Formation of an m-sequence over the Galois residue field

Abstract

The latest information transfer technologies use cryptographic algorithms to protect data from unauthorized access. As a result of accidental interference, the code words transmitted over the communication channel may be distorted. Cryptographic algorithms are sensitive to such distortions. Therefore, the development of an algorithm that provides not only information protection, but also + the detection of code errors is very relevant. The analysis of cryptographic algorithms has shown that the influence of interference in the information channel can be reduced if the method of expanding the spectrum by a pseudorandom recurrent M-sequence of maximum length is used for encryption and decryption of code words. In this case, two tasks can be solved simultaneously: to create a hidden communication channel and minimize the risks associated with the impact of random interference created in the information channel. The article considers the problem of constructing an algorithm based on the method of spectrum expansion by an M-sequence of maximum length formed over the Galois residue field. A brief description of the main types of algorithms and methods for statistical evaluation of the quality of generated M-sequences is given. The results of modeling the information channel in the Wolfram Mathematica software environment using a neural network are presented. Analysis of previously published works and patent information has shown that the use of floating code for cryptographic protection of a high-speed M-sequence generator does not exclude errors that occur when exposed to random interference. Therefore, in order to create an interference-proof communication channel, an algorithm is proposed in which the transmitted code combination is supplemented with a verification bit, which makes it possible to detect distortions of code words. To change the order of irreducible polynomials forming M-sequences of different lengths and increase the linear complexity of the generator, a shift register scheme is proposed that allows changing the sequence of connecting triggers. The results of a comparative analysis of the testing codes showed that the use of this algorithm makes it possible to improve the quality of the generated M-sequences. The results of the work can be used in communication and navigation systems, automatic control systems.