On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators

In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates than in the general case and thus can be of use for pseudorandom number generation.Comment: Mathematics of Computation (to appear

Fractional jumps: complete characterisation and an explicit infinite family

In this paper we provide a complete characterisation of transitive fractional jumps by showing that they can only arise from transitive projective automorphisms. Furthermore, we prove that such construction is feasible for arbitrarily large dimension by exhibiting an infinite class of projectively primitive polynomials whose companion matrix can be used to define a full orbit sequence over an affine space

Pseudorandom number generator by cellular automata and its application to cryptography.

by Siu Chi Sang Obadiah.Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.Includes bibliographical references (leaves 66-68).Abstracts in English and Chinese.Chapter 1 --- Pseudorandom Number Generator --- p.5Chapter 1.1 --- Introduction --- p.5Chapter 1.2 --- Statistical Indistingushible and Entropy --- p.7Chapter 1.3 --- Example of PNG --- p.9Chapter 2 --- Basic Knowledge of Cellular Automata --- p.12Chapter 2.1 --- Introduction --- p.12Chapter 2.2 --- Elementary and Totalistic Cellular Automata --- p.14Chapter 2.3 --- Four classes of Cellular Automata --- p.17Chapter 2.4 --- Entropy --- p.20Chapter 3 --- Theoretical analysis of the CA PNG --- p.26Chapter 3.1 --- The Generator --- p.26Chapter 3.2 --- Global Properties --- p.27Chapter 3.3 --- Stability Properties --- p.31Chapter 3.4 --- Particular Initial States --- p.33Chapter 3.5 --- Functional Properties --- p.38Chapter 3.6 --- Computational Theoretical Properties --- p.42Chapter 3.7 --- Finite Size Behaviour --- p.44Chapter 3.8 --- Statistical Properties --- p.51Chapter 3.8.1 --- statistical test used --- p.54Chapter 4 --- Practical Implementation of the CA PNG --- p.56Chapter 4.1 --- The implementation of the CA PNG --- p.56Chapter 4.2 --- Applied to the set of integers --- p.58Chapter 5 --- Application to Cryptography --- p.61Chapter 5.1 --- Stream Cipher --- p.61Chapter 5.2 --- One Time Pad --- p.62Chapter 5.3 --- Probabilistic Encryption --- p.63Chapter 5.4 --- Probabilistic Encryption with RSA --- p.64Chapter 5.5 --- Prove yourself --- p.65Bibliograph

Applications of MATLAB in Science and Engineering

The book consists of 24 chapters illustrating a wide range of areas where MATLAB tools are applied. These areas include mathematics, physics, chemistry and chemical engineering, mechanical engineering, biological (molecular biology) and medical sciences, communication and control systems, digital signal, image and video processing, system modeling and simulation. Many interesting problems have been included throughout the book, and its contents will be beneficial for students and professionals in wide areas of interest