Effective implementation of modern McEliece cryptosystem on generalized (L,G)-codes

Abstract

Subject of Research. The paper presents the study of methods and approaches to implementation of the modern McEliece cryptosystem based on separable generalized (L, G)-codes. Method. A method is proposed based on the analysis of the well-known public sources on implementation of the modern McEliece cryptosystem that uses the generalized (L, G)-codes with locators of degree greater than or equal to the second one without using an extended field. Mаin Results. Approaches to implementation of the modern McEliece cryptosystem based on the generalized (L, G)-codes are developed, namely: creation of a parity check matrix for the generalized (L, G)-code using a separable Goppa polynomial and locators of various degrees, description of an approach to the implementation of encryption and decryption of messages in the modern McEliece cryptosystem, presentation of the Chein’s procedure for numerators of degree greater than or equal to the second one without expanding the field. Practical Relevance. The proposed methods can be used in the development of cryptographic systems that can withstand attacks from quantum computers and ensure data confidentiality, as well as improve the security and performance of cryptosystems. Aerospace, automobile, railway, network multimedia, telecommunication and mobile information protection systems can also be the scope of the work results.