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**2003/094**

**Title:**

Trace Zero Subvariety for Cryptosystems

**Authors:**
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.

**ePrint:**
https://eprint.iacr.org/2003/094

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