Cellular Automata in Cryptographic Random Generators

Cryptographic schemes using one-dimensional, three-neighbor cellular automata as a primitive have been put forth since at least 1985. Early results showed good statistical pseudorandomness, and the simplicity of their construction made them a natural candidate for use in cryptographic applications. Since those early days of cellular automata, research in the field of cryptography has developed a set of tools which allow designers to prove a particular scheme to be as hard as solving an instance of a well-studied problem, suggesting a level of security for the scheme. However, little or no literature is available on whether these cellular automata can be proved secure under even generous assumptions. In fact, much of the literature falls short of providing complete, testable schemes to allow such an analysis. In this thesis, we first examine the suitability of cellular automata as a primitive for building cryptographic primitives. In this report, we focus on pseudorandom bit generation and noninvertibility, the behavioral heart of cryptography. In particular, we focus on cyclic linear and non-linear automata in some of the common configurations to be found in the literature. We examine known attacks against these constructions and, in some cases, improve the results. Finding little evidence of provable security, we then examine whether the desirable properties of cellular automata (i.e. highly parallel, simple construction) can be maintained as the automata are enhanced to provide a foundation for such proofs. This investigation leads us to a new construction of a finite state cellular automaton (FSCA) which is NP-Hard to invert. Finally, we introduce the Chasm pseudorandom generator family built on this construction and provide some initial experimental results using the NIST test suite

Identification of cellular automata based on incomplete observations with bounded time gaps

In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed

Pseudorandom number generation with self programmable cellular automata

In this paper, we propose a new class of cellular automata – self programming cellular automata (SPCA) with specific application to pseudorandom number generation. By changing a cell's state transition rules in relation to factors such as its neighboring cell's states, behavioral complexity can be increased and utilized. Interplay between the state transition neighborhood and rule selection neighborhood leads to a new composite neighborhood and state transition rule that is the linear combination of two different mappings with different temporal dependencies. It is proved that when the transitional matrices for both the state transition and rule selection neighborhood are non-singular, SPCA will not exhibit non-group behavior. Good performance can be obtained using simple neighborhoods with certain CA length, transition rules etc. Certain configurations of SPCA pass all DIEHARD and ENT tests with an implementation cost lower than current reported work. Output sampling methods are also suggested to improve output efficiency by sampling the outputs of the new rule selection neighborhoods

Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestion

A Cellular Automata Simulation of the 1990s Russian Housing Privatization Decision

The study uses a computational approach to study the phenomenon of housing privatization in Russia in the 1990s. As part of the housing reform flats in multi-family buildings were offered to their residents free of payment. Nevertheless rapid mass housing privatization did not take place. While this outcome admits a number of explanations this analysis emphasizes the fact that the environment in which the decision-making households were operating had a high degree of uncertainty and imposed a high information-processing requirement on the decision-makers. Using the bounded rationality paradigm, the study builds a case for a cellular automata simulation of household decision-making in the context of housing privatization reforms in Russia in the 1990s. Cellular automata is then used to simulate a household’s decision to become the owner of its dwelling.cellular automata, complex systems, housing reform, Russia, simulation

Can geocomputation save urban simulation? Throw some agents into the mixture, simmer and wait ...

There are indications that the current generation of simulation models in practical, operational uses has reached the limits of its usefulness under existing specifications. The relative stasis in operational urban modeling contrasts with simulation efforts in other disciplines, where techniques, theories, and ideas drawn from computation and complexity studies are revitalizing the ways in which we conceptualize, understand, and model real-world phenomena. Many of these concepts and methodologies are applicable to operational urban systems simulation. Indeed, in many cases, ideas from computation and complexity studies—often clustered under the collective term of geocomputation, as they apply to geography—are ideally suited to the simulation of urban dynamics. However, there exist several obstructions to their successful use in operational urban geographic simulation, particularly as regards the capacity of these methodologies to handle top-down dynamics in urban systems. This paper presents a framework for developing a hybrid model for urban geographic simulation and discusses some of the imposing barriers against innovation in this field. The framework infuses approaches derived from geocomputation and complexity with standard techniques that have been tried and tested in operational land-use and transport simulation. Macro-scale dynamics that operate from the topdown are handled by traditional land-use and transport models, while micro-scale dynamics that work from the bottom-up are delegated to agent-based models and cellular automata. The two methodologies are fused in a modular fashion using a system of feedback mechanisms. As a proof-of-concept exercise, a micro-model of residential location has been developed with a view to hybridization. The model mixes cellular automata and multi-agent approaches and is formulated so as to interface with meso-models at a higher scale

Non-concave fundamental diagrams and phase transitions in a stochastic traffic cellular automaton

Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions between these phases, allows us to establish a rigorous classification based on their tempo-spatial behavioral characteristics. As a result from the system's complex dynamics, its flow-density relation exhibits a non-concave region in which forward propagating density waves are encountered. All four phases furthermore share the common property that moving vehicles can never increase their speed once the system has settled into an equilibrium