On the Number of Random Bits in Totally Private Computation

We consider the classic problem of n honest but curious players with private inputs x1,...,x n who wish to compute the value of a fixed function f(x1,...,x n ) in such way that at the end of the protocol every player knows the value f(x1,..., x n ). Each pair of players is connected by a secure point-to-point communication channel. The players have unbounded computational resources and they intend to compute f in a totally private way. That is, after the execution of the protocol no coalition of arbitrary size can get any information about the inputs of the remaining players other than what can be deduced by their own inputs and the value of f.

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

[2]  Eyal Kushilevitz.  Privacy and Communication Complexity , 1992, SIAM J. Discret. Math..

[3]  Eyal Kushilevitz,et al.  A Communication-Privacy Tradeoff for Modular Addition , 1993, Inf. Process. Lett..

[4]  Eli Upfal,et al.  A time-randomness tradeoff for oblivious routing , 1988, STOC '88.

[5]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[6]  Russell Impagliazzo,et al.  How to recycle random bits , 1989, 30th Annual Symposium on Foundations of Computer Science.

[7]  Kurt Mehlhorn,et al.  A Time-Randomness Tradeoff for Communication Complexity , 1990, WDAG.

[8]  Prabhakar Raghavan,et al.  Memory versus randomization in on-line algorithms , 1994, IBM J. Res. Dev..

[9]  Eyal Kushilevitz,et al.  A Randomnesss-Rounds Tradeoff in Private Computation , 1994, CRYPTO.

[10]  David Zuckerman,et al.  Simulating BPP using a general weak random source , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[11]  Andrew Chi-Chih Yao,et al.  The complexity of nonuniform random number generation , 1976 .

[12]  Prabhakar Raghavan,et al.  Memory Versus Randomization in On-line Algorithms (Extended Abstract) , 1989, ICALP.

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

[14]  Eyal Kushilevitz,et al.  A Zero-One Law for Boolean Privacy , 1991, SIAM J. Discret. Math..

[15]  Aravind Srinivasan,et al.  Randomness-optimal unique element isolation, with applications to perfect matching and related problems , 1993, STOC '93.