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

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.