Classification of pseudo-random number generators by complex networks and computational geometry analysis

Many fields need random and pseudorandom numbers, especially in cryptographic applications. d-bit segment binary pseudorandom numbers can be more easily used for block encryption. This paper studies on the statistical test for binary d string pseudorandom number generator (PRNG). Three postulates on the randomness for ideal pseudorandom d-bit segment sequences have been proposed. Based on the FIPS140-2 tests, a statistical test suite for d-bit segment sequences generated by PRNG has been proposed. Using the test suite tests the 100 key streams generated by RC4 PRNG and Matlab PRNG, respectively. The test results show that in the two 100 key streams generated via the two PRNGs with different seeds, about 97% 8-bit strings have passed the test suite, respectively. Using the key streams generated via the two PRNGs encrypts an RGB image. The results have shown that the encrypted RGB images have significant stream encryption avalanche effect.KeywordsInformation TheoryPseudorandom Number StringRandomness PostulateFIPS 140-2 TestNew Test Standard

Random numbers have a wide usage in the area of cryptography. In practice, pseudo random number generators are used in place of true random number generators, as regeneration of them may be required. Therefore because of generation methods of pseudo random number sequences, statistical randomness tests have a vital importance. In this paper, a randomness test suite is specified for long binary sequences. In literature, there are many randomness tests and test suites. However, in most of them, to apply randomness test, long sequences are partitioned into a certain fixed length and the collection of short sequences obtained is evaluated instead. In this paper, instead of partitioning a long sequence into fixed length subsequences, a concept of dynamic partitioning is introduced in accordance with the random variable in consideration. Then statistical methods are applied. The suggested suite, containing four statistical tests: Collision Tests, Weight Test, Linear Complexity Test and Index Coincidence Test, all of them work with the idea of dynamic partitioning. Besides the adaptation of this approach to randomness tests, the index coincidence test is another contribution of this work. The distribution function and the application of all tests are given in the paper.

Random sequences are widely used in the field of computer science. In practice, random sequences are generated by pseudorandom number generators which are in fact deterministic algorithms. Statistical tests are used to check whether there are regularities in a sequence generated by a pseudorandom number generator. Currently there are many statistical tests available, which focus on different aspects of a sequence, but it remains open how these tests are correlated. In this paper, we select a set of statistical tests from different test suites, adapt them for testing short sequences if necessary, and evaluate these tests by calculating their conditional entropy, which reflects the coverage of each test in the whole test suite. Finally we propose a new test suite which has a larger coverage than the original test suite.

The article is dedicated to a detailed review of pseudorandom number generators (PRNGs), their operating principles, features, advantages, limitations, and various implementation methods. Pseudorandom number generators have become an integral part of modern information security, leveraging advanced cryptographic algorithms to ensure reliability and resistance to attacks. Pseudorandom numbers are widely used in cryptography, simulation, computer games, and many other fields. The main goal of the article is to analyze various methods of generating pseudorandom numbers, their features, advantages, and disadvantages, as well as to study their impact on cryptographic strength. The article begins with the basic principles of PRNG operation, focusing on linear congruential generators (LCGs) as the simplest example. Although LCGs are easy to implement, they have significant limitations in the context of cryptographic security, such as short periods and relative predictability. For higher security requirements, cryptographically secure pseudorandom number generators (CSPRNGs) based on block ciphers, hash functions, or other complex mathematical algorithms are recommended. Additional attention is given to generators such as ChaCha20 and NORX, which demonstrate high speed and resistance to cryptanalytic attacks. Theoretical cryptographic strength is also analyzed for generators based on modified algorithms, such as BBS and BM, supported by the complexity of computational problems. In conclusion, the article emphasizes the critical importance of understanding the operation of various PRNGs for information security professionals, as the choice of generator can significantly impact the overall security level of a system. A comparison of the efficiency and cryptographic strength of different pseudorandom number generation methods is presented in a table, supplemented by program algorithms, their characteristics, and examples of their use in cryptography.

Chaos has been widely combined with cryptography in the field of information security, especially, a considerable amount of studies of generating pseudo-random numbers based on chaotic systems have been proposed in recent decades. However, many of them are easy to be attacked via utilizing the nonlinear prediction method based on phase space reconstruction and other analysis. Furthermore, under the finite precision environment of computer simulation, there does not exist a random sequence which is truly non-periodic. Unfortunately, few researches had made a related analysis on the above two discussions. This paper is devoted to designing a pseudo-random number generator based on coupled map lattice with time-varying delay, analyzing the random properties of the generated pseudo-random numbers and discussing the dynamical degradation of the system under finite precision of computer simulation. The proposed scheme merely depends on the determining equation; thus, the algorithm itself is not complex, which does not impose high demand on computer hardware and its efficiency is excellent. In order to meet the requirements of using the proposed pseudo-random number generator in cryptography and other practical engineering applications, the proposed pseudo-random number generator is subjected to statistical tests utilizing the well-known test suites, such as NIST SP800-22 and TestU01. Moreover, other related properties, such as permutation entropy, invariant distribution, degradation of dynamical characteristics and parameter test, are also investigated. All results illustrate that the new pseudo-random number generator can generate a high percentage of available pseudo-random numbers for scientific computer simulation and practical applications in the field of information security.

