Randomness in Distributed Protocols

In this paper we give a systematic analysis of the amount of randomness needed by Secret Sharing Schemes and Secure Key Distribution Schemes. We give both upper and lower bounds on the number of random bits needed by secret sharing schemes; such bounds match for several classes of secret sharing schemes. For secure key distribution schemes we provide a lower bound on the amount of randomness needed, thus showing the optimality of a recently proposed key distribution protocol.

[1]  Alfredo De Santis,et al.  On the Information Rate of Secret Sharing Schemes (Extended Abstract) , 1992, CRYPTO.

[2]  Douglas R. Stinson,et al.  Decomposition constructions for secret-sharing schemes , 1994, IEEE Trans. Inf. Theory.

[3]  R. J. McEliece,et al.  On sharing secrets and Reed-Solomon codes , 1981, CACM.

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

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

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

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

[8]  Moti Yung,et al.  Perfectly Secure Key Distribution for Dynamic Conferences , 1992, Inf. Comput..

[9]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[10]  Rolf Blom,et al.  An Optimal Class of Symmetric Key Generation Systems , 1985, EUROCRYPT.

[11]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[12]  Carlo Blundo,et al.  Space Requirements for Broadcast Encryption , 1994, EUROCRYPT.

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

[14]  Matthew K. Franklin,et al.  Communication complexity of secure computation (extended abstract) , 1992, STOC '92.

[15]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[16]  Catherine A. Meadows,et al.  Security of Ramp Schemes , 1985, CRYPTO.

[17]  Alfredo De Santis,et al.  Graph Decompositions and Secret Sharing Schemes , 1992, EUROCRYPT.

[18]  Alfredo De Santis,et al.  Efficient Sharing of Many Secrets , 1993, STACS.

[19]  Michael O. Rabin,et al.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989, JACM.

[20]  Douglas R. Stinson,et al.  On the Dealer's Randomness Required in Secret Sharing Schemes , 1994, EUROCRYPT.

[21]  Douglas R. Stinson,et al.  An explication of secret sharing schemes , 1992, Des. Codes Cryptogr..

[22]  Ehud D. Karnin,et al.  On secret sharing systems , 1983, IEEE Trans. Inf. Theory.

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

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