Application of edge local complementation to McEliece cryptosystem structural analysis

McEliece cryptosystem is considered as one of the alternatives to RSA cryptosystem, so its cryptanalysis is one of the actual questions nowadays. Cyclic codes' equivalence is a fundamental problem here, so it was chosen as the topic of the research. This article proposes an algorithm for finding and listing cyclic codes' equivalence classes using graphs and edge local complementation operation. The algorithm has succeeded in increasing the maximum amount of processed vertices from 10 to 17. The work also includes the description of an algorithm for two codes equivalence determination in case of cyclicity of one of them. The codes with the length up to 19 can be processed by this algorithm. Furthermore, the work includes a full classification of cyclic codes with the length up to 19. All algorithms have been implemented in C programming language.