Feistel-inspired scrambling improves the quality of linear congruential generators

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Asia Aljahdali ◽  
Michael Mascagni
Keyword(s):  
Randomized Algorithms ◽  
Statistical Properties ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Pseudorandom Sequences ◽  
Linear Congruential Generators ◽  
Pseudorandom Number Generation ◽  
Linear Congruential ◽  
Test Suites

AbstractGenerating pseudorandom numbers is a prerequisite for many areas including Monte Carlo simulation and randomized algorithms. The performance of pseudorandom number generators (PRNGs) depends on the quality of the generated random sequences. They must be generated quickly and have good statistical properties. Several statistical test suites have been developed to evaluate a single stream of random numbers such as those from the TestU01 library, the DIEHARD test suite, the tests from the SPRNG package, and a set of tests designed to evaluate bit sequences developed at NIST. This paper presents a new pseudorandom number generation scheme that produces pseudorandom sequences with good statistical properties via a scrambling procedure motivated by cryptographic transformations. We will specifically apply this to a popular set of PRNGs called the Linear Congruential generators (LGCs). The scrambling technique is based on a simplified version of a Feistel network. The proposed method seeks to improve the quality of the LCGs output stream. We show that this Feistel-inspired scrambling technique breaks up the regularities that are known to exist in LCGs. The Feistel-inspired scrambling technique is modular, and can be applied to any 64-bit PRNG, and so we believe that it can serve as an inexpensive model for a scrambler that can be used with most PRNGs via post-processing.

Pseudorandom Number Generators

2017 ◽  
pp. 1-25
Keyword(s):  
Random Number ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Pseudorandom Sequences ◽  
Random Number Generators ◽  
Random Sequences ◽  
Pseudorandom Number Generators ◽  
Pseudo Random Number

In this chapter, the author considers existing methods and means of forming pseudo-random sequences of numbers and also are described the main characteristics of random and pseudorandom sequences of numbers. The main theoretical aspects of the construction of pseudo-random number generators are considered. Classification of pseudorandom number generators is presented. The structures and models of the most popular pseudo-random number generators are considered, the main characteristics of generators that affect the quality of the formation of pseudorandom bit sequences are described. The models of the basic mathematical generators of pseudo-random numbers are considered, and also the principles of building hardware generators are presented.

scholarly journals A FAMILY OF CONTROLLABLE CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

2002 ◽  
Vol 13 (08) ◽  
pp. 1047-1073 ◽  
Author(s):  
SHENG-UEI GUAN ◽  
SHU ZHANG
Keyword(s):  
Genetic Algorithm ◽  
Cellular Automata ◽  
Pseudorandom Number ◽  
Test Results ◽  
Randomness Test ◽  
Different Types ◽  
Pseudorandom Number Generation ◽  
Test Suites ◽  
Better Than

In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1D CA. Moreover, their randomness can be comparable to that of 2D CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved as compared with any individual CCA PRNG.

scholarly journals ON THE DISTRIBUTION OF NONLINEAR CONGRUENTIAL PSEUDORANDOM NUMBERS IN RESIDUE RINGS

2006 ◽  
Vol 02 (01) ◽  
pp. 163-168 ◽  
Author(s):  
EDWIN D. EL-MAHASSNI ◽  
ARNE WINTERHOF
Keyword(s):  
Pseudorandom Number ◽  
Attractive Alternative ◽  
Pseudorandom Numbers ◽  
Ring Of Integers ◽  
Number Generation ◽  
New Type ◽  
Congruential Method ◽  
Pseudorandom Number Generation ◽  
Linear Congruential

The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present a new type of discrepancy bound for sequences of s-tuples of successive nonlinear congruential pseudorandom numbers over a ring of integers ℤM.

scholarly journals Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations

2017 ◽  
Vol 27 (01) ◽  
pp. 1750014 ◽  
Author(s):  
Sylvain Contassot-Vivier ◽  
Jean-François Couchot ◽  
Christophe Guyeux ◽  
Pierre-Cyrille Heam
Keyword(s):  
Uniform Distribution ◽  
Hamiltonian Cycle ◽  
Chaotic Behavior ◽  
Statistical Tests ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Expected Length ◽  
Obvious Consequence ◽  
Pseudorandom Number Generation

Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a [Formula: see text]-cube where a balanced Hamiltonian cycle has been removed as the basis of a chaotic PRNG. In this article, all the difficult issues observed in the previous work have been tackled. The chaotic behavior of the whole PRNG is proven. The construction of the balanced Hamiltonian cycle is theoretically and practically solved. An upper bound of the expected length of the walk to obtain a uniform distribution is calculated. Finally practical experiments show that the generators successfully pass the classical statistical tests.

scholarly journals Linear Congruential Pseudorandom Numbered Hybrid Crypto-System with Genetic Algorithms

2020 ◽  
Vol 10 (2) ◽  
pp. 159-163
Keyword(s):  
Genetic Algorithms ◽  
Network Security ◽  
Small Business ◽  
Hybrid Systems ◽  
Pseudorandom Number ◽  
Security Services ◽  
Business Applications ◽  
Congruential Pseudorandom Number ◽  
Linear Congruential

While using networks that may be in any form more and more problems related to securityrises within the network as well as outside the network. To resolve the security problems network security is the science that facilitatesto safeguard the resources and the quality of the network and data. At different workstations filters and firewalls are used in protecting the resources. But while the data is in transmission security services are needed to protect. These services are to be altered frequently to prevent from attacks. In developing such system, this work uses linear congruential pseudorandom number with multiple genetic algorithms. In small business applications these types of hybrid systems can be used to prevent from hackers.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

scholarly journals A Guideline on Pseudorandom Number Generation (PRNG) in the IoT

2021 ◽  
Vol 54 (6) ◽  
pp. 1-38
Author(s):  
Peter Kietzmann ◽  
Thomas C. Schmidt ◽  
Matthias Wählisch
Keyword(s):  
General Purpose ◽  
Packet Transmission ◽  
Limited Resources ◽  
Systematic Evaluation ◽  
The Internet ◽  
Random Numbers ◽  
Essential Input ◽  
Attack Surface ◽  
Pseudorandom Number Generation ◽  
The Internet Of Things

Random numbers are an essential input to many functions on the Internet of Things (IoT). Common use cases of randomness range from low-level packet transmission to advanced algorithms of artificial intelligence as well as security and trust, which heavily rely on unpredictable random sources. In the constrained IoT, though, unpredictable random sources are a challenging desire due to limited resources, deterministic real-time operations, and frequent lack of a user interface. In this article, we revisit the generation of randomness from the perspective of an IoT operating system (OS) that needs to support general purpose or crypto-secure random numbers. We analyze the potential attack surface, derive common requirements, and discuss the potentials and shortcomings of current IoT OSs. A systematic evaluation of current IoT hardware components and popular software generators based on well-established test suits and on experiments for measuring performance give rise to a set of clear recommendations on how to build such a random subsystem and which generators to use.

Research Notes: Binary Test-Suites Using Covering Arrays

2018 ◽  
Vol 28 (09) ◽  
pp. 1321-1337 ◽  
Author(s):  
Jose Torres-Jimenez ◽  
Himer Avila-George ◽  
Ezra Federico Parra-González
Keyword(s):  
Software Testing ◽  
Test Generation ◽  
Software Systems ◽  
Combinatorial Testing ◽  
Covering Array ◽  
Covering Arrays ◽  
Almost All ◽  
Generation Problem ◽  
Test Suites

Software testing is an essential activity to ensure the quality of software systems. Combinatorial testing is a method that facilitates the software testing process; it is based on an empirical evidence where almost all faults in a software component are due to the interaction of very few parameters. The test generation problem for combinatorial testing can be represented as the construction of a matrix that has certain properties; typically this matrix is a covering array. Covering arrays have a small number of tests, in comparison with an exhaustive approach, and provide a level of interaction coverage among the parameters involved. This paper presents a repository that contains binary covering arrays involving many levels of interaction. Also, it discusses the importance of covering array repositories in the construction of better covering arrays. In most of the cases, the size of the covering arrays included in the repository reported here are the best upper bounds known, moreover, the files containing the matrices of these covering arrays are available to be downloaded. The final purpose of our Binary Covering Arrays Repository (BCAR) is to provide software testing practitioners the best-known binary test-suites.

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