This paper explores the security aspects of federated learning applications in medical image analysis. Current robustness-oriented methods like adversarial training, secure aggregation, and homomorphic encryption often risk privacy compromises. The central aim is to defend the network against potential privacy breaches while maintaining model robustness against adversarial manipulations. We show that incorporating distributed noise, grounded in the privacy guarantees in federated settings, enables the development of a adversarially robust model that also meets federated privacy standards. We conducted comprehensive evaluations across diverse attack scenarios, parameters, and use cases in cancer imaging, concentrating on pathology, meningioma, and glioma. The results reveal that the incorporation of distributed noise allows for the attainment of security levels comparable to those of conventional adversarial training while requiring fewer retraining samples to establish a robust model.