# Defence Efficiency

## TL;DR

This paper proposes a formal, axiomatic framework for quantifying the efficiency of network defenses, ensuring the measure aligns with natural criteria and extending it to multiple variables.

## Contribution

It introduces a unique, axiomatic definition of defense efficiency and generalizes it to multiple input variables, providing a rigorous foundation for automated defense evaluation.

## Key findings

- The proposed efficiency measure satisfies natural axiomatic requirements.
- The measure is uniquely characterized by these axioms.
- Two natural generalizations of the measure are compared.

## Abstract

In order to automate actions, such as defences against network attacks, one needs to quantify their efficiency. This can subsequently be used in post-evaluation, learning, etc. In order to quantify the defence efficiency as a function of the impact of the defence and its total cost, we present several natural requirements from such a definition of efficiency and provide a natural definition that complies with these requirements. Next, we precisely characterize our definition of efficiency by the axiomatic approach; namely, we strengthen the original requirements from such a definition and prove that the given definition is the unique definition that satisfies those requirements. Finally, we generalize the definition to the case of any number of input variables in two natural ways, and compare these generalizations.