Most commonly-used pseudo-random number generators (PNGs) in computer systems are based on linear recurrence. These deterministic PNGs have fast and compact implementations, andean ensure very long periods. However, the points generated by linear PNGs in fact have a regular lattice structure and are thus not suit able for applications that rely on the assumption of uniformly distributed pseudo-random numbers (PNs). In this paper we propose and evaluate several fast and compact linear, non-linear, and hybrid PNGs for a field- programmable gate array (FPGA). The PNGs have excellent equidistribution properties and very small autocorrelations, and have very long repetition periods. The distribution and long-range correlation properties of the new generators are efficiently, and much more rapidly, estimated at hardware speeds using designed modules within the FPGA. The results of these statistical tests confirm that the combination of several linear PNGs or the combination of even one small non-linear PNG with a linear PNG significantly improves the statistical properties of the generated PNs.

A new Pseudo random number generator based on generalized Newton complex map with dynamic key

Background: Pseudo random numbers have indispensable role in designing cryptography systems such as key stream in stream ciphers. Efficiency of most crypto systems are in depend on the quality of secret key generated by a pseudo random number generator. Improvements/Methods: In the present paper, an efficient pseudo random number generator is presented for cryptographic applications. The algorithm is based on controlling distribution of generated random numbers with the chaotic henon congruential generator. Statistical Analyses: Statistical tests and histograms are performed over the proposed generator and the results confirm the improvements over the proposed algorithms. According to the results of statistical tests, proposed algorithms generate pseudo random numbers with acceptable independency and uniformity and random sequences with long enough period. Applications: Key streams in stream cipher system can be considered as the most important applications of pseudo random numbers. With this regard proposed generators are statistically proved as proper key stream generator for designing stream cipher systems.

Introduction to Machine Learning with Applications in Information Security provides a class-tested introduction to a wide variety of machine learning algorithms, reinforced through realistic applications. The book is accessible and doesn’t prove theorems, or otherwise dwell on mathematical theory. The goal is to present topics at an intuitive level, with just enough detail to clarify the underlying concepts. The book covers core machine learning topics in-depth, including Hidden Markov Models, Principal Component Analysis, Support Vector Machines, and Clustering. It also includes coverage of Nearest Neighbors, Neural Networks, Boosting and AdaBoost, Random Forests, Linear Discriminant Analysis, Vector Quantization, Naive Bayes, Regression Analysis, Conditional Random Fields, and Data Analysis. Most of the examples in the book are drawn from the field of information security, with many of the machine learning applications specifically focused on malware. The applications presented are designed to demystify machine learning techniques by providing straightforward scenarios. Many of the exercises in this book require some programming, and basic computing concepts are assumed in a few of the application sections. However, anyone with a modest amount of programming experience should have no trouble with this aspect of the book. Instructor resources, including PowerPoint slides, lecture videos, and other relevant material are provided on an accompanying website: http://www.cs.sjsu.edu/~stamp/ML/. For the reader’s benefit, the figures in the book are also available in electronic form, and in color. About the Author Mark Stamp has been a Professor of Computer Science at San Jose State University since 2002. Prior to that, he worked at the National Security Agency (NSA) for seven years, and a Silicon Valley startup company for two years. He received his Ph.D. from Texas Tech University in 1992. His love affair with machine learning began in the early 1990s, when he was working at the NSA, and continues today at SJSU, where he has supervised vast numbers of master’s student projects, most of which involve a combination of information security and machine learning.

The evolution of communication networks and information systems, to support wireless access, cloud and grid computing, and big data, provides great business opportunities. However, it also generates a new trend of sophisticated network threats and offers several challenges in securing information and systems confidentiality, integrity and availability. The traditional techniques used by security experts are mostly static and lack the much needed characteristics of adaptation and self-organization, computational efficiency and error resilience to deal with evolving attacks. The inherent characteristics of computational intelligence (CI) paradigms provide a promising alternative that has gained popularity resulting in significant applications in information security. There is a plethora of CI paradigms commonly used in this domain including artificial neural networks, evolutionary computing, fuzzy systems, and swarm intelligence. This chapter provides an overview of the widely-recognized CI paradigms and shades the light on some of their potential applications in information security.

The evolution of communication networks and information systems, to support wireless access, cloud and grid computing, and big data, provides great business opportunities. However, it also generates a new trend of sophisticated network threats and offers several challenges in securing information and systems confidentiality, integrity and availability. The traditional techniques used by security experts are mostly static and lack the much needed characteristics of adaptation and self-organization, computational efficiency and error resilience to deal with evolving attacks. The inherent characteristics of computational intelligence (CI) paradigms provide a promising alternative that has gained popularity resulting in significant applications in information security. There is a plethora of CI paradigms commonly used in this domain including artificial neural networks, evolutionary computing, fuzzy systems, and swarm intelligence. This chapter provides an overview of the widely-recognized CI paradigms and shades the light on some of their potential applications in information security.

