Abstracts for talks to be presented in the CCCS 98 Workshop Instructional

s for talks to be presented in the CCCS 98 Workshop Instructional Lectures Cryptography and Combinatorial Designs Charles J. Colbourn, Dorothean Professor of Computer Science University of Vermont In this series of five lectures, we explore some of the many problems in cryptography where combinatorial designs have played a substantial role. To set the stage, we review some ideas from classical cryptography and cryptanalysis, and briefly outline the major advances in public key cryptography. Using this foundation, we examine problems in authentication, secret sharing and threshold schemes, key distribution schemes, and visual cryptography. Our theme is how requirements for balance and regularity lead to well-studied combinatorial designs; how the cryptographic problem leads to challenging combinatorial problems; and, in a few cases, how combinatorial existence theorems provide useful information in the application. With this in mind, the focus is on applicable mathematics. The lectures are accessible to those without substantial background in either cryptography or combinatorial designs. Mathematics and Computer Security Jennifer Seberry Director of the Centre for Computer Security Research, School of Information Technology and Computer Science, University of Wollongong, Wollongong, Australia We give five talks on the mathematics associated with aspects of computer security including complexity, elliptic curves, secret sharing, authentication and bent functions. The talks start from first principles and move to recent research in the area. Coding Theory Vladimir D. Tonchev Michigan Technological University The first three lectures provide a brief introduction to coding theory and its links to combinatorial designs in the spirit of Chapter “Codes” of the CRC Handbook of Combinatorial Designs, with mentioning some new results that have occurred after the publication of the handbook. The third lecture discusses a class of codes arising from graphs, with an application to quantum error-correcting codes. The fifth lecture describes how linear perfect codes are used to characterize the classical geometric designs by the minimum dimension of their codes. This characterization generalizes a result by Hamada and Ohmori (1975) for the binary case, and proves a conjecture of Assmus.