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Disguising tori and elliptic curves

Authors:
Steven D. Galbraith
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URL: http://eprint.iacr.org/2006/248
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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.
BibTeX
@misc{eprint-2006-21741,
  title={Disguising tori and elliptic curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Elliptic curves, algebraic tori, weil descent},
  url={http://eprint.iacr.org/2006/248},
  note={ Steven.Galbraith@rhul.ac.uk 13349 received 20 Jul 2006},
  author={Steven D. Galbraith},
  year=2006
}