Feistel-inspired scrambling improves the quality of linear congruential generators

Aljahdali Asia () and Mascagni Michael ()
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Aljahdali Asia: Department of Computer Science, Florida State University, Tallahassee,FL 32306–4530, USA; and Faculty of Computing and Information Technology, King Abdulaziz University, P.O. Box 80221, Jeddah 21589, Saudi Arabia
Mascagni Michael: Departments of Computer Science, Mathematics, Computational Science, and Institute for MolecularBiophysics, Florida State University, Tallahassee, FL 32306–4530, USA

Monte Carlo Methods and Applications, 2017, vol. 23, issue 2, 89-99

Abstract: Generating 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.

Keywords: Pseudorandom numbers; Linear congruential generators; Feistel network (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/mcma-2017-0105

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