Methods and means for analysing, evaluating and comparing properties of random sequences and random numbers

Methods and means for analysing, assessing and comparing properties of random sequences and random numbers are considered in the work. The article also discusses such aspects as mathematical modeling of random processes, statistical methods for estimating distribution parameters, comparative analysis of the properties of random variables. To date, random sequences (RS) and random numbers (RN), produced by physically real (PT RNG) and non-physically real (NPT RNG) generators, are widely used in practice, they essentially legislate key generation mechanisms in cryptographic systems. Depending on the cryptographic transformations, they are used to generate long-term keys and session keys of symmetric cryptographic transformations, long-term asymmetric key pairs and session key pairs, general parameters of cryptographic transformations and cryptographic protocols, specific one-time values (nonces), challenges (challenges), blinding and masking values, etc. Among the set of requirements for such generators is the provision of the maximum possible value of the initial entropy in a number of, and possibly most, cryptographic applications. The analysis of international and national legal documents regarding the requirements for PT RNG and NPT RNG sources and, accordingly, generators, carried out in the work showed that they, taking into account the significant challenges associated with expanding the possibilities of cryptanalysis based on application, in addition to classical, quantum and side channel attacks should be significantly improved and evaluated using complex methods using a system of unconditional criteria. The purpose of this article is to substantiate, develop and confirm experimentally the correct application of RS and RN generation algorithms based on PTRNG and NPTRNG, including in the application of classical and quantum microelectronics, as well as the development of recommendations for their use for generating keys and parameters for quantum stable methods and standards of cryptographic transformations.