Trace Zero Subvarieties of Genus 2 Curves for Cryptosystems

  title={Trace Zero Subvarieties of Genus 2 Curves for Cryptosystems},
  author={Tanja Lange},
In this paper we present a kind of group suitable for cryptographic applications: the trace zero subvariety. We describe in detail the case of trace zero varieties constructed from genus 2 curves over prime fields. The curve is considered over an extension field of degree 3 and one performs Weil descent from its Jacobian to the prime field leading to a variety of dimension 6. The trace zero variety is a subvariety thereof. As a group it is isomorphic to a subgroup of the Jacobian of the… CONTINUE READING