In recent years, differential privacy has gained substantial traction in the medical domain, where the need to balance privacy preservation with data utility is paramount. As medical data increasingly relies on cloud platforms and distributed sharing among multiple stakeholders, such as healthcare providers, researchers, and policymakers, the importance of privacy-preserving techniques has become more pronounced. Trends in the field focus on designing efficient algorithms tailored to high-dimensional medical datasets, incorporating privacy guarantees into federated learning for distributed medical devices, and addressing challenges posed by adversarial attacks. Our work lays a foundation for these emerging applications by emphasizing the role of randomized response within the broader differential privacy framework, paving the way for advancements in secure medical data sharing and analysis. In this paper, we analyze the classical concept of a randomized response and investigate how it relates to the fundamental concept of differential privacy. Our approach is both mathematical and algorithmic in nature, and our purpose is twofold. On the one hand, we provide a formal and precise definition of differential privacy within a natural and convenient probabilistic—statistical framework. On the other hand, we position a randomized response as a special yet significant instance of differential privacy, demonstrating its utility in preserving individual privacy in sensitive data scenarios. To substantiate our findings, we include key theoretical proofs and provide indicative simulations, accompanied by open-access code to facilitate reproducibility and further exploration.
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