SQIsign is the leading digital signature protocol based on isogenies and
the only isogeny-based construction in the NIST standardisation
process. In this talk, we introduce the SQIsign protocol, presenting its
design and its connections to the most fundamental isogeny problems. We
also discuss the many variants of SQIsign that have appeared over the
last few years, with a particular focus on the recent changes that have
become the round-2 NIST submission. Lastly, we discuss some recent
results that provide a formal and complete proof of security of SQIsign,
which fills a long-standing gap in the literature.