On the existence of distortion maps on ordinary elliptic curves

Denis Charles

Paper 2006/128

On the existence of distortion maps on ordinary elliptic curves

Denis Charles

Abstract

Distortion maps allow one to solve the Decision Diffie-Hellman problem on subgroups of points on an elliptic curve. In the case of ordinary elliptic curves over finite fields, it is known that in most cases there are no distortion maps for the Frobenius eigenspaces. In this article we characterize the existence of distortion maps in the remaining cases.

Note: Updated version, corrects an error in the previous proof.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic curves Decision Diffie-Hellman problem Distortion maps
Contact author(s): cdx @ microsoft com
History: 2006-08-15: revised; 2006-04-03: received; See all versions
Short URL: https://ia.cr/2006/128
License: CC BY

BibTeX

@misc{cryptoeprint:2006/128,
      author = {Denis Charles},
      title = {On the existence of distortion maps on ordinary elliptic curves},
      howpublished = {Cryptology ePrint Archive, Paper 2006/128},
      year = {2006},
      note = {\url{https://eprint.iacr.org/2006/128}},
      url = {https://eprint.iacr.org/2006/128}
}