On Actively Secure Fine-grained Access Structures from Isogeny Assumptions

Philipp Muth; Fabio Campos

Paper 2021/1109

On Actively Secure Fine-grained Access Structures from Isogeny Assumptions

Philipp Muth, Technische Universität Darmstadt, Germany

Fabio Campos, RheinMain University of Applied Sciences, Wiesbaden, Germany, Radboud University, Nijmegen, The Netherlands

Abstract

We present an actively secure threshold scheme in the setting of Hard Homogeneous Spaces (HHS) which allows ﬁne-grained access structures. More precisely, we elevate a passively secure isogeny-based threshold scheme to an actively secure setting. We prove the active security and simulatability of our advanced schemes. By characterising the necessary properties, we open our schemes to a signiﬁcantly wider ﬁeld of applicable secret sharing schemes. Furthermore, we show that Shamir’s scheme has our generalised properties, and thereby our approach truly represents a less restrictive generalisation.

Metadata

Available format(s): PDF
Category: Applications
Publication info: Preprint.
Keywords: post-quantum cryptography isogeny-based cryptography
Contact author(s): philipp muth @ tu-darmstadt de
campos @ sopmac de
History: 2022-09-12: last of 2 revisions; 2021-08-31: received; See all versions
Short URL: https://ia.cr/2021/1109
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1109,
      author = {Philipp Muth and Fabio Campos},
      title = {On Actively Secure Fine-grained Access Structures from Isogeny Assumptions},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1109},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/1109}},
      url = {https://eprint.iacr.org/2021/1109}
}