Periodic Properties of Cryptographically Strong Pseudorandom Sequences

"Provable" strength generators of pseudo-random sequences have been considered in this paper, whose cryptanalysis problem reduces to solving a well-known and extremely complex mathematical problem related to the NP-complex class. In particular, the generators Blum-Blum-Shub, Rivest-Shamir-Adleman, Dual Elliptic Curve Deterministic Random Bit Generator and Pseudo-Random Generator Provably as Secure as Syndrome Decoding are considered. The periodic properties of generated pseudorandom sequences are investigated. It is shown that the considered generators do not allow forming sequences of the maximum period. In addition, for each generator there are initial states (weak keys), leading to catastrophically small lengths of the periods of generated sequences.