Post-quantum cryptosystems: open problems and current solutions. Isogeny-based and code-based cryptosystems

This paper is a survey of modern post-quantum cryptographic schemes based on codes and isogenies. Special attention is paid to cryptanalysis of these schemes. In particular, for code-based cryptosystems we describe the information set decoding and the support splitting algorithm as main attacks, and for cryptosystems based on isogenies we describe in detail the Castryck — Decru attack on SIDH/SIKE. Tab. 2, bibliogr. 43.