4.5NTMar 10
The SQInstructor: a guide to SQIsign and the Deuring Correspondence with level structuresGiacomo Borin, Luca De Feo, Guido Maria Lido et al.
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.