Polynomials over Finite Fields and Applications

Self-reciprocal irreducible monic (srim) polynomials over finite fields have been studied in the past. These polynomials can be studied in the context of quadratic transformation of irreducible polynomials over finite fields. In this talk we present the generalization of some of the results known about srim polynomials to polynomials obtained by quadratic transformation of irreducible polynomials over finite fields. Speaker: Dan Bernstein (University of Illinois at Chicago) Title: Faster factorization into coprimes Abstract: How quickly can we factor a set of univariate polynomials into coprimes? See http://cr.yp.to/coprimes.html for examples and applications. Bach, Driscoll, and Shallit achieved time n in 1990, where n is the number of input coefficients; I achieved time n(lg n) in 1995; much more recently I achieved time n(lgn). Speaker: Antonia Bluher (National Security Agency) Title: Hyperquadratic elements of degree 4 Abstract: I will describe joint work with Alain Lasjaunias about the construction of degree-4 polynomials over fields K of char p whose roots α have a Frobenius property: