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The Laplace mechanism and the Gaussian mechanism are primary mechanisms indifferential privacy, widely applicable to many scenarios involving numericaldata. However, due to the infinite-range random variables they generate, theLaplace and Gaussian mechanisms may return values that are semanticallyimpossible, such as negative numbers. To address this issue, we have designedthe truncated Laplace mechanism and Gaussian mechanism. For a given truncationinterval [a, b], the truncated Gaussian mechanism ensures the same RenyiDifferential Privacy (RDP) as the untruncated mechanism, regardless of thevalues chosen for the truncation interval [a, b]. Similarly, the truncatedLaplace mechanism, for specified interval [a, b], maintains the same RDP as theuntruncated mechanism. We provide the RDP expressions for each of them. Webelieve that our study can further enhance the utility of differential privacyin specific applications.

Truncated Laplace and Gaussian mechanisms of RDP