**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.

**Category / Keywords: **Public key cryptography, discrete logarithm, hyperelliptic curves, abelian varieties, Frobenius endomorphism, fast arithmetic

**Publication Info: **submitted

**Date: **received 16 May 2003, last revised 22 May 2003

**Contact author: **lange at itsc rub de

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Note: **Nicer picture

**Version: **20030522:213035 (All versions of this report)

**Short URL: **ia.cr/2003/094

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