Paper 2017/383

Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography

Travis Scholl

Abstract

We call a simple abelian variety over $\mathbb{F}_p$ super-isolated if its ($\mathbb{F}_p$-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about isogeny based attacks on the discrete log problem. We heuristically estimate that the number of super-isolated elliptic curves over $\mathbb{F}_p$ with prime order and $p \leq N$, is roughly $\tilde{\Theta}(\sqrt{N})$. In contrast, we prove that there are only 2 super-isolated surfaces of cryptographic size and near-prime order.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
elliptic curve cryptosystemnumber theory
Contact author(s)
tscholl2 @ uw edu
History
2017-05-04: received
Short URL
https://ia.cr/2017/383
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/383,
      author = {Travis Scholl},
      title = {Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2017/383},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/383}},
      url = {https://eprint.iacr.org/2017/383}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.