Increasing the Fault Tolerance of the Pseudo-Random Code Generator with Substitution–Permutation Network “Kuznechik” Transformation Through the Use of Residue Code

Abstract

The emergence and widespread use of low-orbit satellite communication systems has become one of the triggers for the development of the Internet of Vehicles (IoV) technology. The main goal of this integration was to increase the level of vehicle safety not only in cities and their suburbs but especially in remote areas of the country. Despite its effectiveness, satellite IoV remains susceptible to attacks on the radio channel. One of the effective ways to counter such attacks is to use wireless transmission systems with the Frequency-Hopping Spread Spectrum (FHSS) method. The effectiveness of FHSS systems largely depends on the operation of the pseudorandom code generator (PRCG), which is used to calculate the new operating frequency code (number). This generator must have the following properties. Firstly, it must have high cryptographic resistance to guessing a new operating frequency number by an attacker. Secondly, since this generator will be located on board the spacecraft, it must have high fault tolerance. The conducted studies have shown that substitution–permutation network “Kuznechik” (SPNK) meets these requirements. To ensure the property of resilience to failures and malfunctions, it is proposed to implement SPNK in codes of redundant residual class systems in polynomials (RCSP) using the isomorphism of the Chinese Remainder Theorem in polynomials. RCSP codes are an effective means of eliminating computation errors caused by failures and malfunctions. The aim of this work is to increase the fault tolerance of PRCG based on SPNK transformation by using the developed error correction algorithm, which has lower hardware and time costs for implementation compared to the known ones. The comparative analysis showed that the developed algorithm for error correction in RCSP codes provides higher fault tolerance of PRCG compared with other redundancy methods. Unlike the “2 out of 3” method of duplication, the developed algorithm ensures the operational state of PRCG not only when the first failure occurs but also during the subsequent second one. In the event of a third failure, RCSP is able to correct 73% of errors in the informational residues of code combination, while the “2 out of 3” duplication method makes it possible to fend off the consequences of only the first failure.