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

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 another. 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.

Source: arXiv:2603.09899v1 - http://arxiv.org/abs/2603.09899v1 PDF: https://arxiv.org/pdf/2603.09899v1 Original Link: http://arxiv.org/abs/2603.09899v1