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Isogenies of Elliptic Curves and their Application to Cryptography

Location

Popayán, Colombia

Dates

26/07/2021 to 06/08/2021

Presentation

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 isogeny of elliptic curves from cryptographers. The main reason lies in quantum computer as Luca de Feo eloquently puts it: ''The main reason for this is the sudden realization by the cryptographic community of the very possibly near arrival of a general purpose quantum computer. While the capabilities of such futuristic machine would render all of Elliptic Curves Cryptography and Pairing Based Cryptography suddenly worthless, Isogeny Based Cryptography seems to resist much better to the cryptanalytic powers of the quantum computer'' (Mathematics of Isogeny Based Cryptography, arXiv:1711.04062).

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 this courses are introductory and the will have exercise/training session. In the second week we have one introductory course Elliptic curves over Finite fields and their Endomorphisms Rings, and two advanced courses Isogenies of Elliptic curves and Isogeny based cryptography. For the courses of the second week we plan to have hands on training sessions (i.e. on computers) as well as exercises sessions.

Official language of the school: English

Administrative and scientific coordinators

Carlos Alberto Trujillo Solarte (Universidad del Cauca, Colombia, trujillo@unicauca.edu.co)
Marusia Rebolledo (Université Clermont Auvergne, France, marusia.rebolledo@uca.fr)

Scientific committee

Marusia Rebolledo (Université Clermont Auvergne, France)
Luca De Feo (Université de Versailles – Saint-Quentin, France)
Sorina Ionica (Université de Picardie, France)
Amalia Pizarro (Universidad de Valparaíso, Chile)
Valerio Talamanca (Università Roma Tre, Italy)
Carlos Alberto Trujillo Solarte (Universidad del Cauca, Colombia)

Scientific program

Course 1: "Number Theory", Yuri Bilu (Université de Bordeaux, France) & Amalia Pizarro (Universidad de Valparaíso, Chile)
Course 2: "Finite Fields", Michel Waldschmidt (Sorbonne Université, France) & Florian Luca (University of the Witwatersrand, South Africa)
Course 3: "Elliptic Curves", Cecila Salgado (Universidade Federal do Rio de Jainero, Brazil) & Fernando Rodriguez Villegas (ICTP, Italy)
Course 4: "Graph Theory", Amanda Montejano (Universidad Nacional Autónoma de México Juriquilla, Mexico) & Carlos Alberto Trujillo Solarte (Universidad del Cauca, Colombia)
Course 5: "Further Topics in the Theory of Elliptic Curves", Francesco Pappalardi (Università Roma Tre, Italy) & Valerio Talamanca (Università Roma Tre, Italy)
Course 6: "Isogenies of Elliptic Curves", Marusia Rebolledo (Université Clermont Auvergne, France) & Sorina Ionica (Picardie Jules Verne, France)
Course 7: "Isogeny Based Cryptography", Luca De Feo (Université de Versailles – Saint-Quentin, France) & Julio Lopez (Universidad de Campinas, Brazil)

Website of the school

http://www.rnta.eu/Popayan2021/

How to participate:

For registration and application to a CIMPA financial support, follow the instructions given here

Deadline for registration and application:  May 30, 2021