A $\lambda$-adic family of Funke-Millson cycles and a $\lambda$-adic Funke-Millson lift
De Paul Kiefer
Modularity of special cycles in orthogonal and unitary Shimura varieties
De Salim Tayou
De Yan Bo Ti
Apparaît dans la collection : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codes 2023
It is an understatement to say that isogeny-based cryptography has been on a journey of ups and downs. Through the course of this journey, various techniques have been used to analyse isogeny-based cryptosystems. One of which, is using genus two methods to examine and build isogeny-based cryptosystems, and ultimately break one of the most promising key exchange schemes, SIDH. In this talk, we will look at cameos and appearances of genus two in isogeny-based cryptography. We will survey the landscape and see how genus two can be used constructively and sometimes destructively on isogeny-based cryptography.