The Laplace mechanism and the Gaussian mechanism are primary mechanisms in differential privacy, widely applicable to many scenarios involving numerical data. However, due to the infinite-range random variables they generate, the Laplace and Gaussian mechanisms may return values that are semantically impossible, such as negative numbers. To address this issue, we have designed the truncated Laplace mechanism and Gaussian mechanism. For a given truncation interval [a, b], the truncated Gaussian mechanism ensures the same Renyi Differential Privacy (RDP) as the untruncated mechanism, regardless of the values chosen for the truncation interval [a, b]. Similarly, the truncated Laplace mechanism, for specified interval [a, b], maintains the same RDP as the untruncated mechanism. We provide the RDP expressions for each of them. We believe that our study can further enhance the utility of differential privacy in specific applications.

翻译：拉普拉斯机制与高斯机制是差分隐私中的基础机制，广泛适用于涉及数值数据的众多场景。然而，由于这两种机制生成的随机变量具有无限取值范围，拉普拉斯机制与高斯机制可能返回语义上不可行的结果，例如负数。为解决这一问题，我们设计了截断拉普拉斯机制与截断高斯机制。对于给定的截断区间[a,b]，无论截断区间[a,b]取何值，截断高斯机制均能保持与未截断机制相同的Rényi差分隐私（RDP）保障。类似地，对于指定区间[a,b]，截断拉普拉斯机制也能维持与未截断机制相同的RDP保障。我们分别给出了这两种机制的RDP表达式。我们相信本研究可进一步提升差分隐私在特定应用场景中的实用性。