SQIsign: how to get a digital signature from the Deuring correspondence

The Deuring correspondence establishes an interesting link between the geometric world of supersingular elliptic curves and the arithmetic world of quaternion algebras over Q. In this talk, after reviewing the mathematical background of such correspondence, we are going to present the digital signature scheme of SQIsign by De Feo et al., which is based on it. We will analyze the scheme's structure, properties, security assumptions and backdraws, and we will mention how some of these limitations are resolved by the higher dimensional scheme SQIsignHD by Dartois et al.