Sensitive data release is vulnerable to output-side privacy threats such as membership inference, attribute inference, and record linkage. This creates a practical need for release mechanisms that provide formal privacy guarantees while preserving utility in measurable ways. We propose REAEDP, a differential privacy framework that combines entropy-calibrated histogram release, a synthetic-data release mechanism, and attack-based evaluation. On the theory side, we derive an explicit sensitivity bound for Shannon entropy, together with an extension to Rényi entropy, for adjacent histogram datasets, enabling calibrated differentially private release of histogram statistics. We further study a synthetic-data mechanism $\mathcal{F}$ with a privacy-test structure and show that it satisfies a formal differential privacy guarantee under the stated parameter conditions. On multiple public tabular datasets, the empirical entropy change remains below the theoretical bound in the tested regime, standard Laplace and Gaussian baselines exhibit comparable trends, and both membership-inference and linkage-style attack performance move toward random-guess behavior as the privacy parameter decreases. These results support REAEDP as a practically usable privacy-preserving release pipeline in the tested settings. Source code: https://github.com/mabo1215/REAEDP.git

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