Starts 7 Jul 2014

Ends 19 Jul 2014

Central European Time

Algebraic Number Theory and Applications | (smr 2627)

Starts 7 Jul 2014

Ends 19 Jul 2014

Central European Time

Dangbo - Benin

The Abdus Salam International Centre for Theoretical Physics (ICTP) and the Centre International de Mathématiques Pures et Appliquées (International Center for Pure and Applied Mathematics - CIMPA) are jointly organizing the activity "Algebraic Number Theory and Applications", to be held in Dangbo, Benin from 7 to 19 July 2014.

**PURPOSE OF THE ACTIVITY** Algebraic number theory is a very active field of mathematics. The purpose of the activity is to introduce the subject and its application to cryptography. After given courses in elementary arithmetic, algebraic numbers and p-adic numbers, we will focus on the basics of elliptic curves and finite fields. Applications will also figure prominently in the programme, (see courses 'Introduction to cryptography' and 'Elliptic curves and cryptography'. Moreover, we plan to cover the explicit construction of elliptic curves over finite fields with group of point of large prime order (as needed by cryptographic applications) via complex multiplication.

**TOPICS to be covered by the activity include:**

1.Introduction aux formes quadratiques binaires (Speaker : Claude Levesque, Université Laval, Canada)

**2.Introduction to the elementary arithmetic** (Speaker : Alain Togbe, Westville, USA)

**3.Introduction to the algebraic number theory** (Speaker : Franscesco Pappalardi, Roma, Italy)

**4.Elliptic curves and cryptography** (Speaker : Jorge Jimenez Urroz, UPC, Barcelona, Spain)

**5.Diophantine equations** (Speaker : Florian Luca, Morelia, Mexico)

**6.Introduction to the theory of finite fields with application to error correcting codes** (Speaker : Michel Waldschmidt, Paris 6, France)

**7.Introduction to p-adic numbers** (Speaker : Adriana Salerno, Lewiston, USA)

1.Introduction aux formes quadratiques binaires