Private Information Delivery

We introduce the problem of private information delivery (PID), comprised of K messages, a user, and N servers (each holds M≤K messages) that wish to deliver one out of K messages to the user privately, i.e., without revealing the delivered message index to the user. The information theoretic capacity of PID is defined as the maximum number of bits of the desired message that can be privately delivered per bit of total communication to the user. For the PID problem with K messages, N servers and M messages stored per server, we show that the capacity is M/K when N≥gcd K/gcd(K,M)-(M/gcd(K,M)-1) (⌊K/M⌋-1).