Exploring SIDH-based Signature Parameters

Andrea Basso; Mingjie Chen; Tako Boris Fouotsa; Péter Kutas; Abel Laval; Laurane Marco; Gustave Tchoffo Saah

Paper 2023/1906

Exploring SIDH-based Signature Parameters

Andrea Basso

, University of Bristol

Mingjie Chen, University of Birmingham

Tako Boris Fouotsa

, École Polytechnique Fédérale de Lausanne

Péter Kutas

, Eötvös Loránd University and University of Birmingham

Abel Laval, Université Libre de Bruxelles

Laurane Marco, École Polytechnique Fédérale de Lausanne

Gustave Tchoffo Saah, Université de Yaoundé 1, Cameroon

Abstract

Isogeny-based cryptography is an instance of post-quantum cryptography whose fundamental problem consists of finding an isogeny between two (isogenous) elliptic curves $E$ and $E'$. This problem is closely related to that of computing the endomorphism ring of an elliptic curve. Therefore, many isogeny-based protocols require the endomorphism ring of at least one of the curves involved to be unknown. In this paper, we explore the design of isogeny based protocols in a scenario where one assumes that the endomorphism ring of all the curves are public. In particular, we identify digital signatures based on proof of isogeny knowledge from SIDH squares as such a candidate. We explore the design choices for such constructions and propose two variants with practical instantiations. We analyze their security according to three lines, the first consists of attacks based on KLPT with both polynomial and superpolynomial adversary, the second consists of attacks derived from the SIDH attacks and finally we study the zero-knowledge property of the underlying proof of knowledge.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. ACNS 2024
Keywords: Isogeny-based cryptography Sigma protocols Signatures
Contact author(s): andrea basso @ bristol ac uk
m chen 1 @ bham ac uk
tako fouotsa @ epfl ch
p kutas @ bham ac uk
abel laval @ ulb be
laurane marco @ epfl ch
gustavesaah @ gmail com
History: 2023-12-15: approved; 2023-12-12: received; See all versions
Short URL: https://ia.cr/2023/1906
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1906,
      author = {Andrea Basso and Mingjie Chen and Tako Boris Fouotsa and Péter Kutas and Abel Laval and Laurane Marco and Gustave Tchoffo Saah},
      title = {Exploring SIDH-based Signature Parameters},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1906},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/1906}},
      url = {https://eprint.iacr.org/2023/1906}
}