SQIsign is an isogeny-based signature scheme in Round 1 of NIST’s recent alternate call for signature schemes. In this talk, we will take a closer look at SQIsign verification and demonstrate that it can be performed completely on Kummer surfaces. In this way, one-dimensional SQIsign verification can be viewed as a two-dimensional isogeny between products of elliptic curves. Curiously, the isogeny is then defined over Fp rather than Fp2. Furthermore, we will introduce new techniques that enable verification for compression signatures using Kummer surfaces, in turn creating a toolbox for isogeny-based cryptography in dimension 2.This is based on joint work with Krijn Reijnders.