Main approaches in post-quantum cryptography: description, a comparative study

Post-quantum cryptography is an area of theoretical and applied research with the goal to develop cryptographic systems that are secure against both quantum and classical computers. Now, among the most promising directions one can mention the lattice-based cryptography, code-based cryptography and isogenies. This paper is a review, it includes a summary of two papers previously prepared by the authors and devoted to the description of the main approaches to the construction of post-quantum cryptosystems. Hard problems from these areas are considered, known results on resilience and performance of the corresponding cryptosystems are analyzed.