Cyberspace Assurance Metrics: Utilizing Models of Networks, Complex Systems Theory, Multidimensional Wavelet Analysis, and Generalized Entrophy Measures

摘要

The problem is addressed of developing a very general mathematical foundation for networks that permits practical application in the monitoring of large networks such as the internet for both known and unknown attacks, intrusions, worms, viruses, and generally for destructive agents and processes. The PI, under the funding of this grant, has discovered a strong connection between the topological specification of a network in the form of a connection matrix and the branches of mathematics known as continuous group theory and Markov processes. Based upon this research he has proposed that entropy metrics, and the associated cluster analysis of the network so measured by these metrics, can be useful indicators of aberrant processes and behavior. Other team members have obtained important connections using higher order Renyi entropy metrics, and complexity theory to both monitor real networks and to study networks by simulation.