Random Number Generator Based on the Prime Factorization

This paper is devoted to the study of the random number generator based on factorization. The paper proposes an algorithm for generating pseudorandom bits from the canonical representation of the number, as well as the results of the study of this algorithm on the period length of the generated sequence, the proximity of its statistical properties to the properties of a random sequence, as well as a complexity estimation of generating a new bit. Based on the results, recommendations on the choice of the main constants of this generator are given, and a comparison with popular analogues is done. In addition, this paper describes the algorithm for finding the period in the sequence, which is faster than the existing Brent algorithm for sequences with time-consuming generating the next element, in particular for some pseudo-random number generators. This paper contains 35 pages, 4 chapters, 6 illustrations, 8 tables, 7 bibliography items, 4 appendices. Keywords: random number generator, factorization, period search, NIST statistical tests.