Paper 2003/094 Original: eprint.iacr.org/2003/094 ↗

Trace Zero Subvariety for Cryptosystems

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.