At the Institute for Mathematics a working group led by Prof. Hermann Kautschitsch and Prof. Winfried Müller has been involved in solving problems in algebra and applications for more then thirty years now. In addition to regular lectures in this field the group has been working on pure research in algebra as well as in projects on data security. Investigations on “Public-key Cryptosystems and Permutation Polynomials” and “Polynomials and Polynomial Functions in Cryptography” and several co-operations with enterprises have led to the development and cryptanalysis of a number of cipher functions and cryptosystems based on polynomials and rational functions. An access control threshold scheme for computer systems based on algebraic equations was designed as well. The group’s main objectives at the moment are to study polynomial functions and formal power series in rings and to contribute high-tech security systems based on polynomial functions.