Multiradical isogenies

Wouter Castryck; Thomas Decru

Paper 2021/1133

Multiradical isogenies

Wouter Castryck and Thomas Decru

Abstract

We argue that for all integers and there exist "multiradical" isogeny formulae, that can be iteratively applied to compute -isogenies between principally polarized -dimensional abelian varieties, for any value of . The formulae are complete: each iteration involves the extraction of different th roots, whence the epithet multiradical, and by varying which roots are chosen one computes all extensions to an -isogeny of the incoming -isogeny. Our group-theoretic argumentation is heuristic, but it is supported by concrete formulae for several prominent families. As our main application, we illustrate the use of multiradical isogenies by implementing a hash function from -isogenies between Jacobians of superspecial genus- curves, showing that it outperforms its -counterpart by an asymptotic factor in terms of speed.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: isogeny abelian variety Jacobian hash function
Contact author(s): wouter castryck @ esat kuleuven be
thomas decru @ esat kuleuven be
History: 2021-12-01: last of 2 revisions; 2021-09-07: received; See all versions
Short URL: https://ia.cr/2021/1133
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1133,
      author = {Wouter Castryck and Thomas Decru},
      title = {Multiradical isogenies},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/1133},
      year = {2021},
      url = {https://eprint.iacr.org/2021/1133}
}