Random and pseudo-random number and bit sequence generators with a uniform distribution law are the most widespread and in demand in the market of pseudo-random generators. Depending on the specific field of application, the requirements for their implementation and the quality of the generator’s output sequence change. In this article, we have optimized the structures of the classical additive Fibonacci generator and the modified additive Fibonacci generator when they work together. The ranges of initial settings of structural elements (seed) of these generators have been determined, which guarantee acceptable statistical characteristics of the output pseudo-random sequence, significantly expanding the scope of their possible application, including cybersecurity. When studying the statistical characteristics of the modified additive Fibonacci generator, it was found that they significantly depend on the signal from the output of the logic circuit entering the structure. It is proved that acceptable statistical characteristics of the modified additive Fibonacci generator, and the combined generator realized on its basis, are provided at odd values of the module of the recurrent equation describing the work of such generator. The output signal of the combined generator has acceptable characteristics for a wide range of values of the initial settings for the modified additive Fibonacci generator and the classic additive Fibonacci generator. Regarding the use of information security, it is worth noting the fact that for modern encryption and security programs, generators of random numbers and bit sequences and approaches to their construction are crucial and critical.

Pseudorandom sequence generation is used in many industries, including cryptographic information security devices, measurement technology, and communication systems. The purpose of the present work is to research additive Fibonacci generators (AFG) and modified AFG (MAFG) with modules p prime numbers, designed primarily for their hardware implementation. The known AFG and MAFG, as with any cryptographic generators of pseudorandom sequences, are used in arguments with tremendous values. At the same time, there are specific difficulties in defining of their statistical characteristics. In this regard, the following research methodologies were used in work: for each variant of AFG and MAFG, two models were created—abstract, which is not directly related to the circuit solution, and hardware, which corresponds to the proposed structure; for relatively small values of arguments, the identity of models was proved; the research of statistical characteristics, with large values of arguments, was carried out using an abstract model and static tests NIST. Proven identity of hardware and abstract models suggest that the principles laid down in the organization of AFG and MAFG structures with modules of prime numbers ensure their effective hardware implementation in compliance with all requirements for their statistical characteristics and the possibility of application in cryptographic information security devices.

Poisson pulse sequence generators are quite well studied, have good statistical properties, are implemented both in software and hardware, but have not yet been used for the purpose of authentication. The work was devoted to modeling authenticators of information-processing electronic devices by creating a bit template simulator based on a Poisson pulse sequence generator (PPSG). The generated templates imitated an important property of real bit templates, which reflected the physical uniqueness of electronic devices, namely Hamming distances between arbitrary template pairs for the same device were much smaller than the distance between arbitrary template pairs for two different devices. The limits of the control code values were determined by setting the range of the average frequency values of the output pulse sequence with the Poisson distribution law. The specified parameters of the output pulse sequence were obtained due to the optimization of the parameters of the PPSG structural elements. A combination of pseudo-random sequences with the control code’s different values formed the bit template. The comparison of the Hamming distance between the standard and real-time templates with a given threshold value was used as a validation mechanism. The simulation experiment results confirmed the unambiguous authentication of devices. The simulation results also showed similarities with the real data obtained for the bit templates of personal computers’ own noise. The proposed model could be used for improving the cybersecurity of a corporate network as an additional factor in the authentication of information-processing electronic devices for which the measurement of noise with the required accuracy is not possible or significantly difficult.

Pseudorandom number and bit sequence generators are widely used in cybersecurity, measurement, and other technology fields. A special place among such generators is occupied by additive Fibonacci generators (AFG). By itself, such a generator is not cryptographically strong. Nevertheless, when used as a primary it can be quite resistant to cryptanalysis generators. This paper proposes a modification to AGF, the essence of which is to use prime numbers as modules of recurrent equations describing the operation of generators. This modification made it possible to ensure the constancy of the repetition period of the output pseudorandom pulse sequence in the entire range of possible values of the initial settings–keys (seed) at specific values of the module. In addition, it has proposed a new generator scheme, which consists of two generators: the first of which is based on a modified AFG and the second is based on a linear feedback shift register (LFSR). The output pulses of both generators are combined through a logic element XOR. The results of the experiment show that the specific values of modules provide a constant repetition period of the output pseudorandom pulse sequence in a whole range of possible values of the initial settings–keys (seed) and provide all the requirements of the NIST test to statistical characteristics of the sequence. Modified AFGs are designed primarily for hardware implementation, which allows them to provide high performance.

Repetition periods, and statistical characteristics of the pseudorandom bit sequence for predicting the statistically secure generator keyspace on the basis of the modified additive Fibonacci generator with a delay, are investigated.