# What is the relation between differential-privacy mechanism and entropy?

Why do differential-privacy people care whether or not the noise function saturates the lower bound of Shannon entropy?

For example : Laplace distribution that is used to model the noise function happens to saturate the lower bound of Shannon entropy under epsilon differential privacy constraints. See Theorem 8 in Yu Wang, Zhenqi Huang, Sayan Mitra and Geir E. Dullerud, Entropy-minimizing Mechanism for Differential Privacy of Discrete-time Linear Feedback Systems for an example.

But what is the significance of this saturation?

• We expect you to do a significant amount of research and/or self-study before asking. What research/self-study have you done? What possible explanations have you considered? What are your thoughts? You seem to have concluded that differential-privacy people care whether or not (...) -- what's the basis for this conclusion? Please flesh out your question. Generally speaking, a one-sentence question is often a red flag indicating that you should take another look at your question to see if you've done as much research as you could have and provided enough context. – D.W. Jun 22 '15 at 22:47
• You've been given similar advice before: 1, 2, 3. I see you've already got quite a bit of experience on this site, but you might want to spend a little time at our help center, e.g., cs.stackexchange.com/help/how-to-ask, to refresh your knowledge of advice for how to ask good questions and use this site effectively. – D.W. Jun 22 '15 at 22:51
• I have added some more details. (I didn't give my specific details because I felt that this is a generic question and not tied to the examples I have seen) – user6818 Jun 23 '15 at 16:45
• Thanks for the citation. That helps. However, I couldn't find a Lemma 8 in that paper. Do you mean Theorem 8? – D.W. Jun 23 '15 at 17:57
• FYI The link to the above paper is dead, but it can be found here: publish.illinois.edu/science-of-security-lablet/files/2014/06/… – Racing Tadpole May 15 at 5:33

we first study an $\epsilon$-differentially private noise-adding mechanism for one-shot queries that provides the best output accuracy, which is measured by the Shannon entropy. [...]
In Section III, we prove that, for a one-shot $n$-dimensional input, there is a lower bound $n + n \ln(2\epsilon)$ on the entropy of the output for an $\epsilon$-differentially private noise-adding mechanism, and the lower bound is achieved by Laplacian noise with parameter $\epsilon$.