I'm new in Differential Privacy (DP) and I have two questions:
- Why do we have the term differential in differential privacy?
- Are The local and global differential privacy and global and local sensitivity referring to different concepts?
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The term "differential" was proposed by Mike Schroeder, to characterize the guarantee as being a relationship between distributions with and without any input record. At the time most papers simply defined "(x,y,z)-privacy as ..." and the work felt of a sufficiently different character (both weaker and stronger than prior work) to call out the distinction.
Other adjectives that were discarded were "incremental privacy" and "marginal privacy", for retrospectively obvious reasons.
The name stuck in part due to the analogy to differential cryptanalysis.
Yes, per Ted's answer, which is exactly correct.
On the first question — see Frank McSherry's answer.
On the second question, no, these are largely unrelated concepts. Local vs. global DP refers to the context in which DP is applied: whether there is a central aggregator that knows the data of all individuals, or whether each individual adds noise to their own data before passing it on to the aggregator. You can read about it in this blog post.
By contrast, local and global sensitivity are only tools to build differentially private mechanisms: they measure how much changing the data of one user will change the output of the statistic you're trying to compute. Global sensitivity measures how big that change can get for every possible database, while local sensitivity measures it for a single database. Local sensitivity is mostly used to define another concept, smooth sensitivity, which in turn is used to design DP mechanisms.