This is a paper about private data analysis, in which a trusted curator
holding a confidential database responds to real vector-valued queries. A
common approach to ensuring privacy for the database elements is to add
appropriately generated random noise to the answers, releasing only these {\em
noisy} responses. In this paper, we investigate various lower bounds on the
noise required to maintain different kind of privacy guarantees.Comment: Corrected some minor errors and typos. To appear in Theory of
Cryptography Conference (TCC) 201
