CSIDH with Level Structure

Steven D. Galbraith; Derek Perrin; José Felipe Voloch

Paper 2023/1726

CSIDH with Level Structure

Steven D. Galbraith

, University of Auckland

Derek Perrin

, University of Canterbury

José Felipe Voloch

, University of Canterbury

Abstract

We construct a new post-quantum cryptosystem which consists of enhancing CSIDH and similar cryptosystems by adding a full level $N$ structure. We discuss the size of the isogeny graph in this new cryptosystem which consists of components which are acted on by the ray class group for the modulus $N$. We conclude by showing that, if we can efficiently find rational isogenies between elliptic curves, then we can efficiently find rational isogenies that preserve the level structure. We show that one can reduce the group action problem for the ray class group to the group action problem for the ideal class group. This reduces the security of this new cryptosystem to that of the original one

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Isogenies CSIDH level structure
Contact author(s): s galbraith @ auckland ac nz
derek perrin @ pg canterbury ac nz
felipe voloch @ canterbury ac nz
History: 2023-11-13: approved; 2023-11-07: received; See all versions
Short URL: https://ia.cr/2023/1726
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1726,
      author = {Steven D. Galbraith and Derek Perrin and José Felipe Voloch},
      title = {CSIDH with Level Structure},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1726},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/1726}},
      url = {https://eprint.iacr.org/2023/1726}
}