14 citations · 22 across the 4 of their papers we have counts for
4 papers
Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
Benjamin Smith
We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperell…
Distortion maps for genus two curves
Steven D. Galbraith, Jordi Pujolàs, Christophe Ritzenthaler +1
Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full…
Discrete Logarithms in Generalized Jacobians
S. D. Galbraith, B. A. Smith
Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal g…
Efficiently computable endomorphisms for hyperelliptic curves
David R. Kohel, Benjamin A. Smith
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. R…