Knowledge Distillation (KD) facilitates the transfer of discriminative capabilities from an advanced teacher model to a simpler student model, ensuring performance enhancement without compromising accuracy. It is also exploited for model stealing attacks, where adversaries use KD to mimic the functionality of a teacher model. Recent developments in this domain have been influenced by the Stingy Teacher model, which provided empirical analysis showing that sparse outputs can significantly degrade the performance of student models. Addressing the risk of intellectual property leakage, our work introduces an approach to train a teacher model that inherently protects its logits, influenced by the Nasty Teacher concept. Differing from existing methods, we incorporate sparse outputs of adversarial examples with standard training data to strengthen the teacher's defense against student distillation. Our approach carefully reduces the relative entropy between the original and adversarially perturbed outputs, allowing the model to produce adversarial logits with minimal impact on overall performance. The source codes will be made publicly available soon.