Isogenies of certain abelian varieties over finite fields with p-ranks zero

Steve Thakur

Paper 2020/212

Isogenies of certain abelian varieties over finite fields with p-ranks zero

Steve Thakur

Abstract

We study the isogenies of certain abelian varieties over finite fields with non-commutative endomorphism algebras with a view to potential use in isogeny-based cryptography. In particular, we show that any two such abelian varieties with endomorphism rings maximal orders in the endomorphism algebra are linked by a cyclic isogeny of prime degree.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Isogenies abelian varieties non-commutative endomorphism rings
Contact author(s): stevethakur01 @ gmail com
History: 2020-05-19: last of 2 revisions; 2020-02-19: received; See all versions
Short URL: https://ia.cr/2020/212
License: CC BY

BibTeX

@misc{cryptoeprint:2020/212,
      author = {Steve Thakur},
      title = {Isogenies of certain abelian varieties over finite fields with p-ranks zero},
      howpublished = {Cryptology ePrint Archive, Paper 2020/212},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/212}},
      url = {https://eprint.iacr.org/2020/212}
}