Paper 2026/493

The SQInstructor: a guide to SQIsign and the Deuring Correspondence with level structures

Luca De Feo, IBM Research - Zurich

Guido Maria Lido, University of Rome Tor Vergata

Sina Schaeffler, IBM Research - Zurich, ETH Zurich

Abstract

We explore the use of level structures to generalize the SQIsign signature scheme. We give a general framework where, given the public key and the commitment, the challenge is to exhibit an isogeny between them with an additional requirement, namely to map a chosen level structure to nother. We then instantiate the framework using 1-dimensional and 2-dimensional isogenies. In doing that we provide a new explicit Deuring correspondence for supersingular elliptic curves with level structures and solve new constrained norm equations.

@misc{cryptoeprint:2026/493,
      author = {Giacomo Borin and Luca De Feo and Guido Maria Lido and Sina Schaeffler},
      title = {The {SQInstructor}: a guide to {SQIsign} and the Deuring Correspondence with level structures},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/493},
      year = {2026},
      url = {https://eprint.iacr.org/2026/493}
}