Cryptology ePrint Archive: Report 2019/1288

Threshold Schemes from Isogeny Assumptions

Luca De Feo and Michael Meyer

Abstract: We initiate the study of threshold schemes based on the Hard Homogeneous Spaces (HHS) framework of Couveignes. Quantum-resistant HHS based on supersingular isogeny graphs have recently become usable thanks to the record class group precomputation performed for the signature scheme CSI-FiSh. Using the HHS equivalent of the technique of Shamir's secret sharing in the exponents, we adapt isogeny based schemes to the threshold setting. In particular we present threshold versions of the CSIDH public key encryption, and the CSI-FiSh signature schemes. The main highlight is a threshold version of CSI-FiSh which runs almost as fast as the original scheme, for message sizes as low as 1880 B, public key sizes as low as 128 B, and thresholds up to 56; other speed-size-threshold compromises are possible.

Category / Keywords: public-key cryptography / Threshold cryptography, Hard homogeneous spaces, Isogeny-based cryptography, CSIDH, CSI-FiSh

Date: received 6 Nov 2019

Contact author: luca de-feo at uvsq fr, michael meyer@hs-rm de

Available format(s): PDF | BibTeX Citation

Version: 20191107:101852 (All versions of this report)

Short URL: ia.cr/2019/1288


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