# Uncertainty in Security Analysis - July 2022

PI: David M. Nicol

Researcher: Hoang Hai Ngyuen

HARD PROBLEM(S) ADDRESSED

*This refers to Hard Problems, released November 2012.*

This research intersects the predictive security *metric* problem since we are attempting to predict uncertainty associated with a system model. It also intersects with resilience as a system's resilience will be established by analysis of some model and decisions (e.g., how significant breach may be, whether to interdict and where, where to focus recovery activity) will be made as a result. Those decisions will be better informed when some notion of uncertainty is built into the model predictions, or accompanies those model predictions.

PUBLICATIONS

*Papers written as a result of your research from the current quarter only.*

None to report

KEY HIGHLIGHTS

*Each effort should submit one or two specific highlights. Each item should include a paragraph or two along with a citation if available. Write as if for the general reader of IEEE S&P. *

*The purpose of the highlights is to give our immediate sponsors a body of evidence that the funding they are providing (in the framework of the SoS lablet model) is delivering results that "more than justify" the investment they are making.*

Our research focuses on understanding the network security risk and the uncertainty associated with the estimate when security properties of the network components are not exactly known. In previous study, we used Bernoulli random variables to model the existence of a link between two immediate hosts in the network, which indicates the possibility of a lateral movement [1]. Our current investigation generalized this model by modeling the uncertainty in the link existence using Beta distribution, a more versatile class of distributions that takes one of many different shapes depending on its two parameters.

Computing the existence of a pathway between two specifically chosen hosts (i.e. reachability analysis) in the generalized model reduces to identifying the reachability distribution, in the form of a multivariate reliability polynomial of Betas. This is a hard problem. However, our initial results highly suggest that in many cases, the reliability distribution can be well-approximated by another beta distribution. This observation aligns with several results from previous studies [2] [3] regarding approximating Betas. Our finding however applies to a much more general setup. The implication of this result is that under conditions in which the approximation is sufficiently good, the computational cost of reachability analysis can be significantly reduced.

COMMUNITY ENGAGEMENTS

No community engagements this quarter.

EDUCATIONAL ADVANCES:

No educational advances this quarter.