The Isogeny Problems

Wouter Castryck; Luca De Feo; Steven D. Galbraith; Péter Kutas; Krijn Reijnders; Benjamin Wesolowski

Paper 2026/1431

The Isogeny Problems

Wouter Castryck

, KU Leuven

Luca De Feo

, IBM Research - Zurich

Steven D. Galbraith

, University of Auckland

Péter Kutas

, University of Birmingham, Eötvös Loránd University

Krijn Reijnders

, KU Leuven

Benjamin Wesolowski

, École Normale Supérieure de Lyon

Abstract

This work contains an exposition of the seven foremost unsolved problems in the domain of isogeny-based cryptography, obtained by asking eleven experts in isogeny-based cryptography what they considered to be the most important unsolved problems in isogeny-based cryptography, and curated down to the seven problems in this document. For each problem, an expert wrote a short write-up giving the precise statements and descriptions per problem.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: isogeny isogenies open problems
Contact author(s): reijnderskrijn @ gmail com
History: 2026-07-16: approved; 2026-07-13: received; See all versions
Short URL: https://ia.cr/2026/1431
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1431,
      author = {Wouter Castryck and Luca De Feo and Steven D. Galbraith and Péter Kutas and Krijn Reijnders and Benjamin Wesolowski},
      title = {The Isogeny Problems},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1431},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1431}
}