Many recent researches on privacy (of multi-agent systems), have proposed the use of differential privacy. To my understanding, differential privacy works by adding noise to a state, that is communicated through an affected channel. This random noise is generated using Laplacian distribution, Lap(cq^t), where q=(0,1).
Is it possible for the adversary, who is listening to the noisy state, to filter out the noise and obtain the state?
In this context, there is an important difference between information about the entire set of individuals, and information about the individuals involved. You can filter out the noise for the entire set, without knowing or being able to identify which indivduals where affected by that noise.
To give a heavily simplified example: assume you have a table with yes-no-answers to an embarrassing question, e.g. "have you ever stolen anything?" Based in some random function, e.g. throwing a dice, you add noise by changing the answer to "yes" in 25% of the cases, and to "no" in another 25% of the cases.
Afterwards, for any specific individual you do not know whether the stored answer is the true or the modified answer, so you cannot remove noise on that detailed level.
However, you can filter out noise on the level of the entire dataset, by removing 25% yes and 25% no answers. From the data set left you can still compute properties such as the mean of the original set, though the variation is going to be higher.
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