English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we consider a layered-security model in which the containersand their nestings are given in the form of a rooted tree $T$. A {\emcyber-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 {\emtarget-acquisition values\/} for the prizes that are located within thecontainers, respectively, both of the same cardinality as the set of thenon-root vertices of $T$. The problem that we study is to assign thepenetration costs to the edges and the target-acquisition values to thevertices of the tree $T$ in such a way that minimizes the total prize that anattacker can acquire given a limited {\em budget}. For a given assignment ofcosts and target values we obtain a {\em security system}, and we discuss threetypes of them: {\em improved}, {\em good}, and {\em optimal}. We show that ingeneral it is not possible to develop an optimal security system for a givencyber-security model $M$. We define P- and C-models where the penetration costsand prizes, respectively, all have unit value. We show that if $T$ is a rootedtree 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 $T$ isone 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 dualitybetween P- and C-models that allows us to translate results for P-models intocorresponding results for C-models and vice versa. The results obtained give ussome mathematical insights into how layered-security defenses should beorganized.

The structure and topology of rooted weighted trees modeling layered cyber-security systems