# Weaknesses in ENT Battery Design

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## Abstract

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## Featured Application

**The ENT battery presents vulnerabilities that will be shown in this work. The scope of this work is important because, in the light of the results obtained, the design of the battery tests should be reconsidered for its more effective use.**

## Abstract

## 1. Introduction

## 2. ENT Battery

#### 2.1. Entropy

#### 2.2. Chi-Square

#### 2.3. Arithmetic Mean

#### 2.4. Monte Carlo Estimation of $\pi $

#### 2.5. Serial Correlation

## 3. Experimentation Design and Results

#### 3.1. AES $\sigma $-Counter

#### 3.2. $\u03f5$-Hole

#### 3.3. t-Counter

#### 3.4. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Wang, L.; Cheng, H. Pseudo-Random Number Generator Based on Logistic Chaotic System. Entropy
**2019**, 21, 960. [Google Scholar] [CrossRef] [Green Version] - Figueroa-García, J.C.; Varón-Gaviria, C.A.; Barbosa-Fontecha, J.L. Fuzzy Random Variable Generation Using α-Cuts. IEEE Trans. Fuzzy Syst.
**2021**, 29, 539–548. [Google Scholar] [CrossRef] - Cotrina, G.; Peinado, A.; Ortiz, A. Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields. Mathematics
**2021**, 9, 556. [Google Scholar] [CrossRef] - Gergely, A.M.; Crainicu, B. A succinct survey on (Pseudo)-random number generators from a cryptographic perspective. In Proceedings of the 2017 5th International Symposium on Digital Forensic and Security (ISDFS), Tirgu Mures, Romania, 26–28 April 2017; pp. 1–6. [Google Scholar] [CrossRef]
- Wang, P.; You, F.; He, S. Design of Broadband Compressed Sampling Receiver Based on Concurrent Alternate Random Sequences. IEEE Access
**2019**, 7, 135525–135538. [Google Scholar] [CrossRef] - Gómez, A.I.; Gómez-Pérez, D.; Pillichshammer, F. Secure pseudorandom bit generators and point sets with low star-discrepancy. J. Comput. Appl. Math.
**2021**, 396, 113601. [Google Scholar] [CrossRef] - Hurley-Smith, D.; Hernández-Castro, J. Certifiably Biased: An In-Depth Analysis of a Common Criteria EAL4+ Certified TRNG. IEEE Trans. Inf. Forensics Secur.
**2018**, 13, 1031–1041. [Google Scholar] [CrossRef] [Green Version] - Lee, S.; Jho, N.S.; Chung, D.; Kang, Y.; Kim, M. Rcryptect: Real-Time Detection of Cryptographic Function in the User-Space Filesystem. Comput. Secur.
**2021**, 112, 1–26. [Google Scholar] [CrossRef] - 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.
**2021**, 16, 466–481. [Google Scholar] [CrossRef] - Rukhin, A.L.; Soto, J.; Nechvatal, J.R.; Smid, M.E.; Barker, E.; Leigh, S.; Levenson, M.; Vangel, M.; Banks, D.; Heckert, A.; et al. SP 800-22 Rev. 1a. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications; Technical Report; Special Publication (NIST SP); National Institute of Standards and Technology: Gaithersburg, MD, USA, 2010. Available online: https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=906762 (accessed on 9 February 2022).
- Marsaglia, G. The Marsaglia Random Number CDROM Including the Diehard Battery of Tests of Randomness; National Science Foundation: Alexandria, VA, USA, 1995. [Google Scholar]
- Brown, R.G.; Eddelbuettel, D.; Bauer, D. Dieharder: A Random Number Test Suite (Version 3.31.1). 2014. Available online: https://webhome.phy.duke.edu/~rgb/General/dieharder.php (accessed on 9 February 2022).
- Gustafson, H.; Dawson, E.; Nielsen, L.; Caelli, W. A computer package for measuring the strength of encryption algorithms. Comput. Secur.
**1994**, 13, 687–697. [Google Scholar] [CrossRef] - Walker, J. ENT: A Pseudorandom Number Sequence Test Program. 2018. Available online: https://www.fourmilab.ch/random/ (accessed on 9 February 2022).
- Almaraz Luengo, E.; García Villalba, L.J. Recommendations on Statistical Randomness Test Batteries for Cryptographic Purposes. ACM Comput. Surv.
**2021**, 54. [Google Scholar] [CrossRef] - Gray, R.M. Entropy and Information Theory, 2nd. ed.; Springer: New York, NY, USA, 2011. [Google Scholar]
- Hurley-Smith, D.; Patsakis, C.; Hernández-Castro, J. On the unbearable lightness of FIPS 140-2 randomness tests. IEEE Trans. Inf. Forensics Secur.
**2020**, 1–13. [Google Scholar] [CrossRef]

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## Share and Cite

**MDPI and ACS Style**

Almaraz Luengo, E.; Alaña Olivares, B.; García Villalba, L.J.; Hernández-Castro, J.
Weaknesses in ENT Battery Design. *Appl. Sci.* **2022**, *12*, 4230.
https://doi.org/10.3390/app12094230

**AMA Style**

Almaraz Luengo E, Alaña Olivares B, García Villalba LJ, Hernández-Castro J.
Weaknesses in ENT Battery Design. *Applied Sciences*. 2022; 12(9):4230.
https://doi.org/10.3390/app12094230

**Chicago/Turabian Style**

Almaraz Luengo, Elena, Bittor Alaña Olivares, Luis Javier García Villalba, and Julio Hernández-Castro.
2022. "Weaknesses in ENT Battery Design" *Applied Sciences* 12, no. 9: 4230.
https://doi.org/10.3390/app12094230