PSAM 16 - Paper Overview

PSAM 16 Conference Paper Overview

Welcome to the PSAM 16 Conference paper and speaker overview page.

Lead Author: Vladimir Marbukh

Towards Reliability/Security Risk Metrics for Large-Scale Networked Infrastructures: Work in Progress
Realistic systems contain potential vulnerabilities which can be activated by some natural events or by malicious agents. System reliability/security risk metrics quantify the potential economic and other system losses due to possible activation of potential system vulnerabilities. Evaluation of these metrics requires assessment of unconditional probabilities of successful activation of various subsets of potential vulnerabilities. These probabilities are affected by (a) Dependency Relationships (DeR) among potential system vulnerabilities encoded by fault tree, attack graph, etc., and (b) conditional probabilities of the individual exploits, when all the prerequisites for a given potential vulnerability are satisfied. While reliability models assume fixed conditional probabilities of individual exploits, security models assume a possibility of adversarial selection of these probabilities. Combination of system DeR without cycles with conditional probabilities of individual exploits allows one to employ powerful methodologies of Bayesian Network (BaN) analysis for evaluation of the system reliability/risk metrics. However, DeR for highly interconnected large-scale networked infrastructures are often contain cycles. In such cases combination of system DeR with conditional probabilities of individual exploits may not uniquely determine the corresponding unconditional probabilities of exploits and thus the system reliability/security risk metrics. Existing attempts to resolve this issue are not completely satisfactory since they effectively alter system DeR either by removing cycles or imposing additional constraints which are not intrinsic to the system. Another unresolved issue is modelling security risk metrics by accounting for adversarial selection of the conditional probabilities of the individual exploits. Our work in progress proposes resolving the issue of cycles in the system DeR by assuming that the unconditional probability distribution of the successful exploits maximizes entropy over all probability distributions on the subsets of the feasible vulnerabilities which are consistent with the system DeR. In addition to methodological plausibility of this procedure as yielding the “most typical” unconditional distribution, which is consistent with the empirical data, advantages also include consistency with BaN approach for DeRs without cycles, computational advantages for large-scale infrastructures due to leveraging approximations developed in statistical physics, etc. Our analysis under mean-field approximation suggests that cycles in the system DeR may indicate a possibility of cascading failures, and thus are essential for systemic risk assessment. We also discuss evaluation of system security metrics by replacing expected system losses with risk adjusted system losses, which are based on Value at Risk (VaR), Conditional VaR (CVaR), or Entropic VaR (EVaR) measures of risk adjusted performance.

Towards Reliability/Security Risk Metrics for Large-Scale Networked Infrastructures: Work in Progress

Realistic systems contain potential vulnerabilities which can be activated by some natural events or by malicious agents. System reliability/security risk metrics quantify the potential economic and other system losses due to possible activation of potential system vulnerabilities. Evaluation of these metrics requires assessment of unconditional probabilities of successful activation of various subsets of potential vulnerabilities. These probabilities are affected by (a) Dependency Relationships (DeR) among potential system vulnerabilities encoded by fault tree, attack graph, etc., and (b) conditional probabilities of the individual exploits, when all the prerequisites for a given potential vulnerability are satisfied. While reliability models assume fixed conditional probabilities of individual exploits, security models assume a possibility of adversarial selection of these probabilities. Combination of system DeR without cycles with conditional probabilities of individual exploits allows one to employ powerful methodologies of Bayesian Network (BaN) analysis for evaluation of the system reliability/risk metrics. However, DeR for highly interconnected large-scale networked infrastructures are often contain cycles. In such cases combination of system DeR with conditional probabilities of individual exploits may not uniquely determine the corresponding unconditional probabilities of exploits and thus the system reliability/security risk metrics. Existing attempts to resolve this issue are not completely satisfactory since they effectively alter system DeR either by removing cycles or imposing additional constraints which are not intrinsic to the system. Another unresolved issue is modelling security risk metrics by accounting for adversarial selection of the conditional probabilities of the individual exploits. Our work in progress proposes resolving the issue of cycles in the system DeR by assuming that the unconditional probability distribution of the successful exploits maximizes entropy over all probability distributions on the subsets of the feasible vulnerabilities which are consistent with the system DeR. In addition to methodological plausibility of this procedure as yielding the “most typical” unconditional distribution, which is consistent with the empirical data, advantages also include consistency with BaN approach for DeRs without cycles, computational advantages for large-scale infrastructures due to leveraging approximations developed in statistical physics, etc. Our analysis under mean-field approximation suggests that cycles in the system DeR may indicate a possibility of cascading failures, and thus are essential for systemic risk assessment. We also discuss evaluation of system security metrics by replacing expected system losses with risk adjusted system losses, which are based on Value at Risk (VaR), Conditional VaR (CVaR), or Entropic VaR (EVaR) measures of risk adjusted performance.

Paper MA26 Preview

Author and Presentation Info

Lead Author Name: Vladimir Marbukh (marbukh@nist.gov)

Bio: Vladimir Marbukh was born and educated in Leningrad, Soviet Union. His professional interests cover various areas of applied mathematics. In 1989 he moved to the United States. Since then, his affiliation included Math Department of Bell Labs at Murray Hill and NIST Mathematical and Computational Sciences Division in Gaithersburg, Maryland.

Country: United States of America
Company: NIST
Job Title: technical staff member

PSAM 16 Conference Paper Overview

Welcome to the PSAM 16 Conference paper and speaker overview page.

Paper MA26 Preview

Author and Presentation Info

Download paper MA26.

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