Abstract:
Abstract:
Supersingular elliptic curves are a special kind of elliptic curves over finite fields. Their study, that had begun more than a century ago, is intimately connected to quaternion algebra and modular forms. In recent years supersingular elliptic curves (and their generalizations) have found several cryptographic applications that, in turn, led to further theoretical developments.
Assuming minimal background, we will explains what are these elliptic curves and what is their connection to quaternion algebras and applications to cryptography. We will present several new results inspired by cryptographic problems, but that are eventually stand-alone results concerning lattices and modular forms
