Return of the Kummer: a toolbox for genus 2 cryptography

ePrint Report: Return of the Kummer: a toolbox for genus 2 cryptography

Maria Corte-Real Santos, Krijn Reijnders

This work expands the machinery we have for isogeny-based cryptography in genus 2 by developing a toolbox of several essential algorithms for Kummer surfaces, the dimension 2 analogue of x-only arithmetic on elliptic curves. Kummer surfaces have been suggested in (hyper-)elliptic curve cryptography since at least the 1980s and recently these surfaces have reappeared to efficiently compute (2,2)-isogenies. We construct several essential analogues …

algorithms cryptography elliptic eprint report real report return toolbox work