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TestU01: A C library for empirical testing of random number generators

Published: 15 August 2007 Publication History

Abstract

We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator's period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely used software. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the article provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.

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Charles Raymond Crawford

Algorithms and software for computing pseudorandom number sequences have a wide range of applications. There are many acceptable methods, but each has its drawbacks. This paper summarizes the published research on the testing of random sequences. The discussion is focused on specific statistical tests, and how they might expose weaknesses in a given random number generator (RNG). The software library that accompanies the paper addresses this problem directly. "The aim of [the library] is to provide a general and extensive set of software tools for statistical testing of RNGs." Although the library does include RNGs, the important modules allow the user to test sequences from generators, both those within the library and ones supplied by the user. The ANSI C source for the library is available for free on the Web, along with extensive documentation. The paper concludes with an application of the library tests to a large set of RNGs, including the default generators used by some popular software packages. The authors plan to maintain and update the Web files, which should provide software developers as well as researchers with rigorous tools to design dependable generators. Online Computing Reviews Service

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cover image ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software  Volume 33, Issue 4
August 2007
147 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/1268776
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  • (2025)Two-Dimensional Coupled Complex Chaotic MapIEEE Transactions on Industrial Informatics10.1109/TII.2024.343108521:1(85-95)Online publication date: Jan-2025
  • (2025)Two-Dimensional Cyclic Chaotic System for Noise-Reduced OFDM-DCSK CommunicationIEEE Transactions on Circuits and Systems I: Regular Papers10.1109/TCSI.2024.345453572:1(323-336)Online publication date: Jan-2025
  • (2025)Forecasting chaotic time series: Comparative performance of LSTM-based and Transformer-based neural networkChaos, Solitons & Fractals10.1016/j.chaos.2025.116034192(116034)Online publication date: Mar-2025
  • (2025)Observations on NIST SP 800-90B entropy estimatorsCryptography and Communications10.1007/s12095-025-00778-7Online publication date: 30-Jan-2025
  • (2025)Enhancing image security through a fusion of chaotic map and multi-level scrambling techniquesSignal, Image and Video Processing10.1007/s11760-025-03814-419:3Online publication date: 23-Jan-2025
  • (2024)STUDY OF THE STATISTICAL SECURITY OF THE AL04 ENCRYPTION ALGORITHMBULLETIN Series of Physics & Mathematical Sciences10.51889/2959-5894.2024.87.3.01487:3Online publication date: Sep-2024
  • (2024)Предельные совместные распределения статистик критериев пакета NIST и их обобщенийThe limit joint distributions of statistics of tests of the NIST package and their generalizationsДискретная математикаDiskretnaya Matematika10.4213/dm182436:2(71-116)Online publication date: 28-May-2024
  • (2024)STATISTICAL PROPERTIES OF THE PSEUDORANDOM SEQUENCE GENERATION ALGORITHMScientific Journal of Astana IT University10.37943/18LYCW2723(107-119)Online publication date: 30-Jun-2024
  • (2024)Design of a New Neuro-Generator with a Neuronal Module to Produce Pseudorandom and Perfectly Pseudorandom SequencesElectronics10.3390/electronics1310195513:10(1955)Online publication date: 16-May-2024
  • (2024)Statistical Testing of Random Number Generators and Their Improvement Using Randomness ExtractionEntropy10.3390/e2612105326:12(1053)Online publication date: 4-Dec-2024
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