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Paper 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.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
A minor revision of an IACR publication in PKC 2020
Keywords
Threshold cryptographyHard homogeneous spacesIsogeny-based cryptographyCSIDHCSI-FiSh
Contact author(s)
luca de-feo @ uvsq fr
michael meyer @ hs-rm de
History
2020-02-07: revised
2019-11-07: received
See all versions
Short URL
https://ia.cr/2019/1288
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2019/1288,
      author = {Luca De Feo and Michael Meyer},
      title = {Threshold Schemes from Isogeny Assumptions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1288},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1288}
}
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