This work inspects a privacy metric based on Chernoff information, \textit{Chernoff differential privacy}, due to its significance in characterization of the optimal classifier's performance. Adversarial classification, as any other classification problem is built around minimization of the (average or correct detection) probability of error in deciding on either of the classes in the case of binary classification. Unlike the classical hypothesis testing problem, where the false alarm and mis-detection probabilities are handled separately resulting in an asymmetric behavior of the best error exponent, in this work, we focus on the Bayesian setting and characterize the relationship between the best error exponent of the average error probability and $\varepsilon\textrm{-}$differential privacy \cite{D06}. Accordingly, we re-derive Chernoff differential privacy in terms of $\varepsilon\textrm{-}$differential privacy using the Radon-Nikodym derivative and show that it satisfies the composition property for sequential composition. Subsequently, we present numerical evaluation results, which demonstrates that Chernoff information outperforms Kullback-Leibler divergence as a function of the privacy parameter $\varepsilon$, the impact of the adversary's attack and global sensitivity for the problem of adversarial classification in Laplace mechanisms.