  We study a binary hypothesis testing problem in which a defender must decide
whether or not a test sequence has been drawn from a given memoryless source
$P_0$ whereas, 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,
in order 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 to characterize the conditions for the distinguishability of
the two sources given the distortion levels.
