DIMACS Working Group on Applications of Order Theory to Homeland Defense and Computer Security

September 30, 2004
DIMACS Center, CoRE Building, Rutgers University

Jonathan Farley, Massachusetts Institute of Technology
Anthony A. Harkin, Harvard University, harkin@deas.harvard.edu
Mel Janowitz, DIMACS / Rutgers University, melj@dimacs.rutgers.edu
Stefan Schmidt, Physical Science Laboratory, schmidt@psl.nmsu.edu
DIMACS Workshop on Applications of Order Theory to Homeland Defense and Computer Security.

During the Second World War, the mathematics underlying game theory and cryptography played an important role in military planning. This workshop will draw renowned international researchers who bring two important branches of mathematics to bear in aiding the understanding of terrorist groups and developing strategies for defense against possible external threats to the security of countries: Order Theory and Reflexive Theory.

Terrorist cells are often modeled as graphs, yet they are composed of leaders and of followers. Hence, neglecting the fact that they have a hierarchy leaves out an important aspect of their structure. The proper framework is therefore that of Order Theory (Lattice Theory).

In the 1980's, Ivan Rival coordinated three NATO Advanced Study Institutes that explored applications of Order Theory to different settings. In our case, tools from Order Theory will be applied to help intelligence agencies determine whether they have disrupted a terrorist cell.

The same tools (along with some extra mathematical analysis) will help law enforcement agencies determine which individuals in a terrorist cell should be captured first, in order to maximize the chances of disrupting a cell by expending as few resources as possible.

Information security is also a vital component in issues related to Homeland Defense. Lattices of antichains have been applied recently by, among others, Jason Crampton of the Information Security Group at Royal Holloway (see "The Da Vinci Code"). The idea is to provide new models for improved computer security, specifically, in analyzing separation of duties, policies, and role-based access control models. Lattices of submodules of finite rings have been applied by Stefan Schmidt and Marcus Greferath to provide new models for secret sharing schemes, whereby secrets of different levels of importance can be divided up among individuals with different levels of authority in an organization. (This work was further developed at AT&T's Shannon Laboratory.) Matroids, which are correlated with geometric lattices, have also been used in this context by Siaw-Lynn Ng.

Concept lattices have been used to find hierarchical relationships in terrorist-related data sets. (See Los Alamos National Laboratory Technical Report LAUR 02-7867, "Advanced Knowledge Integration in Assessing Terrorist Threats.")

Reflexive Theory, developed by the mathematician and psychologist Vladimir Lefebvre, originally in the Soviet Union and subsequently in the United States, has been applied to model the threat of border penetration by terrorists. It also can be used to understand stock market trends in the post-September 11 world economy.

A primary intention of this workshop is to present talks that are accessible to the broader public, especially policy makers, politicians, and members of the intelligence and law enforcement communities. The workshop will feature several plenary lectures, whose goal will be to give a broad background to the workshop. These lectures will be complemented by several shorter talks that will focus on particular areas of applications.

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Document last modified on August 11, 2004.