Paper 2022/1469
Supersingular Curves You Can Trust
, University of Bristol, University of Birmingham, University of Rome Tor Vergata, IBM Research Europe, École Polytechnique Fédérale de Lausanne, University of Rome Tor Vergata, Virginia Tech, IBM Research India, University of Bordeaux, French Institute for Research in Computer Science and Automation, École Normale Supérieure de LyonAbstract
Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a notoriously hard task, despite several isogeny-based protocols relying on such an object. A trusted setup is often proposed as a workaround, but several aspects remain unclear. In this work, we develop the tools necessary to practically run such a distributed trusted-setup ceremony. Our key contribution is the first statistically zero-knowledge proof of isogeny knowledge that is compatible with any base field. To prove statistical ZK, we introduce isogeny graphs with Borel level structure and prove they have the Ramanujan property. Then, we analyze the security of a distributed trusted-setup protocol based on our ZK proof in the simplified universal composability framework. Lastly, we develop an optimized implementation of the ZK proof, and we propose a strategy to concretely deploy the trusted-setup protocol.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- A minor revision of an IACR publication in EUROCRYPT 2023
- Keywords
- IsogeniesRamanajuan GraphsZero-knowledge ProofsTrusted Setup
- Contact author(s)
-
andrea basso @ bristol ac uk
codogni @ mat uniroma2 it
durumcrustulum @ gmail com
secuer @ defeo lu
tako fouotsa @ epfl ch
guidomaria lido @ uniroma2 it
tmo @ vt edu
lorenz @ yx7 cc
sikhar patranabis @ ibm com - History
- 2023-02-24: revised
- 2022-10-26: received
- See all versions
- Short URL
- https://ia.cr/2022/1469
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2022/1469,
author = {Andrea Basso and Giulio Codogni and Deirdre Connolly and Luca De Feo and Tako Boris Fouotsa and Guido Maria Lido and Travis Morrison and Lorenz Panny and Sikhar Patranabis and Benjamin Wesolowski},
title = {Supersingular Curves You Can Trust},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1469},
year = {2022},
url = {https://eprint.iacr.org/2022/1469}
}
