Development of Modified Blum-Blum-Shub Pseudorandom Sequence Generator and its Use in Education

Authors

  • Shanshan Yu Hubei University of Technology, Wuhan, China
  • Przystupa Krzysztof Department of Automation, Lublin University of Technology, Nadbystrzycka 36, Lublin 20-618, Poland
  • Lingyu Yan Hubei University of Technology, Wuhan, China
  • Volodymyr Maksymovych Lviv Polytechnic National University, 12 Bandera Str., Lviv, Ukraine
  • Roman Stakhiv Lviv Polytechnic National University, 12 Bandera Str., Lviv, Ukraine
  • Andrii Malohlovets Lviv Polytechnic National University, 12 Bandera Str., Lviv, Ukraine
  • Orest Kochan Lviv Polytechnic National University, 12 Bandera Str., Lviv, Ukraine; Hubei University of Technology, Wuhan, China

DOI:

https://doi.org/10.2478/msr-2022-0018

Keywords:

pseudorandom sequence, pseudorandom sequence generator, one-way function, Blum-Blum-Shub(BBS) generator, computational complexity

Abstract

In information security systems, the algorithm of the Blum-Blum-Shub (BBS) generator, which is based on the use of a one-way function and is a cryptographically secure pseudorandom number generator, became widespread. In this paper, the problem of the analysis of modified algorithms of the BBS generator operation is considered to improve their statistical characteristics, namely, the sequence repetition period. It has been established that in order to improve the characteristics of the classic BBS algorithm, it is necessary to systematize approaches to change the recurrent equation itself, the relationship between the current and the previous members of the sequence. For this purpose, a generalized unified model of the modification of the classical BBS algorithm is derived. The repetition period with computational complexity were analyzed for classical algorithm and 80 proposed modifications. A gain in statistical characteristics is improved with slight increase in the required computing power of the system. The proposed modified BBS pseudorandom sequence generator can be used in training of students when teaching cryptographic stability of information security systems. The study of this generator combines the knowledge of students acquired in both digital electronics and mathematics.

Author Biographies

Shanshan Yu, Hubei University of Technology, Wuhan, China

ORCID: 0000-0002-5164-3132

Przystupa Krzysztof, Department of Automation, Lublin University of Technology, Nadbystrzycka 36, Lublin 20-618, Poland

ORCID: 0000-0003-4361-2763

Lingyu Yan, Hubei University of Technology, Wuhan, China

ORCID 0000-0003-2468-3881

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Published

22.04.2022

How to Cite

Yu, S., Krzysztof, P., Yan, L., Maksymovych, V., Stakhiv, R., Malohlovets, A., & Kochan, O. (2022). Development of Modified Blum-Blum-Shub Pseudorandom Sequence Generator and its Use in Education. Measurement Science Review, 22(3), 143–151. https://doi.org/10.2478/msr-2022-0018

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