CoolTest: Improved Randomness Testing Using Boolean Functions

D 2025

CoolTest: Improved Randomness Testing Using Boolean Functions

GAVENDA, Jiří and Marek SÝS

Basic information

Original name

CoolTest: Improved Randomness Testing Using Boolean Functions

Authors

GAVENDA, Jiří and Marek SÝS

Edition

Cham, ICT Systems Security and Privacy Protection. SEC 2025. IFIP Advances in Information and Communication Technology, p. 3-17, 15 pp. 2025

Publisher

Springer Nature Switzerland

Other information

Language

English

Type of outcome

Proceedings paper

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Switzerland

Confidentiality degree

is not subject to a state or trade secret

Publication form

electronic version available online

References:

URL

Marked to be transferred to RIV

Yes

RIV identification code

RIV/00216224:14330/25:00140774

Organization unit

Faculty of Informatics

ISBN

978-3-031-92885-7

ISSN

Keywords in English

Statistical randomness testing; Boolean functions; Random number generators

Abstract

In the original language

In this work, we present a new randomness test, CoolTest. CoolTest finds the optimal Boolean function from functions over $k$ variables for distinguishing tested data from random. CoolTest generalizes and improves BoolTest (ICETE'17) as it can find an arbitrary correlation among $k$ variables with comparable complexity, while BoolTest searches only for functions of a predefined form. CoolTest uses the innovative idea of Chatterjee et al. (INDOCRYPT'22), allowing to test $2^{2^k}$ Boolean functions while evaluating only $2^k$ of them. The test of Chatterjee et al. works only for rare cases when the correlated bits are close in the data. CoolTest makes the idea practically usable by selecting only a subset of bits on which it looks for a distinguisher. We evaluated CoolTest on outputs of 14 reduced-round cryptographic functions (e.g., AES, Twofish, Keccak, MD5). The results show that CoolTest significantly improves compared to BoolTest in almost all cases. On 100 MB of data, CoolTest provides better results for SHA-2, SHA-1, MD6, and SHACAL-2 than statistical test suites NIST STS, Dieharder, and TestU01, which consist of many different tests. We provide an estimate of the amount of data necessary to find a distinguisher based on the type and relative frequency of a non-random pattern.

Links

MUNI/A/1709/2024, interní kód MU

Name: Aplikovaný výzkum na FI: Důvěra v dynamických softwarových ekosystémech, kryptografické implementace včetně uživatelských aspektů, kyberbezpečnostní cvičení, fúze dat pro fyzikální sensory a algoritmy plánování v logistice

Investor: Masaryk University, Applied research at FI: Trust in dynamic software ecosystems, cryptographic implementations, cybersecurity trainings, data fusion for physical sensors and scheduling algorithms in logistics

Cite

GAVENDA, Jiří and Marek SÝS. CoolTest: Improved Randomness Testing Using Boolean Functions. Online. In Lili Nemec Zlatolas, Kai Rannenberg, Tatjana Welzer, Joaquin Garcia-Alfaro. ICT Systems Security and Privacy Protection. SEC 2025. IFIP Advances in Information and Communication Technology. Cham: Springer Nature Switzerland, 2025, p. 3-17. ISBN 978-3-031-92885-7. Available from: https://doi.org/10.1007/978-3-031-92886-4_1.

@inproceedings{2482401,
   author = {Gavenda, Jiří and Sýs, Marek},
   address = {Cham},
   booktitle = {ICT Systems Security and Privacy Protection. SEC 2025. IFIP Advances in Information and Communication Technology},
   doi = {https://doi.org/10.1007/978-3-031-92886-4_1},
   editor = {Lili Nemec Zlatolas, Kai Rannenberg, Tatjana Welzer, Joaquin Garcia-Alfaro},
   keywords = {Statistical randomness testing; Boolean functions; Random number generators},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Cham},
   isbn = {978-3-031-92885-7},
   pages = {3-17},
   publisher = {Springer Nature Switzerland},
   title = {CoolTest: Improved Randomness Testing Using Boolean Functions},
   url = {https://link.springer.com/chapter/10.1007/978-3-031-92886-4_1},
   year = {2025}
}

TY  - CONF
ID  - 2482401
AU  - Gavenda, Jiří - Sýs, Marek
PY  - 2025
TI  - CoolTest: Improved Randomness Testing Using Boolean Functions
PB  - Springer Nature Switzerland
CY  - Cham
SN  - 9783031928857
KW  - Statistical randomness testing
KW  - Boolean functions
KW  - Random number generators
UR  - https://link.springer.com/chapter/10.1007/978-3-031-92886-4_1
N2  - In this work, we present a new randomness test, CoolTest. CoolTest finds the optimal Boolean function from functions over $k$ variables for distinguishing tested data from random. CoolTest generalizes and improves BoolTest (ICETE'17) as it can find an arbitrary correlation among $k$ variables with comparable complexity, while BoolTest searches only for functions of a predefined form. CoolTest uses the innovative idea of Chatterjee et al. (INDOCRYPT'22), allowing to test $2^{2^k}$ Boolean functions while evaluating only $2^k$ of them. The test of Chatterjee et al. works only for rare cases when the correlated bits are close in the data. CoolTest makes the idea practically usable by selecting only a subset of bits on which it looks for a distinguisher. We evaluated CoolTest on outputs of 14 reduced-round cryptographic functions (e.g., AES, Twofish, Keccak, MD5). The results show that CoolTest significantly improves compared to BoolTest in almost all cases. On 100 MB of data, CoolTest provides better results for SHA-2, SHA-1, MD6, and SHACAL-2 than statistical test suites NIST STS, Dieharder, and TestU01, which consist of many different tests. We provide an estimate of the amount of data necessary to find a distinguisher based on the type and relative frequency of a non-random pattern.
ER  -

GAVENDA, Jiří and Marek SÝS. CoolTest: Improved Randomness Testing Using Boolean Functions. Online. In Lili Nemec Zlatolas, Kai Rannenberg, Tatjana Welzer, Joaquin Garcia-Alfaro. \textit{ICT Systems Security and Privacy Protection. SEC 2025. IFIP Advances in Information and Communication Technology}. Cham: Springer Nature Switzerland, 2025, p.~3-17. ISBN~978-3-031-92885-7. Available from: https://doi.org/10.1007/978-3-031-92886-4\_{}1.

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