and cryptographical points of view, thus to explore connection between these two fields. In the due course, we also apply dynamical system theory to create cryptographically secure transformations and evaluate cryptographical security measures

Chaotic block ciphers: from theory to practical algorithms

We review some of the recent work on chaos-based cryptography. We argue that if a chaotic map f is used in cryptography, then it should be implemented as a bijection FM : D → D, where D is a finite set with cardinality M, such that, for large M, FM ‘approximates well’ the chaotic map f . Several examples, including chaotic block cypher and chaotic public-key encryption algorithm, are given.

Chaos-based Cryptography: an overview

There are many security defects in existing mobile communication systems, such as unidirectional authentication and cipher key transmission in plaintext. With the expansion of the mobile communication services, the mobile security becomes more and more important, but the existing communication systems can not prevent hostile attacks to supply high-quality service because of their defects in security. To solve these problems, we propose a new Security Architecture for Mobile Communication (SAMC), which employs new authentication protocols, chooses different encryption algorithms for different requirements and implements integrity control mechanism. Good security is developed in an open environment with the collaboration of experts. It has the robust security and the outstanding performance, just a slight and acceptable loss.

A new security architecture for mobile communication

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.

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Chaos Cryptography with prescribed Entropy Production

Kocarev gave the first cryptosystems based on the semi-group property of Chebyshev polynomials, which seemed excellent but actually insecure Due to the inherent periodicity of trigonometric function, an attack can easily get plaintext given ciphertext In this paper, we extend Chebyshev polynomials from real number to finite fields to avoid the attack and present the corresponding key exchange scheme, which is secure and practical

A new key exchange scheme based on extended Chebyshev polynomials

We propose a public-key encryption algorithm based on torus automorphisms, which is secure, practical, and can be used for both encryption and digital signature. Software implementation and properties of the algorithm are discussed in detail. We show that our algorithm is as secure as RSA algorithm. In this paper we have generalized RSA algorithm replacing powers with matrix powers, choosing the matrix to be a matrix which defines a two-torus automorphisms, an example of strongly chaotic system.

M. Sterjev

Papers

RSA encryption algorithm based on torus automorphisms