This Visiting Professorship award at the California Institute of Technology will allow the investigator to broaden and strengthen her research. Research will be conducted in two areas of mathematics, combinatorics and cryptography. Both of these fields are interdisciplinary and fall in the intersection of mathematics and computer science. They have important applications in Information Theory. The research projects in combinatorics are on existence problems in combinatorial design theory and applications of decompositions of edge-colored complete graphs in design theory. The emphasis is on explicit constructions using both recursive and direct, efficient computational methods. Applications of combinatorial designs can be found in cryptography, scheduling, coding theory, statistics, computer science, and molecular biology. The projects in cryptography are of two types. The first is research in the intersection of combinatorics and cryptography: an investigation of combinatorial constructions for authentication schemes and of designs which provide important cryptographic properties. The second is to expand and broaden the investigator's research in cryptography. Areas of particular interest for research include applications of finite field theory, finite geometry, and other combinatorial constructions used for public key cryptography. An extended visit to the new Center for Applied Cryptographic Research at the University of Waterloo will provide a unique opportunity for collaboration and research in cryptography. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).