Cryptology ePrint Archive: Report 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.

Category / Keywords: applications / post-quantum cryptography, isogeny-based cryptography

Date: received 30 Aug 2021, last revised 31 Aug 2021

Contact author: muth at seceng informatik tu-darmstadt de, campos at sopmac de

Available format(s): PDF | BibTeX Citation

Version: 20210831:133334 (All versions of this report)

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