Paper 2020/348

Constructing hidden order groups using genus three Jacobians

Steve Thakur

Abstract

Groups of hidden order have gained a surging interest in recent years due to applications to cryptographic commitments, verifiable delay functions and zero knowledge proofs. Recently, Dobson and Galbraith ([DG20]) proposed Jacobians of genus three hyperelliptic curves as a suitable candidate for such a group. While this looks like a promising idea, certain Jacobians are less secure than others and hence, the curve has to be chosen with caution. In this short note, we explore the types of Jacobians that would be suitable for this purpose.

Note: Comments/corrections/suggestions welcome