Paper Info
Title
The structure and topology of rooted weighted trees modeling layered cyber-security systems.
Abstract
In this paper we consider a layered-security model in which the containers and their nestings are given in the form of a rooted tree $T$. A {em cyber-security model/} is an ordered three-tuple $M = (T, C, P)$ where $C$ and $P$ are multisets of {em penetration costs/} for the containers and {em target-acquisition values/} for the prizes that are located within the containers, respectively, both of the same cardinality as the set of the non-root vertices of $T$. The problem that we study is to assign the penetration costs to the edges and the target-acquisition values to the vertices of the tree $T$ in such a way that minimizes the total prize that an attacker can acquire given a limited {em budget}. For a given assignment of costs and target values we obtain a {em security system}, and we discuss three types of them: {em improved}, {em good}, and {em optimal}. We show that in general it is not possible to develop an optimal security system for a given cyber-security model $M$. We define P- and C-models where the penetration costs and prizes, respectively, all have unit value. We show that if $T$ is a rooted tree such that any P- or C-model $M = (T,C,P)$ has an optimal security system, then $T$ is one of the following types: (i) a rooted path, (ii) a rooted star, (iii) a rooted 3-caterpillar, or (iv) a rooted 4-spider. Conversely, if $T$ is one of these four types of trees, then we show that any P- or C-model $M = (T,C,P)$ does have an optimal security system@. Finally, we study a duality between P- and C-models that allows us to translate results for P-models into corresponding results for C-models and vice versa. The results obtained give us some mathematical insights into how layered-security defenses should be organized.
Year
Venue
Field
2016
arXiv: Discrete Mathematics
Discrete mathematics,Combinatorics,Vertex (geometry),Security system,Cardinality,Duality (optimization),Mathematics
DocType
Volume
Citations 
Journal
abs/1605.03569
0
PageRank 
References 
Authors
0.34
6
3
Name
Order
Citations
PageRank
Geir Agnarsson110314.69
Raymond Greenlaw214218.56
Sanpawat Kantabutra3134.88