• Svitlana Popereshnyak


Algorithms, multidimensional statistics, random sequence, s-chains, cryptography, pseudorandom sequence, statistical testing


The article is dedicated to systematization of scientific positions about the static testing of sequences, widely used in cryptographic systems of information protection for the production of key and additional information (random numbers, vectors of initialization, etc.). Existing approaches to testing pseudorandom sequences, their advantages and disadvantages are considered. It is revealed that for sequences of length up to 100 bits there are not enough existing statistical packets. Perspective direction of research – static testing of sequences using n- dimensional statistics is considered. The joint distributions of 2-chains and 3-chains of a fixed type of random (0, 1) -sequences allow for statistical analysis of local sections of this sequence. Examples, tables, diagrams that can be used to test for randomness of the location of zeros and ones in the bit section are 16 lengths. The paper proposes a methodology for testing pseudorandom sequences, an explicit form of the joint distribution of 2- and 3-chains numbers of various options of random bit sequence of a given small length is obtained. As a result of the implementation of this technique, an information system will be created that will allow analyzing the pseudorandom sequence of a small length and choosing a quality pseudorandom sequence for use in a particular subject area.


A.V. Arhangelskaya, “Analysis of approaches to the definition of the term ‘randomness’,” Proceedings of the Russian Conference “Problems of Information Security in University Education System”, MIFI-2007, Moscow Engineering-Physical Institute, Moscow, 2007, pp. 22–23. (in Russian)

S. Popereshnyak “Analysis of pseudorandom small sequences using multidimensional statistics” Proceedings of the 2019 3rd IEEE International Conference on Advanced Information and Communication Technologies (AICT’2019), Lviv, Ukraine, 2019, pp. 5.4.1-5.4.4.

M. McLoone, J. V. McCanny, “High-performance FPGA implementation of DES using a novel method for implementing the key schedule,” IEE Proceedings – Circuits, Devices and Systems, vol. 150, no. 5, pp. 373-378, October 2003.

F. H. Nejad, S. Sabah, A. J. Jam, “Analysis of avalanche effect on advance encryption standard by using dynamic S-Box depends on rounds keys,” Proceedings of the 2014 International Conference on Computational Science and Technology (ICCST), Kota Kinabalu, 2014, pp. 1-5.

H. Liu, C. Jin, “Lower bounds of differential and linear active S-boxes for 3D-like structure,” The Computer Journal, vol. 58, no. 4, pp. 904-921, April 2015.

C. U. Bhaskar, C. Rupa, “An advanced symmetric block cipher based on chaotic systems,” Proceedings of the 2017 Innovations in Power and Advanced Computing Technologies (i-PACT), Vellore, 2017, pp. 1-4.

N. Ferguson, B. Schneier, Practical Cryptography, John Wiley & Sons, 2003, 432 p.

A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997, 794 р.

B. N. Tran, T. D. Nguyen and T. D. Tran, “A new S-box structure to increase complexity of algebraic expression for block cipher cryptosystems,” Proceedings of the 2009 International Conference on Computer Technology and Development, Kota Kinabalu, 2009, pp. 212-216.

P. Busireddygari, S. Kak, “Pseudorandom tableau sequences,” Proceedings of the IEEE 51st Asilomar Conference on Signals, Systems, and Computers, 2017, pp. 1733-1736.

S. Gurugopinath, B. Samudhyatha, “Multi-dimensional AndersonDarling statistic based goodness-of-fit test for spectrum sensing,” Proceedings of the IEEE Seventh International Workshop on Signal Design and its Applications in Communications (IWSDA), Bengaluru, India, 2015, pp. 165-169.

H. Wang, E.-H. Yang, Z. Zhao, W. Zhang, “Spectrum sensing in cognitive radio using goodness of fit testing,” IEEE Transactions on Wireless Communications, vol. 8, issue 11, pp. 5427-5430, 2009.

D. Teguig, V. Le Nir, B. Scheers, “Spectrum sensing method based on goodness of fit test using chi-square distribution,” Electronics Letters, vol. 50, issue 9, pp. 713-715, 2014.

