A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a “deep-zoom” manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i.e., time-evolution, bifurcation diagram, Lyapunov exponent, Poincare diagram, and frequency distribution). Moreover, taking advantage of this randomization improvement, we propose a Pseudo-Random Number Generator (PRNG) based on the k-logistic map. The pseudo-random qualities of the proposed PRNG passed both tests successfully, i.e., DIEHARD and NIST, and were comparable with other traditional PRNGs such as the Mersenne Twister. The results suggest that simple maps ...

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Internet of things (IoT) devices should be designed taking security requirements into consideration, so that they can be used securely in open environments. Designing secure IoT devices requires the ability to design fast and secure cryptography modules. A component in these modules is the pseudorandom number generator (PRNG), which can be built using different strategies. Some of these strategies use chaotic maps, and in such cases, the chaotic map that is selected must be simple and feasible to implement in a digital device by using the IEEE-754 floating-point standard. The chaotic map must also generate number sequences whose statistical distribution looks uniform. In this way, this paper shows the digital implementation of a PRNG by using a non-scaled non-discretized skew tent map (STM). The proposed PRNG can produce uniformly distributed number sequences when the annulling chaos conditions are identified and avoided on the chaotic map. Furthermore, the pseudorandom sequences are generated in few milliseconds. Compared to similar PRNGs recently reported, the proposed PRNG has been successful, based on tests, such as the correlation coefficient, key sensitivity, statistical analysis, entropy analysis, key space and randomness.

PRNG Based on Skew Tent Map

FPGA optimized cellular automaton random number generator

Algorithms for constructing tree-based classifiers are aimed at building an optimal set of rules implicitly described by some dataset of training samples. As the number of samples and/or attributes in the dataset increases, the required construction time becomes the limiting factor for interactive or even functional use. The problem is emphasized if tree derivation is part of an iterative optimization method, such as boosting. Attempts to parallelize the construction of classification trees have therefore been presented in the past. This paper describes a parallel method for binary classification tree construction implemented on a graphics processing unit GPU using compute unified device architecture CUDA. By employing node-level, attribute-level, and split-level parallelism, the task parallel and data parallel sections of tree induction are mapped to the architecture of a modern GPU. The GPU-based solution is compared with the sequential and multi-threaded CPU versions on public access datasets, and it is shown that an order of magnitude acceleration can be achieved on this data-intensive task using inexpensive commodity hardware. The influence of dataset characteristics on the efficiency of parallel implementation is also analyzed. Copyright © 2015 John Wiley & Sons, Ltd.

Parallel construction of classification trees on a GPU

MACHICAO, J. Patterns and pseudo-randomness using complex systems. 2017. 198p. Tese (Doutorado em Ciências) Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, 2017. In this work, we demonstrate that patterns and randomness are close related, contrary to what intuitively is considered as opposite fields. We aimed for a pattern recognition approach that aims for two purposes: (i) to take advantages from the chaotic properties as a source of pseudo-randomness in order to “measure” pseudo-randomness and (ii) to extract patterns from spatio-temporal diagrams obtained from complex systems models as a pattern recognition method. This work has focused on different complex systems such as discrete dynamical systems, complex networks, cellular automata (CA), and their combinations. The first method was to explore the chaotic properties in a deep-zoom manner as a source of pseudo-randomness from chaotic dynamical systems such as the logistic map and the tent map. We observed that the patterns vanish and therefore pseudo-randomness is increased by removing k right digits from the original orbit sequences. Therefore, we found an interesting chaotic source to obtain pseudo-randomness number generators (PRNGs). A second method was proposed based on the embedding of cellular automata (CA) over a network topology, also called network automata, aiming to characterize networks from the intrinsic spatio-temporal dynamics of these networks. Various on-demand problems were explored such as (i) identifying online social networks; (ii) identifying organisms from distinct domains of life through their metabolic networks; (iii) classifying stomata distribution patterns varying according to different environmental conditions; and (iv) the authorship identification problem. Finally, this same approach was used to analyze the sequences of pseudo-random numbers generated by the gold standard k-logistic map in the context of pattern recognition. So far, the proposed pattern recognition approach based on non-linear systems allowed us to explored patterns and pseudo-randomness extracted from a myriad of systems with successful results in terms of accuracy and good pseudorandomness. The proposed method has made significant progress in real-world pattern recognition applications from a wide branch of fields such as Cryptography, Cryptanalysis, Biology and Data Science.

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Padrões e pseudo-aleatoriedade usando sistemas complexos

Methods and devices for optimizing classification tree evaluation for online and real-time characterization of tissue by using GPUs are disclosed that give a significant improvement in run time compared to data decomposition. The methods and devices use a parallel algorithm designed for single instruction, multiple data (SIMD) architectures commonly found in GPUs. Various optimizations and their effects are also disclosed.

Classification Trees on GPGPU Compute Engines

Pseudorandom Bit Generators from Enhanced Cellular Automata.

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 effort, we focus on pseudorandom bit generation and noninvertibility, the behavioral heart of cryptography. In particular, we focus on cyclic linear and non-linear au- tomata 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.

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Cellular Automata in Cryptographic Random Generators

We examine the problem of optimizing classification tree evaluation for on-line and real-time applications by using GPUs Looking at trees with continuous attributes often used in image segmentation, we first put the existing algorithms for serial and data-parallel evaluation on solid footings We then introduce a speculative parallel algorithm designed for single instruction, multiple data (SIMD) architectures commonly found in GPUs A theoretical analysis shows how the run times of data and speculative decompositions compare assuming independent processors To compare the algorithms in the SIMD environment, we implement both on a CUDA 20 architecture machine and compare timings to a serial CPU implementation Various optimizations and their effects are discussed, and results are given for all algorithms Our specific tests show a speculative algorithm improves run time by 25% compared to a data decomposition

Jason Spencer

Papers

Classification Trees on GPGPU Compute Engines

Pseudorandom Bit Generators from Enhanced Cellular Automata.

Cellular Automata in Cryptographic Random Generators

Speculative Parallel Evaluation Of Classification Trees On GPGPU Compute Engines

Method and device for classifying vascular objects using classification trees evaluated on a graphics processing unit