The SQInstructor: a guide to SQIsign and the Deuring Correspondence with level structures
This work addresses cryptographic security and efficiency in post-quantum signature schemes for cryptographers, but appears incremental as it builds on existing SQIsign and Deuring correspondence frameworks.
The authors generalized the SQIsign signature scheme by incorporating level structures, requiring an isogeny that maps a chosen level structure between public key and commitment, and instantiated this with 1D and 2D isogenies, providing a new explicit Deuring correspondence for supersingular elliptic curves with level structures and solving new constrained norm equations.
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.