Proposal for A CIMPA research school on

Isogenies of elliptic curves
and their applications to cryptography


Universidad del Cauca, Popayán, Colombia, July 2021






     

 

Isogenies of elliptic curves, or more generally of abelian varieties, are surjective homomorphism having finite kernel and they play an important role in the study of arithmetic and geometric properties of elliptic curves. Moreover in recent years there has been an increasing interest in isogenies of elliptic curves from cryptographers. The reason being that, in all likelihood, isogeny based cryptography should be more resistant to the cryptanalytic powers of the quantum computer. The first week of the school will be devoted to lay down the basis for the more advanced courses of the second week, in particular we will have courses on algebraic number theory, finite fields, elliptic curves, graph theory (actually this last course is split between the 2 weeks) all these courses are introductory and they will have exercise/training session. In the second week we have one introductory course which will cover elliptic curves over finite fields and endomorphisms rings of elliptic curves, and two advanced courses one on isogenies of elliptic curves and and one on isogeny based cryptography. For the courses of the second week we plan to have computational training sessions (i.e. using computers) as well as exercises sessions.
Scientific Committee

Local Committee

  • Carlos Trujillo (Local coordinator)
    Universidad del Cauca, Popayán
    Colombia

  • Jhon Jairo Bravo Grijalba
    Universidad del Cauca, Popayán
    Colombia

  • Marta Judith Romero Rojas
    Universidad del Cauca, Popayán
    Colombia

  • Maribel del Cármen Diaz Noguera
    Universidad del Cauca, Popayán
    Colombia

  • Ingrid Samín Cerón Bravo
    Universidad del Cauca, Popayán
    Colombia

  • Wilson Arley Martinez Flor
    Universidad del Cauca, Popayán
    Colombia

  • Diego Fernando Ruiz Solarte
    Universidad del Cauca, Popayán
    Colombia