Chaotic Behaviors of Symbolic Dynamics about Rule 58 in Cellular Automata

The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulli στ-shift rule, which is members of Wolfram’s class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected graph of transition matrices of determinative block systems, we divide determinative block systems into two subsets. In addition, it is shown that rule 58 possesses rich and complicated dynamical behaviors in the space of bi-infinite sequences. Furthermore, we prove that four rules of global equivalence class ε43 of CA are topologically conjugate. We use diagrams to explain the attractors of rule 58, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations, and we find that these attractors are not global attractors. The Lameray diagram is used to show clearly the iterative process of an attractor

Application of Cellular Automata to Detection of Malicious Network Packets

A problem in computer security is identification of attack signatures in network packets. An attack signature is a pattern of bits that characterizes a particular attack. Because there are many kinds of attacks, there are potentially many attack signatures. Furthermore, attackers may seek to avoid detection by altering the attack mechanism so that the bit pattern presented differs from the known signature. Thus, recognizing attack signatures is a problem in approximate string matching. The time to perform an approximate string match depends upon the length of the string and the number of patterns. For constant string length, the time to matchnpatterns is approximatelyO(n); the time increases approximately linearly as the number of patterns increases. A binary cellular automaton is a discrete, deterministic system of cells in which each cell can have one of two values. Cellular automata have the property that the next state of each cell can be evaluated independently of the others. If there is a processing element for each cell, the next states of all cells in a cellular automaton can be computed simultaneously. Because there is no programming paradigm for cellular automata, cellular automata to perform specific functions are createdad hocby hand or discovered using search methods such as genetic algorithms. This research has identified, through evolution by genetic algorithm, cellular automata that can perform approximate string matching for more than one pattern while operating in constant time with respect to the number of patterns, and in the presence of noise. Patterns were recognized by using the bits of a network packet payload as the initial state of a cellular automaton. After a predetermined number of cycles, the ones density of the cellular automaton was computed. Packets for which the ones density was below an experimentally determined threshold were identified as target packets. Six different cellular automaton rules were tested against a corpus of 7.2 million TCP packets in the IDEval data set. No rule produced false negative results, and false positive results were acceptably low