Biblio
In this article, we introduce a new method for computing fixed points of a class of iterated functions in a finite time, by exponentiating linear multivalued operators. To better illustrate this approach and show that our method can give fast and accurate results, we have chosen two well-known applications which are difficult to handle by usual techniques. First, we apply the exponentiation of linear operators to a digital filter in order to get a fine approximation of its behavior at an arbitrary time. Second, we consider a PID controller. To get a reliable estimate of its control function, we apply the exponentiation of a bundle of linear operators. Note that, our technique can be applied in a more general setting, i.e. for any multivalued linear map and that the general method is also introduced in this article.
In this paper a random number generation method based on a piecewise linear one dimensional (PL1D) discrete time chaotic maps is proposed for applications in cryptography and steganography. Appropriate parameters are determined by examining the distribution of underlying chaotic signal and random number generator (RNG) is numerically verified by four fundamental statistical test of FIPS 140-2. Proposed design is practically realized on the field programmable analog and digital arrays (FPAA-FPGA). Finally it is experimentally verified that the presented RNG fulfills the NIST 800-22 randomness test without post processing.
The extremely rapid development of the Internet of Things brings growing attention to the information security issue. Realization of cryptographically strong pseudo random number generators (PRNGs), is crucial in securing sensitive data. They play an important role in cryptography and in network security applications. In this paper, we realize a comparative study of two pseudo chaotic number generators (PCNGs). The First pseudo chaotic number generator (PCNG1) is based on two nonlinear recursive filters of order one using a Skew Tent map (STmap) and a Piece-Wise Linear Chaotic map (PWLCmap) as non linear functions. The second pseudo chaotic number generator (PCNG2) consists of four coupled chaotic maps, namely: PWLCmaps, STmap, Logistic map by means a binary diffusion matrix [D]. A comparative analysis of the performance in terms of computation time (Generation time, Bit rate and Number of needed cycles to generate one byte) and security of the two PCNGs is carried out.