Disguising tori and elliptic curves

Steven D.  Galbraith

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Paper 2006/248

Disguising tori and elliptic curves

Steven D. Galbraith

Abstract

Frey proposed the idea of `disguising' an elliptic curve. This is a method to obtain a `black box' representation of a group. We adapt this notion to finite fields and tori and study the question of whether such systems are secure. Our main result is an algebraic attack which shows that it is not secure to disguise the torus $T_2$. We also show that some methods for disguising an elliptic curve are not secure. Finally, we present a method to disguise an elliptic curve which seems to resist our algebraic attack.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic curves algebraic tori weil descent
Contact author(s): Steven Galbraith @ rhul ac uk
History: 2006-07-21: received
Short URL: https://ia.cr/2006/248
License: CC BY

BibTeX

@misc{cryptoeprint:2006/248,
      author = {Steven D.  Galbraith},
      title = {Disguising tori and elliptic curves},
      howpublished = {Cryptology ePrint Archive, Paper 2006/248},
      year = {2006},
      note = {\url{https://eprint.iacr.org/2006/248}},
      url = {https://eprint.iacr.org/2006/248}
}