Applications of exponential sums to solvability of equations, cryptography

Por: Ivelisse Rubio

Miércoles, 20/agosto/2014

11:30 am


The p-divisibility of exponential sums of polynomials over finite fields can be used for a variety of applications. A little improvement on the estimation of the p-divisibility might be important in some applications. For example, the relation between the 2-divisibility of a Boolean function and certain deformations give information about cosets of Reed-Muller codes. Moreover, the computation of the exact p-divisibility of exponential sums associated to families of systems of polynomials guarantees the solvability of the system and, in the case of a Boolean functions, it proves that the functions are not balanced.

In this talk we present the covering method, an elementary method to compute p-divisibility of exponential sums and see how it can be used in some applications.

Posted August 15, 2014 by Computer Science Department