Paper 2021/1109

On Actively Secure Fine-grained Access Structures from Isogeny Assumptions

Philipp Muth and Fabio Campos

Abstract

We present an actively secure threshold scheme in the setting of Hard Homogenous Spaces (HHS) which allows fine-grained access structures. More precisely, we elevate a given passively secure isogeny based threshold scheme to an actively secure setting. We prove the active security and simulatability of our advanced schemes. By defining some characterising properties, we are able to expand the range of secret sharing schemes which support the given scheme. Furthermore, we show that Shamir’s scheme has our generalised properties, and thereby our approach truly represents a less restrictive generalisation.