[Resource Topic] 2003/094: Trace Zero Subvariety for Cryptosystems

Welcome to the resource topic for 2003/094

Trace Zero Subvariety for Cryptosystems

Authors: Tanja Lange


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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