Paper 2020/1323 Original: eprint.iacr.org/2020/1323 ↗
CSI-RAShi: Distributed key generation for CSIDH
Abstract
We present an honest-majority Distributed Key Generation protocol (DKG) based on Shamir's $(k,n)$-threshold secret sharing in the setting of Very Hard Homogenous Spaces (VHHS). DKG's in the DLOG setting use Pedersen commitments, for which there is no known analogue in the VHHS setting. As a replacement, we introduce a new primitive called piecewise verifiable proofs, which allow a prover to prove that a list of NP-statements is valid with respect to a common witness, and such that the different statements can be verified individually. Our protocol is robust and actively secure in the Quantum Random Oracle Model. For $n$ participants, the total runtime of our protocol is\break $2+\lambda+n(1+4\lambda)$ group action evaluations, where $\lambda$ is the underlying security parameter, and is thus independent of the threshold $k$. When instantiated with CSIDH-512, this amounts to approximately $4.5+18n$ seconds.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2020-10-23: last updated
- 2020-10-23: published
- Short URL
- https://ia.cr/2020/1323
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2020/1323,
author = {Ward Beullens and Lucas Disson and Robi Pedersen and Frederik Vercauteren},
title = {CSI-RAShi: Distributed key generation for CSIDH},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/1323},
year = {2020},
url = {https://eprint.iacr.org/2020/1323}
}