Secure computer systems: Mathematical foundations

Abstract

This paper reports the first results of an investigation into solutions to problems of security in computer systems; it establishes the basis for rigorous investigation by providing a general descriptive model of a computer system. Borrowing basic concepts and constructs from general systems theory, we present a basic result concerning security in computer systems, using precise notions of 'security' and 'compromise'. We also demonstrate how a change in requirements can be reflected in the resulting mathematical model. A lengthy introductory section is included in order to bridge the gap between general systems theory and practical problem solving. ii PREFACE General systems theory is a relatively new and rapidly growing mathematical discipline which shows great promise for application in the computer sciences. The discipline includes both 'general systems-theory' and 'general-systems-theory': that is, one may properly read the phrase 'general systems theory' in both ways. In this paper, we have borrowed from the works of general systems theorists, principally from the basic work of Mesarovic, to formulate a mathematical framework within which to deal with the problems of secure computer systems. At the present time we feel that the mathematical representation developed herein is adequate to deal with most if not all of the security problems one may wish to pose. In Section III we have given a result which deals with the most trivial of the secure computer systems one might find viable in actual use. In the concluding section we review the application of our mathematical methodology and suggest major areas of concern in the design of a secure system. The results reported in this paper lay the groundwork for further, more specific investigation into secure computer syst...