Agreed, Differential Privacy is the name for this problem. Quick summary of important results: You will always leak a small amount of information. But it is po

Agreed, Differential Privacy is the name for this problem. Quick summary of important results: You will always leak a small amount of information. But it is possible to bound this leak to whatever level you consider "acceptable." The trade-off is statistical validity of the results (the usual approach adds "noise" to the data and/or analysis).