Privacy and communication complexity

Each of two parties P/sub 1/ and P/sub 2/ holds an n-bit input, x and y, respectively. They wish to compute privately the value of f(x,y). Two questions are considered: (1) Which functions can be privately computed? (2) What is the communication complexity of protocols that privately compute a function f (in the case in which such protocols exist)? A complete combinatorial characterization of privately computable functions is given. This characterization is used to derive tight bounds on the rounds complexity of any privately computable function and to design optimal private protocols that compute these functions. It is shown that for every 1<or=g(n)<or=2*2/sup n/ there are functions that can be privately computed with g(n) rounds of communication, but not with g(n)-1 rounds of communication.<<ETX>>

[1]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[2]  Daniel Lehmann,et al.  On the advantages of free choice: a symmetric and fully distributed solution to the dining philosophers problem , 1981, POPL '81.

[3]  Christos H. Papadimitriou,et al.  Communication complexity , 1982, STOC '82.

[4]  Andrew Chi-Chih Yao,et al.  Protocols for secure computations , 1982, FOCS 1982.

[5]  Kurt Mehlhorn,et al.  Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract) , 1982, STOC '82.

[6]  Andrew C. Yao,et al.  Lower bounds by probabilistic arguments , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[7]  Zvi Galil,et al.  Lower bounds on communication complexity , 1984, STOC '84.

[8]  Vojtech Rödl,et al.  Geometrical realization of set systems and probabilistic communication complexity , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Gabriel Bracha,et al.  An O(lg n) expected rounds randomized Byzantine generals protocol , 1985, STOC '85.

[10]  Andrew Chi-Chih Yao,et al.  How to Generate and Exchange Secrets (Extended Abstract) , 1986, FOCS.

[11]  Gabriel Bracha,et al.  An O(log n) expected rounds randomized byzantine generals protocol , 1987, JACM.

[12]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[13]  Silvio Micali,et al.  Optimal algorithms for Byzantine agreement , 1988, STOC '88.

[14]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[15]  David Chaum,et al.  Multiparty unconditionally secure protocols , 1988, STOC '88.

[16]  Oded Goldreich,et al.  Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity , 1988, SIAM J. Comput..

[17]  Eyal Kushilevitz,et al.  A zero-one law for Boolean privacy , 1989, STOC '89.

[18]  Donald Beaver.  Perfect Privacy For Two-Party Protocols , 1989, Distributed Computing And Cryptography.