Characterizing Linear Size Circuits in Terms of Privacy

In this paper we prove a perhaps unexpected relationship between the complexity class of the boolean functions that have linear size circuits, and n-party private protocols. Speci cally, let f be a boolean function. We show that f has a linear size circuit if and only if f has a 1-private n-party protocol in which the total number of random bits used by all players is constant. From the point of view of complexity theory, our result gives a characterization of the class of linear size circuits in terms of another class of a very di erent nature. From the point of view of privacy, this result provides 1-private protocols that use a constant number of random bits, for many important functions for which no such protocol was previously known. On the other hand, our result suggests that proving, for any N P function, that it has no 1-private constant-random protocol, might be di cult.

• Type: Conference
• Year: 1996
• Where: STOC
• Authors: Eyal Kushilevitz, Rafail Ostrovsky, Adi Rosén
• Keywords: Algorithms, Boolean Function, Linear Size Circuits, Random Bits, STOC 1996