Protecting against multi-step attacks of uncertain start times and duration forces the defenders into indefinite, always ongoing, resource-intensive response. To allocate resources effectively, the defender must analyze and respond to an uncertain stream of potentially undetected multiple multi-step attacks and take measures of attack and response intensity over time into account. Such response requires estimation of overall attack success metrics and evaluating effect of defender strategies and actions associated with specific attack steps on overall attack metrics. We present a novel game-theoretic approach GPLADD to attack metrics estimation and demonstrate it on attack data derived from MITRE’s ATT&CK Framework and other sources. In GPLADD, the time to complete attack steps is explicit; the attack dynamics emerges from attack graph and attacker-defender capabilities and strategies and therefore reflects “physics” of attacks. The time the attacker takes to complete an attack step is drawn from a probability distribution determined by attacker and defender strategies and capabilities. This makes time a physical constraint on attack success parameters and enables comparing different defender resource allocation strategies across different attacks. We solve for attack success metrics by approximating attacker-defender games as discrete-time Markov chains and show evaluation of return on detection investments associated with different attack steps. We apply GPLADD to MITRE’s APT3 data from ATT&CK Framework and show that there are substantial and un-intuitive differences in estimated real-world vendor performance against a simplified APT3 attack. We focus on metrics that reflect attack difficulty versus attacker ability to remain hidden in the system after gaining control. This enables practical defender optimization and resource allocation against multi-step attacks.

In this article, we consider how to increase trust in development processes in which there is a risk for adversarial manipulation, and the adversary's objectives and resources are either ill-specified, imprecisely specified, or unknown. In such problems, we must hedge against the risk of misapprehension of attacker objectives and resources, which is further complicated in the absence of adversarial training data. We show how to model dynamic agent interaction, on the basis of partially observed or noise-corrupted data, using a partially observable Markov game (POMG) framework. We then propose a threefold heuristic solution procedure that: 1) uses the POMG to generate potential adversarial policies; 2) explicitly incorporates these adversarial policies in the construction of a robust defender policy by solving a robust dynamic program (DP); and 3) employs a probability matching heuristic in partially observable environments.

Trust in a microelectronics-based system can be characterized as the level of confidence that a system is free of subversive alterations made during system development, or that the development process of a system has not been manipulated by a malicious adversary. Trust in systems has become an increasing concern over the past decade. This article presents a novel game-theoretic framework, called GPLADD (Graph-based Probabilistic Learning Attacker and Dynamic Defender), for analyzing and quantifying system trustworthiness at the end of the development process, through the analysis of risk of development-time system manipulation. GPLADD represents attacks and attacker-defender contests over time. It treats time as an explicit constraint and allows incorporating the informational asymmetries between the attacker and defender into analysis. GPLADD includes an explicit representation of attack steps via multi-step attack graphs, attacker and defender strategies, and player actions at different times. GPLADD allows quantifying the attack success probability over time and the attacker and defender costs based on their capabilities and strategies. This ability to quantify different attacks provides an input for evaluation of trust in the development process. We demonstrate GPLADD on an example attack and its variants. We develop a method for representing success probability for arbitrary attacks and derive an explicit analytic characterization of success probability for a specific attack. We present a numeric Monte Carlo study of a small set of attacks, quantify attack success probabilities, attacker and defender costs, and illustrate the options the defender has for limiting the attack success and improving trust in the development process.