TITLE: Mathematics of privacy?
QUESTION [17 upvotes]: I wonder to which extent the current public debate on privacy issues (not only by state sniffing, but e.g. by microtargetting ads too an issue) offers interesting questions in mathematics? 
Can we expect proven and durable software solutions? 
Question stimulated by AdLeaks

REPLY [2 votes]: Proving and verifying statements about private data without releasing that data is a nice candidate question/problem with some known solutions. Let me hereby name interactive proof/argument systems, zero knowledge, commitments, oblivious transfer as well as implementations like U-Prove, DAA, Idemix.
"How to prove a theorem so no one else can claim it", Manuel Blum, International Congress of Mathematicians, 1986.