I am going to talk about recent topics in cryptographic theory based on elliptic and hyperelliptic curves. I will start with a general introduction on the elliptic and hyperelliptic curve cryptograpy (ECC) then explain certan recent attacks to ECC and security analysis against these attacks, including results from my own group. In particular, ECC defined…

9:45-10:45 Riccardo Brasca (Université Paris Diderot), “Hida theory over unitary Shimura varieties without ordinary locus” 11:00-12:00 Francesca Gatti (Universitat Politècnica de Catalunya), “Special values of the triple product p-adic L-function and non-cristalline Kolyvagin classes” 12:15-13:15 James Newton (King’s College London), “Local-global compatibility and the cohomology of locally symmetric spaces” 15:00-16:00 Vinayak Vatsal (University of British…

09.30 – 10.15: Dihedral Galois representations and CM forms (Nicolas Billerey (Univ. Clermond-Ferrand)) 11.00 – 11.45: Implementing Algorithms to Compute Elliptic Curves Over Q (A. Gherga (UBC Vancouver)) 12.00 – 12.45: Congruences for sporadic sequences and modular forms for non-congruence subgroups (Matija Kazalicki (Zagreb))