A faster way to the CSIDH

Abstract

Recently Castryck, Lange, Martindale, Panny, and Renes published CSIDH, a new key exchange scheme using supersingular elliptic curve isogenies. Due to its small key sizes and the possibility of a non-interactive and a static-static key exchange, CSIDH seems very interesting for practical applications. However, the performance is rather slow. Therefore, we employ some techniques to speed up the algorithms, mainly by restructuring the elliptic curve point multiplications and by using twisted Edwards curves in the isogeny image curve computations, yielding a speed-up factor of 1.33 in comparison to the implementation of Castryck et al. Furthermore, we suggest techniques for constant-time implementations.