Detection Games under Fully Active Adversaries

Abstract

We study a binary hypothesis testing problem in which a defender must decide whether a test sequence has been drawn from a given memoryless source P 0 , while an attacker strives to impede the correct detection. With respect to previous works, the adversarial setup addressed in this paper considers an attacker who is active under both hypotheses, namely, a fully active attacker, as opposed to a partially active attacker who is active under one hypothesis only. In the fully active setup, the attacker distorts sequences drawn both from P 0 and from an alternative memoryless source P 1 , up to a certain distortion level, which is possibly different under the two hypotheses, to maximize the confusion in distinguishing between the two sources, i.e., to induce both false positive and false negative errors at the detector, also referred to as the defender. We model the defender–attacker interaction as a game and study two versions of this game, the Neyman–Pearson game and the Bayesian game. Our main result is in the characterization of an attack strategy that is asymptotically both dominant (i.e., optimal no matter what the defender’s strategy is) and universal, i.e., independent of P 0 and P 1 . From the analysis of the equilibrium payoff, we also derive the best achievable performance of the defender, by relaxing the requirement on the exponential decay rate of the false positive error probability in the Neyman–Pearson setup and the tradeoff between the error exponents in the Bayesian setup. Such analysis permits characterizing the conditions for the distinguishability of the two sources given the distortion levels.

The Forensicability of Operation Detection in Image Operation Chain

“…The corresponding operation detection relies on destructive ability of the following operations. That process is similar to the game [30] between the forensics analyst and the attacker. In the real scenario, the multiple operations are applied sequentially rather than the anti-forensics attack.…”

Hypothesis Testing Under Subjective Priors and Costs as a Signaling Game

“…For example, detecting attacks, anomalies, and malicious behavior in network security can be analyzed under the game theoretic perspective [2][3][4][5][6]. In this direction, the hypothesis testing and the game theory approaches can be utilized together to investigate attacker-defender type applications [7][8][9][10][11][12][13], multimedia source identification problems [31], inspection games [32][33][34], and deception games [35]. In [8], a Nash equilibrium of a zero-sum game between Byzantine (compromised) nodes and the fusion center (FC) is investigated.…”

“…The strategy of the FC is to set the local sensor thresholds that are utilized in the likelihood-ratio tests, whereas the strategy of Byzantines is to choose their flipping probability of the bit to be transmitted. In [9], a zero-sum game of a binary hypothesis testing problem is considered over finite alphabets. The attacker has control over the channel, and the randomized decision strategy is assumed for the defender.…”

“…In many decentralized and networked control problems, decision makers have either misaligned criteria or have subjective priors, which necessitates solution concepts from game theory. For example, detecting attacks, anomalies, and malicious behavior with regard to security in networked control systems can be analyzed under a game theoretic perspective, see e.g., [2][3][4][5][6][7][8][9][10][11][12][13].…”

An Adversarial Risk Analysis Framework for Batch Acceptance Problems

“…Batch acceptance relates to the more general problem of hypothesis testing (French and Ríos Insua, 2000), which has been extensively studied from a decision theoretic perspective. However, lately, there has been a growing concern about the impact of adversaries in this realm, with recent examples in fields such as adversarial classification (Yu et al, 2018), adversarial machine learning (Jagielski et al, 2018) or adversarial signal processing (Tondi et al, 2019). This consideration of an adversarial component also applies to the more specific batch acceptance framework, where rational opponents have been incorporated to the aforementioned contexts as in Tapiero (1995) (acceptance sampling), Haphuriwat et al (2011) (cargo container screening) and Kantarcioglu et al (2011) (spam detection).…”