Resumen de Permutations of finite fields with prescribed properties

Ayça Çesmelioglu, Wilfried Meidl, Alev Topuzoglu

• Classes of permutations of finite fields with various specific properties are often needed for applications. We use a recent classification of permutation polynomials using their Carlitz rank with advantage, to produce examples of classes of permutations of Fp, for odd p, which for instance are ��random��, have low differential uniformity, prescribed cycle structure, high polynomial degree, large weight and large dispersion. They are also easy to implement. We indicate applications in coding and cryptography.