Time: May 26, 15:00
S2 416-2

Titel: The functional graph of a twisted quadratic binomial map and applications

Abstract: Abstract. Let q be an odd prime power and let Fq denote the finite field with q elements. We study the functional graph structure of the twisted quadratic binomial F(X) = c(Xq+1+aX2) over the quadratic extension Fq2 . By representing Fq2 as a two-dimensional vector space over Fq, we obtain an explicit coordinate form for F that reveals how the parameters a and c control the preimage structure. We use the vector form to introduce a larger family of functions with similar properties. Moreover, we construct three parameterized families of functions derived from F satisfying the conditions for ϵ-strongly universal functions, suggesting their potential use in randomized algorithms and data structures.