Commitment Schemes from Supersingular Elliptic Curve Isogeny Graphs

Bruno Sterner

eprint.iacr.org will be offline for approximately an hour for routine maintenance at 11pm UTC on Tuesday, April 16. We lost some data between April 12 and April 14, and some authors have been notified that they need to resubmit their papers.

Paper 2021/1031

Commitment Schemes from Supersingular Elliptic Curve Isogeny Graphs

Bruno Sterner

Abstract

In this work we present two commitment schemes based on hardness assumptions arising from supersingular elliptic curve isogeny graphs, which possess strong security properties. The first is based on the CGL hash function while the second is based on the SIDH framework, both of which require a trusted third party for the setup phrase. The proofs of security of these protocols depend on properties of non-backtracking random walks on regular graphs. The optimal efficiency of these protocols depends on the size of a certain constant, defined in the paper, related to relevant isogeny graphs, which we give conjectural upper bounds for.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. MathCrypt 2021
Keywords: post-quantum cryptography public-key cryptography commitment schemes isogeny-based cryptography isogeny graphs
Contact author(s): b sterner @ surrey ac uk
History: 2021-08-16: received
Short URL: https://ia.cr/2021/1031
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1031,
      author = {Bruno Sterner},
      title = {Commitment Schemes from Supersingular Elliptic Curve Isogeny Graphs},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1031},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/1031}},
      url = {https://eprint.iacr.org/2021/1031}
}