Chaotic systems are widely used in various aspects such as information security, signal processing, and synchronous control. The structural complexity and the chaotic behavior of chaotic systems are two significant factors affecting their practical applications. In this paper, we propose a universal two-dimensional (2D) absolute-cosine chaotic model (ACCM). The 2D-ACCM is composed of a nonlinear bounded cosine function and an absolute value function. It can construct new chaotic maps with simple structures and complex chaotic behaviors on the basis of existing chaotic systems. To verify the effectiveness of the proposed system, we first choose two existing one-dimensional (1D) chaotic maps and one existing 2D chaotic map as the seed maps of the 2D-ACCM to generate two new maps, respectively. The results of chaotic behavior analysis show that these two new maps have more complex chaotic behavior and wider chaotic ranges than seed maps and some advanced chaotic maps. Then a hardware experiment platform based on a field-programmable gate array (FPGA) is used for the hardware implementation of the new maps. Finally, a simple chaos-based pseudo-random number generator (PRNG) is introduced to show the practical application. The experimental results show that the new maps can be easily implemented on the FPGA and the chaos-PRNGs can generate pseudo-random numbers with excellent randomness.

Transmission of the information in any form requires security. Security protocols used for communication rely on the use of random numbers. Pseudo-random numbers are required with good statistical properties and efficiency. The use of a single chaotic map may not produce enough randomness. The turbulence is padded into the existing map to improve its chaotic behaviour and increase the periodicity. A Pseudo-random number generator (PRNG) with this architecture is devised to generate random bit sequences from secret keys. The statistical properties of newly constructed PRNG are tested with NIST SP 800–22 statistical test suite and were shown to have good randomness. To ensure its usability in cryptographic applications, we analysed the size of its key space, key sensitivity, and performance speed. The test results show that the newly designed PRNG has a 3.6% increase in key space and a 5% increase in its performance speed compared to existing chaotic PRNGs. The novel PRNG with faster performance is found suitable for lightweight cryptographic applications.

This article explores randomness and how general purpose computers generate it. It also discusses the security requirements that a pseudo-random number generator must satisfy for use in cryptographic applications. And also special attention is paid to the known and new methods of testing random bit sequences. Analyzing the effectiveness of pseudo-random sequence generators is a pressing problem for smart cards when using more advanced methods of encryption and information protection. The available methods show low flexibility and versatility in the means of finding hidden patterns in data. To solve this problem, it is proposed to use algorithms based on multivariate statistics. These algorithms combine all the advantages of statistical methods and are the only alternative for analyzing short and medium-length sequences. The paper considers the scheme of operation of pseudo-random number generators in limited devices. The main requirements for modern smart cards are highlighted. A criterion for checking the randomness of bit sequences of small length (up to 100 bits) is proposed. This approach is appropriate for testing a lightweight pseudo-random number generator in devices with certain resource constraints. The paper presents the compatible distributions of the number of 2-strings and the number of 3-strings of a fixed form of a random bit sequence, which make it possible to carry out a statistical analysis of local sections of this sequence. A possible application of the obtained formulas can be to test the hypothesis of the randomness of the arrangement of zeros and ones in a (0, 1) -sequence of finite length. Research has shown that even with limited resources and a limited entropy environment like a smart card, good quality pseudo-random sequences can be created that can satisfy all the requirements for pseudo-random number generators, even those used for general purpose computers. In the work, the set of statistical tests was expanded to include other tests that are not included in the statistical set of NIST tests, and to analyze the work of the proposed algorithms. The paper presents algorithms for testing a pseudo-random sequence using multivariate statistics to illustrate their possible application in a smart card environment.

Trajectory Data have been considered as a treasure for various hidden patterns which provide deeper understanding of the underlying moving objects. Several studies are focused to extract repetitive, frequent and group patterns. Conventional algorithms defined for Sequential Patterns Mining problems are not directly applicable for trajectory data. Space Partitioning strategies were proposed to capture space proximity first and then time proximity to discover the knowledge in the data. Our proposal addresses time proximity first by identifying trajectories which meet at a minimum of [Formula: see text] time stamps in sequence. A novel tree structure is proposed to ease the process. Our method investigates space proximity using Mahalanobis distance (MD). We have used the Manhattan distance to form prior knowledge that helps the supervised learning-based MD to derive the clusters of trajectories along the true spreads of the objects. With the help of minsup threshold, clusters of frequent trajectories are found and then in sequence they form [Formula: see text] length Sequential Patterns. Illustrative examples are provided to compare the MD metric with Euclidean distance metric, Synthetic dataset is generated and results are presented considering the various parameters such as number of objects, minsup, [Formula: see text] value, number of hops in any trajectory and computational time. Experiments are done on available real-time dataset, taxi dataset, too. Sequential Patterns are proved to be worthy of knowledge to understand dynamics of the moving objects and to recommend the movements in constrained networks.