Development of an improved method for forming pseudorandom numbers based on redunte M-ary codes

The development of information technologies in cyberspace is associated with the development of security services in the components of security: cybersecurity, information security and information security. To provide security services, as a rule, cryptographic algorithms and functions based on symmetric and asymmetric cryptography systems are used. An integral part of such cryptosystems are pseudo-random number generators that allow you to generate a random sequence over a period. One of the evaluation criteria is the duration of the period and its guarantee, i.e. ensuring the randomness produced by the random number generator, another criterion is cryptographic strength - the ability to resist hacking by intruders. On the strength of pseudo-random number generators, symmetric flow cryptosystems are formed that ensure the strength of the cryptogram. The article analyzes the methods for constructing symmetric stream cryptosystems, proposes cryptographic generators of pseudo-random number sequences (PRNGs), the security of which is based on the complexity-theoretic problem of syndromic decoding. An improved method for generating PRNGs is proposed, which makes it possible to provide a guaranteed period of generated sequences.