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StringENT test suite: ENT battery revisited for efficient P value computation

Almaraz Luengo, Elena, Alaña Olivares, Bittor, García Villalba, Luis Javier, Hernandez-Castro, Julio C., Hurley-Smith, Darren (2023) StringENT test suite: ENT battery revisited for efficient P value computation. Journal of Cryptographic Engineering, 13 (2). pp. 235-249. ISSN 2190-8516. (doi:10.1007/s13389-023-00313-5) (KAR id:101386)


Random numbers play a key role in a wide variety of applications, ranging from mathematical simulation to cryptography. Generating random or pseudo-random numbers is not an easy task, especially when hardware, time and energy constraints are considered. In order to assess whether generators behave in a random fashion, there are several statistical test batteries. ENT is one of the simplest and most popular, at least in part due to its efficacy and speed. Nonetheless, only one of the tests of this suite provides a p value, which is the most useful and standard way to determine whether the randomness hypothesis holds, for a certain significance level. As a consequence of this, rather arbitrary and at times misleading bounds are set in order to decide which intervals are acceptable for its results. This paper introduces an extension of the battery, named StringENT, which, while sticking to the fast speed that makes ENT popular and useful, still succeeds in providing p values with which sound decisions can be made about the randomness of a sequence. It also highlights a flagrant randomness flaw that the classical ENT battery is not capable of detecting but the new StringENT notices, and introduces two additional tests.

Item Type: Article
DOI/Identification number: 10.1007/s13389-023-00313-5
Additional information: For the purpose of open access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
Uncontrolled keywords: Hypothesis testing, Statistical tests suite, Pseudo-random number generator (PRNG), P values, Cryptography, True random number generator (TRNG), ENT
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Funders: Engineering and Physical Sciences Research Council (
Innovate UK (
SWORD Depositor: JISC Publications Router
Depositing User: JISC Publications Router
Date Deposited: 23 May 2023 15:26 UTC
Last Modified: 27 Feb 2024 10:59 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Hernandez-Castro, Julio C..

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