The prospects for building a satellite Internet based on a low-orbit constellation of satellites (LOСS) are due to the fact that only it allows for stable and reliable communications anywhere on the planet. Therefore, the technology of satellite industrial Internet of things IIoT has become widespread in the oil and gas industry, many of whose facilities are located in the Far North. However, when using satellite low-orbit Internet (SLOEI), new threats and attacks arise against it. Among attacks on LOCS, a special place is occupied by attempts to impose unauthorized content on SLOEI subscribers. This situation can be prevented using a satellite identification system. For the effective operation of the “friend or foe” challenge-response system for LOCS, a copy-resistant authentication protocol with zero knowledge disclosure was developed. This property was achieved by reducing authentication time through the use of modular deduction class codes (MDCC). The use of parallel VDCC codes has led to a change in the method of satellite identification, which entails a revision of the principles for constructing a request-response system. Therefore, the development of a block diagram of a satellite identification system operating in the MDCC for a low-orbit satellite Internet system is relevant.

Keywords: imitation resistance, zero-knowledge authentication protocol, modular codes of residue classes, block diagram of the low-orbit satellite identification system

Frequency multiplexing (OFDM) methods have become the main basis for most outbred systems. These methods have also found application in modern systems of low-orbit satellite Internet (LOSIS). For example, the StarLink system uses OFDM transmission systems that use a signal frame consisting of 52 channels to transmit data. One way to increase the data rate in OFDM is to replace the Fourier transform (FT) with a faster orthogonal transform. As such, the modified wavelet transform (MWT) of Haar was chosen. The Haar MVP allows to reduce the number of arithmetic operations during the orthogonal signal transformation in comparison with the PF. The use of integer algebraic systems, such as Galois fields and modular residue class codes (MCCR), makes it possible to increase the speed of a computing device that performs orthogonal transformations of signals. Obviously, the transition to new algebraic systems should lead to changes in the structure of OFDM systems. Therefore, the development of structural models of an OFDM transmission system using the Haar MWP in the Galois field and the ICCM is an urgent task. Therefore, the aim of the work is to develop structural models of wireless OFDM systems using a modified integer discrete Haar transform, which can reduce the execution time of the orthogonal signal transformation. And this, in turn, will lead to an increase in the data transfer rate in the SNSI.

Keywords: orthogonal frequency multiplexing, modification of the Haar wavelet transform, structural models of execution of the Haar MVP, Galois field, modular residue class codes

To improve the efficiency of low-orbit satellite Internet systems (LOSIS) and ensure high apeed of data exchange, systems supporting orthogonal frequency-division multiplexing (OFDM) technology are widely used. The use of OFDM methods makes it possible to expand the bandwidth of the radio channel based on the increase in spectral efficiency. In order to do this, OFDM systems use orthogonal signal transformation based on fast Fourier transformation (FFT). To reduce the time spent on signal processing, the article proposes to use discrete wavelet transformations of signals (DWT) implemented in modular residue classes codes (MRCC). The scientific novelty of the work lies in the fact that based on the integration of methods for constructing discrete wavelet transforms and methods for developing modular codes, mathematical models of DWT implemented in the MRCC will be created, the use of which will reduce the execution time of orthogonal signal processing in OFDM systems. This result will be achieved by parallelizing arithmetic operations on the modules of the modular code. At the same time, the use of low-bit operands makes it possible to switch from performing multiplication, addition, and subtraction operations in the MRCC to retrieving data from LUT tables. Thus, the development of mathematical models of discrete wavelet transformations implemented in modular codes of residue classes is an urgent task.

Keywords: OFDM systems, discrete wavelet transformation, parallel coding, modular residue classes code

As the number of low-orbit satellite constellations (LEOs) increases, the probability of destructive impact from alien spacecraft (SC) will increase. One of the most effective impacts on the NHS is the setting of relay interference, which is an intercepted and delayed signal. This problem can be eliminated by using the "friend or foe" identification system for the spacecraft. At the same time, in order to reduce the probability of selecting the correct transponder signal by a foreign spacecraft, it is proposed to reduce the time spent on calculating the status of the satellite through the use of parallel calculations using codes of the polynomial residue number system (PRNS). A characteristic feature of these codes is the independent and parallel execution of calculations based on the bases of the PRNS. However, this property of the PRNS code can also be used to correct errors that occur during the operation of the identification system. In this case, the algorithm must perform this procedure at a lower time cost. Therefore, the modification of the error correction algorithm, which makes it possible to provide a higher speed of searching and correcting errors, is an urgent task. The purpose of the work is to reduce the time spent on the execution of the procedure for detecting and correcting errors during the operation of the identification system, by modifying the correction algorithm based on the Chinese residual theorem

Keywords: satellite identification system, codes of the polynomial residue number system, positional characteristic, error detection and correction algorithms

One of the effective ways to increase the information secrecy of a constellation of low-orbit spacecraft (LVS) is the use of a satellite authentication system (SAS). In order to reduce the time spent on determining the status of the satellite, as well as to increase the fault tolerance of the identification system, in a number of works it is proposed to use the codes of the polynomial system of residue classes (PSCS). This paper presents a methodology for constructing a fault-tolerant authentication system for a spacecraft, which is based on exchange operations implemented in PSKV codes. Using exchange operations, that is, changing the number of informational and redundant bases, it is possible to ensure the possibility of maintaining the operational state of the identification system in the event of a sequence of failures, as a result of which the level of information secrecy of the NSA will not be reduced.

Keywords: satellite authentication system, polynomial system of residue classes, exchange operations, method of building a fault-tolerant identification system