Advanced persistent threats (APT) combine a variety of different attack forms ranging from social engineering to technical exploits. The diversity and usual stealthiness of APT turns them into a central problem of contemporary practical system security, since information on attacks, the current system status or the attacker’s incentives is often vague, uncertain and in many cases even unavailable. Game theory is a natural approach to model the conflict between the attacker and the defender, and this work investigates a generalized class of matrix games as a risk mitigation tool for an advanced persistent threat (APT) defense. Unlike standard game and decision theory, our model is tailored to capture and handle the full uncertainty that is immanent to APTs, such as disagreement among qualitative expert risk assessments, unknown adversarial incentives and uncertainty about the current system state (in terms of how deeply the attacker may have penetrated into the system’s protective shells already). Practically, game-theoretic APT models can be derived straightforwardly from topological vulnerability analysis, together with risk assessments as they are done in common risk management standards like the ISO 31000 family. Theoretically, these models come with different properties than classical game theoretic models, whose technical solution presented in this work may be of independent interest.

When undertaking cybersecurity risk assessments, it is important to be able to assign numeric values to metrics to compute the final expected loss that represents the risk that an organization is exposed to due to cyber threats. Even if risk assessment is motivated by real-world observations and data, there is always a high chance of assigning inaccurate values due to different uncertainties involved (e.g., evolving threat landscape, human errors) and the natural difficulty of quantifying risk. Existing models empower organizations to compute optimal cybersecurity strategies given their financial constraints, i.e., available cybersecurity budget. Further, a general game-theoretic model with uncertain payoffs (probability-distribution-valued payoffs) shows that such uncertainty can be incorporated in the game-theoretic model by allowing payoffs to be random. This paper extends previous work in the field to tackle uncertainties in risk assessment that affect cybersecurity investments. The findings from simulated examples indicate that although uncertainties in cybersecurity risk assessment lead, on average, to different cybersecurity strategies, they do not play a significant role in the final expected loss of the organization when utilising a game-theoretic model and methodology to derive these strategies. The model determines robust defending strategies even when knowledge regarding risk assessment values is not accurate. As a result, it is possible to show that the cybersecurity investments’ tool is capable of providing effective decision support.

We introduce the concept of an ε-semimetric that satisfies the same axioms as a topological metric, except for an arbitrarily small allowance to violate the triangle inequality. Under this modification, we demonstrate the possibility of taking arbitrary points in space, assigning arbitrary desired distances between them (independent of their geometric location relative to each other, that is, independent of their “features”), and constructing an ε-semimetric that measures exactly the desired distances in the point cloud. This results in a threat to fairness and objectiveness in applications of clustering algorithms: suppose that an adversary subjectively classifies people according to its whim or discriminatory preferences. Upon accusations of unethical behavior, the malicious data processor can plausibly deny these as follows: s/he designs a distance function (an ε-semimetric) that is (up to a fully controllable numeric “roundoff-error” ε) equivalent to a standard distance like the Euclidean. However, this crafted distance will exactly reproduce the (malicious) results and thus confirm them while pretending objectivity and transparency, since only standard and explainable artificial intelligence was used. This demonstration works without any data poisoning. We illustrate the method on randomly chosen points with stochastically independent random classifications assigned to them. Then, we apply standard implementations of k-Means and DBSCAN on the data points, which both exactly reproduce the desired (randomly chosen) classes. We also discuss non-adversarial applications of ε-semimetrics, and corroborate the construction with examples and an implementation in Octave.

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action can be modeled by a random variable, then the decision problem boils down to comparing different effects (random variables) by comparing their distribution functions. Although the full space of probability distributions cannot be ordered, a properly restricted subset of distributions can be totally ordered in a practically meaningful way. We call these loss-distributions, since they provide a substitute for the concept of loss-functions in decision theory. This article introduces the theory behind the necessary restrictions and the hereby constructible total ordering on random loss variables, which enables decisions under uncertainty of consequences. Using data obtained from simulations, we demonstrate the practical applicability of our approach.

We consider a formal model of password security, in which two actors engage in a competition of optimal password choice against potential attacks. The proposed model is a multi-objective two-person game. Player 1 seeks an optimal password choice policy, optimizing matters of memorability of the password (measured by Shannon entropy), opposed to the difficulty for player 2 of guessing it (measured by min-entropy), and the cognitive efforts of player 1 tied to changing the password (measured by relative entropy, i.e., Kullback–Leibler divergence). The model and contribution are thus twofold: (i) it applies multi-objective game theory to the password security problem; and (ii) it introduces different concepts of entropy to measure the quality of a password choice process under different angles (and not a given password itself, since this cannot be quality-assessed in terms of entropy). We illustrate our approach with an example from everyday life, namely we analyze the password choices of employees.