**Title :** **Modern Cryptography and Permuation ****polynomials**

**Absract**: Cryptography is an indispensable tool used to protect information in computing systems. It is used everywhere. Cryptography is based on basic mathematics called number theory. In this lecture we will talk about the principles of modern cryptography. We specify the different ingredients that characterize cryptography. Then we will focus on public key cryptography and its recent developments. One of the problems that remains open is to find all permutation polynomials of an arbitrary finite field. Progress on this problem will help to make the methods of modern cryptography more convenient. In mathematics, a permutation polynomial over a ring is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x — P(x) is a bijection. In case the ring is a finite field, the Dickson polynomials, which are closely related to the Cheby-shev polynomials, provide examples. Over a finite field, every function, so in particular every permutation of the elements of that field, can be written as a polynomial function. The permutation polynomial P(x) is declared to be a public polynomial for encryption. A public key encryption of given message M(x) is the evaluation of polynomial P(x) at point M(x) where the result of evaluation is calculated via so called White box reduction, which does not reveal the underlying secret polynomial g(x).

**Biography:**

Education :

M.S. Université Bordeaux 1, 1988 (Pure Mathematics). Ph.D. Université Bordeaux 1, 1992 ( Number Theory). Research : Number theory. Currently : Adviser of 3 PHD Thesis.

Award 2012 : Prize of the Excellence in Research by French Gouvernment.