Paper 2020/196

Trustless Groups of Unknown Order with Hyperelliptic Curves

Samuel Dobson and Steven D. Galbraith

Abstract

We suggest an alternative method of generating groups of unknown order for constructions such as cryptographic accumulators, by using the Jacobian groups of hyperelliptic curves (especially of genus 3). We propose that this construction is more efficient in practice than other proposals such as the use of ideal class groups of imaginary quadratic fields. We suggest that both the group operation and the size of element representation is an improvement over class groups. We also offer potential parameter choices for security with respect to best current algorithms for calculating the order of these groups.