Special Publication 800-22, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. [Online]. Available at:

The eSTREAM Project, 2004, [Online]. Available at:

ISO/IEC 18033-4:2011. Information technology – Security techniques – Encryption algorithms – Part 4: Stream ciphers, 2012.

D. D. Ismoyo, R. W. Wardhani, “Block cipher and stream cipher algorithm performance comparison in a personal VPN gateway,” Proceedings of the 2016 International Seminar on Application for Technology of Information and Communication (ISemantic), Semarang, 2016, pp. 207-210.

D. Moody, “Post-quantum cryptography: NIST’s plan for the future,” Proceedings of the Seventh International Conference on Post Quantum Cryptography, Japan, 2016. [Online]. Available at:

The Marsaglia, “Random Number CDROM including the Diehard Battery of Tests of Randomness,” [Online]. Available at:

eSTREAM Optimized Code HOWTO, 2005. [Online]. Available at:

M. Robshaw, O. Billet, “New stream cipher designs: The eSTREAM,” Finalists, Berlin, 2008.

A. A. Zadeh, H. M. Heys, “Application of simple power analysis to stream ciphers constructed using feedback shift registers,” The Computer Journal, vol. 58, no. 4, pp. 961-972, April 2015.

C. Carlet et al., “Analysis of the algebraic side channel attack,” Journal of Cryptographic Engineering, vol. 1, no. 2, pp. 45-62, 2012.

A. R. Kazmi, M. Afzal, M. F. Amjad, A. Rashdi, “Combining algebraic and side channel attacks on stream ciphers,” Proceedings of the 2017 International Conference on Communication Technologies (ComTech), Rawalpindi, 2017, pp. 138-142.

D. P. Upadhyay, P. Sharma, S. Valiveti, “Randomness analysis of A5/1 Stream Cipher for secure mobile communication,” International Journal of Computer Science & Communication, vol. 3, pp. 95-100, 2014.

D. Upadhyay, T. Shah, P. Sharma, “Cryptanalysis of hardware based stream ciphers and implementation of GSM stream cipher to propose a novel approach for designing n-bit LFSR stream cipher,” Proceedings of the 2015 19th International Symposium on VLSI Design and Test, Ahmedabad, 2015, pp. 1-6.

P. Pillai, S. Pote, “Physical layer security using stream cipher for LTE,” Proceedings of the 2015 IEEE Bombay Section Symposium (IBSS), Mumbai, 2015, pp. 1-5.

C. Cassisi, P. Montalto, M.A. Aliotta, A. Pulvirenti, “Similarity measures and dimensionality reduction techniques for time series data mining,” Advances in Data Mining Knowledge Discovery and Applications, Chapter 3, IntechOpen, London, 2012, pp. 71-96.

D. Berndt, J. Clifford, “Using dynamic time warping to find patterns in time series,” Workshop on KDD, vol. 10, no. 16, Seattle, USA, July 31 – August 01, 1994, pp. 359-370.

V. Masol, S. Popereshnyak, “A theorem on the distribution of the rank of a sparse Boolean random matrix and some applications,” Theory of Probability and Mathematical Statistics, vol. 76, pp. 103-116, 2008.

I.P. Gaydyshev, Data analysis software, AtteStat. User's manual. Version 13, 2012, 525 p. (in Russian)

S. Popereshnyak, G. P. Dimitrov, “The testing of pseudorandom sequences using multidimensional statistics,” [Online]. Available at:

V. Маsоl, S. Pоpereshnyаk “Statistical analysis of local sections of bits sequences,” Journal of Automation and Information Sciences, vol. 51, issue 10, pp. 31-45, 2019. DOI: 10.1615/JAutomatInfScien.v51.i10.30.

S. Pоpereshnyаk, “The technique for testing short sequences as a component of cryptography on the Internet of Things,” [Online]. Available at:




How to Cite

Popereshnyak, S. (2020). TECHNIQUE OF THE TESTING OF PSEUDORANDOM SEQUENCES. International Journal of Computing, 19(3), 387-398. Retrieved from