On the key generation in SQISign

Hiroshi Onuki

Paper 2022/900

On the key generation in SQISign

Hiroshi Onuki

, The University of Tokyo

Abstract

SQISign is an isogeny-based signature scheme that has short keys and signatures and is expected to be a post-quantum scheme. Its security depends on the hardness of the problem to find an isogeny between given two elliptic curves over $\mathbb{F}_{p^2}$, where $p$ is a large prime. For efficiency reasons, a public key in SQISign is taken from a set of supersingular elliptic curves with a particular property. In this paper, we investigate the security related to public keys in SQISign. First, we show some properties of the set of public keys. Next, we show that a key generation procedure used in implementing SQISign could not generate all public keys and propose a modification for the procedure. In addition, we confirm the latter result through an experiment.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: isogeny-based cryptography supersingular elliptic curves
Contact author(s): onuki @ mist i u-tokyo ac jp
History: 2023-01-30: revised; 2022-07-11: received; See all versions
Short URL: https://ia.cr/2022/900
License: CC BY

BibTeX

@misc{cryptoeprint:2022/900,
      author = {Hiroshi Onuki},
      title = {On the key generation in SQISign},
      howpublished = {Cryptology ePrint Archive, Paper 2022/900},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/900}},
      url = {https://eprint.iacr.org/2022/900}
}