472UNIVALENT (MONODENTATE) SUBSTITUTION ON CONVEX POLYHEDRA completely overwhelms f/for q=0 and 1, thus falls off very rapidly with q. If the cubic or icosahedral p.g. is purely rotational, 432 or 532, then at q= V/2 for any polyhedron (or assembly of points) of this symmetry with no vertex (point) on a rotation axis ½(1-V)log 2-(3 log e)/4V+log k

This paper describes a framework for implementing intrusion detection systems using fuzzy logic. A fuzzy datamining algorithm is used to extract fuzzy rules for the inference engine. The modular architecture is implemented using the Java Expert System Shell (Jess) and the FuzzyJess toolkit developed by Sandia National Laboratories and the National Research Council of Canada respectively. Experimental results for a hybrid prototype system using anomaly-based and fuzzy signatures are provided using data sets from MIT Lincoln Laboratory.

The layering of protocols in critical infrastructure networks -exemplified by Modbus TCP in the oil and gas sector and SS7oIP in the telecommunications sector -raises important security issues. The individual protocol stacks, e.g., Modbus and SS7, have certain vulnerabilities, and transporting these protocols using carrier protocols, e.g., TCP/IP, brings into play the vulnerabilities of the carrier protocols. Moreover, the layering produces unintended inter-protocol interactions and, possibly, new vulnerabilities. This paper describes a formal methodology for evaluating the security of multilayer SCADA protocols. The methodology, involving the analysis of peer-to-peer communications and multilayer protocol interactions, is discussed in the context of Modbus TCP, the predominant protocol used for oil and gas pipeline operations.

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Cryptographic protocols provide frameworks for communicating, authenticating, and exchanging secrets in sundry situations. Protocol assessment for discovering design flaws requires modeling and analyzing the protocol. Protocol analysis reveals attacks that an intruder can use. The proposed methodology provides an effective means for analyzing protocols by using message-pattern matching and goal extraction. The algorithmic approach for goal extraction and analysis has potential for automated protocol analysis.