Using Multiple-Valued Logic Decision Diagrams to Model System Threat Probabilities

Abstract

Abstract-System security continues to be of increasing importance. To effectively address both natural and intentional threats to large systems, the threats must be cataloged and analyzed. Extremely large and complex systems can have an accordingly large number of threat scenarios. Simply listing the threats and devising countermeasures for each is ineffective and not efficient. We describe a threat cataloging methodology whereby a large number of threats can be efficiently cataloged and analyzed for common features. This allows countermeasures to be formulated that address a large number of threats that share common features. The methodology utilizes MultipleValued Logic for describing the state of a large system and a multiple-valued decision diagram (MDD) for the threat catalog and analysis.Large System Security, Threat cataloging, MDD

System Probability Distribution Modeling Using MDDs

“…The identified parameters are then stored in the MDD data structure as edge value annotations. Using a piecewise polynomial approximation, we can analyze multi-state systems similarly to the previous MDD-based analysis methods [5] [8] [6] [7] that use a single value for each probability. Instead of a single value, we assign a polynomial to each edge of an MDD, as shown in Fig.…”

“…This concept is used for disastertolerance analysis in [3] where a mark-up language, CyTML, represents cyber-threat trees and a companion parser converts the CyTML into a corresponding MDD with edge annotations. The cyber-threat tree approach is generalized for application to other analysis tasks in [5]. The work in [6] extends that of [5] by using an Edge-Valued MDD (EVMDD) software to provide additional experimental results and analysis of the computational memory resource requirements.…”

“…The cyber-threat tree approach is generalized for application to other analysis tasks in [5]. The work in [6] extends that of [5] by using an Edge-Valued MDD (EVMDD) software to provide additional experimental results and analysis of the computational memory resource requirements. New algorithms to minimize the number of edges in the EVMDDs are reported in [7].…”

Edge Reduction for EVMDDs to Speed Up Analysis of Multi-state Systems

“…For fast assessment of the state probabilities, many methods based on binary decision diagrams (BDDs) [2]- [4], [6], [23] and multi-valued decision diagrams (MDDs) [10], [13], [20]- [22] have been proposed, and they have attracted much attention in recent years. Especially, MDD based methods hold promise, as [17] showed that an MDD based method is more efficient than a BDD based one.…”

Modeling Medical System Threats with Conditional Probabilities Using Multiple-Valued Logic Decision Diagrams

“…We have also applied multiple-valued logic decision diagrams to threat trees to determine large-scale system threat probabilities [10]. Our initial approach assumed that system components operated independently.…”