×

A new approach to analyze the independence of statistical tests of randomness. (English) Zbl 1510.62015

Summary: One of the fundamental aspects when working with batteries of statistic tests is that they should be as efficient as possible, i.e. that they should check the properties and do so in a reasonable computational time. This assumes that there are no tests that are checking the same properties, i.e. that they are not correlated. One of the most commonly used measures to verify the interrelation between variables is the Pearson’s correlation. In this case, linear dependencies are checked, but it may be interesting to verify other types of non-linear relationships between variables. For this purpose, mutual information has recently been proposed, which measures how much information, on average, one random variable provides to another. In this work we analyze some well-known batteries by using correlation analysis and mutual information approaches.

MSC:

62-08 Computational methods for problems pertaining to statistics
62B10 Statistical aspects of information-theoretic topics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Kumar, S.; Tiwari, P.; Zymbler, M., Internet of things is a revolutionary approach for future technology enhancement: a review, J. Big Data, 6, 1, 1-21 (2019)
[2] Ejaz, W.; Anpalagan, A.; Imran, M. A.; Jo, M.; Naeem, M.; Qaisar, S. B.; Wang, W., Internet of things (iot) in 5g wireless communications, IEEE Access, 4, 10310-10314 (2016)
[3] Bassham, L. E.; Rukhin, A. L.; Soto, J.; Nechvatal, J. R.; Smid, M. E.; Barker, E. B.; Leigh, S. D.; Levenson, M.; Vangel, M.; Banks, D. L.; Heckert, N. A.; Dray, J. F.; Vo, S., SP 800-22 Rev. 1a. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Technical Report (2010), National Institute of Standards & Technology: National Institute of Standards & Technology Gaithersburg, MD, USA
[4] Álvarez, R.; Climent, J. J.; Tortosa, L.; Zamora, A., An efficient binary sequence generator with cryptographic applications, Appl. Math. Comput., 167, 1, 16-27 (2005), https://www.sciencedirect.com/science/article/pii/S0096300304004709 · Zbl 1086.94019
[5] Baturone, I.; Prada-Delgado, M. A.; Eiroa, S., Improved generation of identifiers, secret keys, and random numbers from srams, IEEE Trans. Inf. Forensics Secur., 10, 2, 2653-2668 (2015)
[6] Khalili-Shoja, M. R.; Amariucai, G. T.; Wei, S.; Deng, J., Secret common randomness from routing metadata in ad hoc networks, IEEE Trans. Inf. Forensics Secur., 11, 8, 1674-1684 (2016)
[7] Hurley-Smith, D.; Hernández-Castro, J., Certifiably biased: an in-depth analysis of a common criteria eal4+ certified trng, IEEE Trans. Inf. Forensics Secur., 13, 4, 1031-1041 (2018)
[8] Choi, J., Physical layer security for channel-aware random access with opportunistic jamming, IEEE Trans. Inf. Forensics Secur., 12, 11, 2699-2711 (2017)
[9] Tang, J.; Jiao, L.; Zeng, K.; Wen, H.; Qin, K.-Y., Physical layer secure mimo communications against eavesdroppers with arbitrary number of antennas, IEEE Trans. Inf. Forensics Secur., 16, 466-481 (2021)
[10] Laeuchli, J.; Ramırez-Cruz, Y.; Trujillo-Rasua, R., Analysis of centrality measures under differential privacy models, Appl. Math. Comput., 412, 126546 (2022), https://www.sciencedirect.com/science/article/pii/S0096300321006305 · Zbl 1510.68022
[11] Gedam, S. G.; Beaudet, S. T., Monte carlo simulation using excel(r) spreadsheet for predicting reliability of a complex system, Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055), 188-193 (2000)
[12] Ching-Jing, K.; Hui-Chin, T., A revised forward and backward heuristic for two-term multiple recursive random number generators, Appl. Math. Comput., 185, 1, 240-246 (2007), https://www.sciencedirect.com/science/article/pii/S0096300306008551 · Zbl 1110.65007
