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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.