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 curvesalgebraic toriweil descent
Contact author(s)
Steven Galbraith @ rhul ac uk
History
2006-07-21: received
Short URL
https://ia.cr/2006/248
License
Creative Commons Attribution
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}
}
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