Trace Zero Subvariety for Cryptosystems

Tanja Lange

Paper 2003/094

Trace Zero Subvariety for Cryptosystems

Tanja Lange

Abstract

We present a kind of group suitable for cryptographic applications: the trace zero subvariety. The construction is based on Weil descent from curves of genus two over extension fields $\F_{p^{n}}$ , $n = 3$ . On the Jacobian of the curve the group can be seen as a prime order subgroup, however, considering the construction as Weil descent we can argue that the security is equivalent to that of groups based on low-genus hyperelliptic curves over prime fields. The advantage is that the complexity to compute scalar multiples is lower, as one can make use of the Frobenius endomorphism of the initial curve. Thus the trace zero subvariety can be used efficiently in protocols based on the discrete logarithm problem.

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Metadata

Available format(s): PDF PS
Publication info: Published elsewhere. submitted
Keywords: Public key cryptography discrete logarithm hyperelliptic curves abelian varieties Frobenius endomorphism fast arithmetic
Contact author(s): lange @ itsc rub de
History: 2003-05-22: revised; 2003-05-17: received; See all versions
Short URL: https://ia.cr/2003/094
License: CC BY

BibTeX

@misc{cryptoeprint:2003/094,
      author = {Tanja Lange},
      title = {Trace Zero Subvariety for Cryptosystems},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/094},
      year = {2003},
      url = {https://eprint.iacr.org/2003/094}
}