Commitment Schemes from Supersingular Elliptic Curve Isogeny Graphs

Bruno Sterner

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},
      url = {https://eprint.iacr.org/2021/1031}
}