In this brief, we consider a class of nonlinear discrete-time systems and prove conditions for the generation of signals with n-dimensional uniform probability distribution. To obtain this result we prove the invariance of the Frobenius-Perron-Operator on a finite-dimensional function space. Spectral properties of the generated signal, as well as the influence of an input signal on the signal characteristics are discussed.

Chaotic and classical (binary) stream ciphers are compared with respect to their cryptographical properties. Possible synchronization schemes, algebraic and analytical properties as well as design and implementation aspects are discussed. For two example classes with similar system structures it is shown that chaotic stream ciphers can achieve a higher level of complexity than classical binary systems due to the algebraic properties of the system structure.

For pt. 2 see Proc. Workshop Nonlinear Dynamic Electron. Syst.., Seville, p. 27-32 (1996). This work deals with the cryptographical analysis of a class of discrete-time continuous-value encryption systems. The design of these systems has been treated in Part I. Here, approaches and criteria used in applied cryptography are adopted for continuous-value systems. Two different ciphertext-only attacks on the encryption system are presented in detail. Based on the analysis, improvements of the coder system are suggested

This paper deals with principles of hiding information by chaotic coders and methods of attacking these encryption systems (cryptoanalysis). After a survey of working principles and cryptographical assumptions the attention is focused on public channel chaotic coding systems where principles of the cryptographical analysis are discussed. Finally a discrete-time chaotic encryption system which has been designed on the condition of public channel and unknown coder structure is treated and two ciphertext-only, public structure attacks are performed.

A systematic top down design of discrete-time continuous-value coder systems for information encryption is presented. From the axioms, that the coder should be a maximally disturbed and invertible (according to the information signal) channel a general structure containing a static nonlinearity and a dynamical subsystem is derived and the system characteristics are specified. It turns out, that the encoder necessarily exhibits chaotic behavior if it satisfies the design axioms. Some examples of systems are given which belong to the designed structural class. Realizations as well as the reliability under the condition of weak disturbances are considered in Part II and a cryptographical analysis is performed in Part III of this paper

This paper deals with the generation of chaotic signals which have a uniform probability distribution up to nth-order. First a generator structure containing a static nonlinearity and a dynamical subsystem is deduced and the system characteristics are specified. Then conditions for the generation of continuous-value signals with nth-order uniform distribution are derived. For the special case of digital filter structures with chaotic behaviour the condition is simply that one specified parameter has to be an integer. Finally problems of continuous-value and discrete-value analysis and realisation are discussed. Some simulation results are provided

This paper describes and analyses a method for coding signals based on digital filter structures with two's complement overflow characteristic. First the basic principle is introduced. Second the encoder-decoder-system is compared with classical (simple) cryptographic systems and analysed using methods known from cryptoanalysis. Then encoding and decoding of ASCII text and bitmap pictures as well as speech and music are shown as application examples. The influence of transmission errors on the decoded signals is discussed