Isolated Curves and the MOV Attack

Travis Scholl

Paper 2018/307

Isolated Curves and the MOV Attack

Travis Scholl

Abstract

We present a variation on the CM method that produces elliptic curves over prime fields with nearly prime order that do not admit many efficiently computable isogenies. Assuming the Bateman-Horn conjecture, we prove that elliptic curves produced this way almost always have a large embedding degree, and thus are resistant to the MOV attack on the ECDLP.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Journal of Mathematical Cryptography
DOI: 10.1515/jmc-2016-0053
Keywords: elliptic curve cryptosystem number theory
Contact author(s): tscholl2 @ uw edu
History: 2018-04-03: received
Short URL: https://ia.cr/2018/307
License: CC BY

BibTeX

@misc{cryptoeprint:2018/307,
      author = {Travis Scholl},
      title = {Isolated Curves and the {MOV} Attack},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/307},
      year = {2018},
      doi = {10.1515/jmc-2016-0053},
      url = {https://eprint.iacr.org/2018/307}
}