[13] Kawai, R.; Masuda, H., On simulation of tempered stable random variates, J. Comput. Appl. Math., 235, 8, 2873-2887 (2011), https://www.sciencedirect.com/science/article/pii/S0377042710006643 · Zbl 1217.65017
[14] Gergely, A. M.; Crainicu, B., A succinct survey on (pseudo)-random number generators from a cryptographic perspective, 2017 5th International Symposium on Digital Forensic and Security (ISDFS), 1-6 (2017)
[15] Wang, P.; You, F.; He, S., Design of broadband compressed sampling receiver based on concurrent alternate random sequences, IEEE Access, 7, 135525-135538 (2019)
[16] Gómez, A. I.; Gómez-Pérez, D.; Pillichshammer, F., Secure pseudorandom bit generators and point sets with low star-discrepancy, J. Comput. Appl. Math., 396, 113601 (2021), https://www.sciencedirect.com/science/article/pii/S0377042721002211 · Zbl 1469.11244
[17] M. Haahr, Introduction to randomness and random numbers, 1999, https://www.random.org/randomness/.
[18] Turan, M. S.; Doganaksoy, A., B. S., On independence and sensitivity of statistical randomness tests, (Golomb, S. W.; Parker, M. G.; Pott, A.; Winterhof, A., Sequences and Their Applications - SETA 2008, volume 4 (2008)), 18-29 · Zbl 1198.65030
[19] Hellekalek, P.; Wegenkittl, S., Empirical evidence concerning aes, ACM Trans. Model. Comput. Simul., 13, 4, 322-333 (2003)
[20] Burciu, P.; Simion, E., A systematic approach of nist statistical tests dependencies, J. Electr. Eng. Electr. Control Comput. Sci., 5, 1, 1-6 (2019), https://jeeeccs.net/index.php/journal/article/view/113
[21] Karell-Albo, J. A.; Legón-Pérez, C. M.; Madarro-Capó, E. J.; Rojas, O.; Sosa-Gómez, G., Measuring independence between statistical randomness tests by mutual information, Entropy, 22, 741, 1-18 (2020)
[22] Fan, L.; Chen, H.; Gao, S., A general method to evaluate the correlation of randomness tests, Lect. Notes Comput. Sci., 8267, 52-62 (2014)
[23] Doganaksoy, A.; Sulak, F.; Uguz, M.; Seker, O.; Akcengiz, Z., Mutual correlation of nist statistical randomness tests and comparison of their sensitivities on transformed sequences, Turkish J. Electr. Eng. Comput. Sci., 25, 655-665 (2017)
[24] Sulak, F.; Uguz, M.; Koçak, O.; Doganaksoy, A., On the independence of statistical randomness tests included in the nist test suite, Turkish J. Electr. Eng. Comput. Sci., 25, 3673-3683 (2017)
[25] Shannon, C. E.; Weaver, W., The mathemtical theory of communication (1962), University of Illinois Press, Urbana.
[26] Cover, T. M., Elements of information theory (2006), John Wiley & Sons. · Zbl 1140.94001
[27] Pardo, J. A., Some applications of the useful mutual information, Appl. Math. Comput., 72, 1, 33-50 (1995), https://www.sciencedirect.com/science/article/pii/009630039400162W · Zbl 0830.62007
[28] https://www.mdpi.com/1099-4300/19/11/631
[29] R.G. Brown, D. Eddelbuettel, D. Bauer, Dieharder: a random number test suite (version 3.31.1), 2014, https://webhome.phy.duke.edu/ rgb/General/dieharder.php.
[30] G. Marsaglia, The marsaglia random number cdrom including the diehard battery of tests of randomness, 1995, https://web.archive.org/web/20160220101002/.
[31] Gutterman, Z.; Pinkas, B.; Reinman, T., Analysis of the linux random number generator, 2006 IEEE Symposium on Security and Privacy (S P’06), 15pp.-385 (2006)
[32] Dorrendorf, L.; Gutterman, Z.; Pinkas, B., Cryptanalysis of the random number generator of the windows operating system, ACM Transactions on Information and System Security (TISSEC), 13, 1, 1-32 (2009)
[33] Marsaglia, G.; Tsang, W. W., Some difficult-to-pass tests of randomness, J Stat Softw, 7, 3, 1-9 (2002)
[34] L’ecuyer, P.; Simard, R., Testu01: ac library for empirical testing of random number generators, ACM Transactions on Mathematical Software (TOMS), 33, 4, 1-40 (2007) · Zbl 1365.65008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.