Investigation of the Structure of the Isogeny Graph for Postquantum Cryptography Protocols

Abstract

The isogeny graphs of supersingular curves are one of the promising mathematical structures in postquantum cryptography algorithms. However, the recently reported attack on the SIDH protocol [1] demonstrates that the isogeny graphs require a more detailed investigation when applied to real protocols. In this study, we analyze the structure of the graphs of isogenies of degree \(\ell > 2\) and consider the set of vertices of a special type to which an attack on reconstruction of the path in the graph is applicable [7].