Privacy, additional information, and communication

Two parties which hold n-b inputs x and y , respectively, wish to cooperate in computing a predetermined function f(x,y). For most functions f, this task cannot be accomplished privately, namely, without revealing some additional information to at least one of the parties. The authors initiate a quantitative study of T(f), the minimum amount of additional information revealed in any computation of f. This quantity is formally defined, and a combinatorial characterization which determines the value T(f) (up to a multiplicative factor of 2) is found. This enables the authors to give tight lower and upper bounds on the amount of additional information required for computing various (explicit and random) functions. It is shown that additional information is a resource which can be traded for communication complexity