DEFEND: Towards Verifiable Delay Functions from Endomorphism Rings

Knud Ahrens; Jens Zumbrägel

Paper 2023/1537

DEFEND: Towards Verifiable Delay Functions from Endomorphism Rings

Knud Ahrens, University of Passau

Jens Zumbrägel, University of Passau

Abstract

We present a verifiable delay function based on isogenies of supersingular elliptic curves, using Deuring correspondence and computation of endomorphism rings for the delay. For each input x a verifiable delay function has a unique output y and takes a predefined time to evaluate, even with parallel computing. Additionally, it generates a proof by which the output can efficiently be verified. In our approach the input is a path in the 2-isogeny graph and the output is the maximal order isomorphic to the endomorphism ring of the curve at the end of that path. This approach is presumably quantum-secure, does not require a trusted setup or special primes and the verification is independent from the delay. It works completely within the isogeny setting and the computation of the proof causes no overhead. The efficient sampling of challenges however remains an open problem.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Verifiable delay function Isogeny walks Modular polynomials Deuring correspondence
Contact author(s): knud ahrens @ uni-passau de
jens zumbraegel @ uni-passau de
History: 2023-10-20: revised; 2023-10-07: received; See all versions
Short URL: https://ia.cr/2023/1537
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1537,
      author = {Knud Ahrens and Jens Zumbrägel},
      title = {{DEFEND}: Towards Verifiable Delay Functions from Endomorphism Rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1537},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1537}
}