Abstract

This paper provides an exposition of methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to recover any information on a key or broadcast message they are not supposed to know. The problems are studied using the tools of information theory, so the security provided is unconditional (i.e., not based on any computational assumption). We begin by surveying some useful schemes schemes for key distribution that have been presented in the literature, giving background and examples (but not too many proofs). In particular, we look more closely at the attractive concept of key distribution patterns, and present a new method for making these schemes more efficient through the use of resilient functions. Then we present a general approach to the construction of broadcast sch...

Citations

1404	How to share a secret - Shamir - 1979
579	Cryptography – Theory and Practice - Stinson - 2006
204	M.: Broadcast encryption - Fiat, Naor - 1994
174	An optimal class of symmetric key generation systems - Blom - 1984
162	Privacy amplification by public discussion - Bennett, Brassard, et al. - 1988
141	The bit extraction problem of t-resilient functions - Chor, Goldreich, et al. - 1985
96	On the classification of ideal secret sharing schemes - Brickell, Davenport - 1991
72	Codes and Cryptography - Welsh - 1988
71	Combinatorics: Topics, Techniques, Algorithms - Cameron - 1994
59	Secret-key agreement without public-key cryptography - Leighton, Micali - 1993
59	An explication of secret sharing schemes - Stinson - 1992
58	How to broadcast a secret - BERKOVITS - 1991
55	Derandomization, witnesses for boolean matrix multiplication and construction of perfect hash functions - Alon, Naor - 1994
52	Perfectly Secure Key Distribution for Dynamic Conferences - Blundo, Santis, et al. - 1998
42	On the size of separating systems and families of perfect hash functions - Fredman, Komlos - 1984
38	Space requirements for broadcast encryption - BLUNDO, A - 1995
38	Trade-offs between communication and storage in unconditionally secure schemes for broadcast encryption and interactive key distribution - Blundo, Mattos, et al. - 1996
34	On key storage in secure networks - Dyer, Fenner, et al. - 1995
31	On the Bit Extraction Problem - Friedman - 1992
30	On the program size of perfect and universal hash functions - Mehlhorn
20	Some Recursive Constructions for Perfect Hash Families - Atici, Magliveras, et al. - 1996
20	A Matrix Key-Distribution Scheme - Gong, Wheeler - 1990
19	R.: Three Characterizations of Non-binary Correlation-immune and Resilient Function - Gopalakrishnan, Stinson - 1995
18	Orthogonal arrays, resilient functions, error correcting codes and linear programming bounds - Bierbrauer, Gopalakrishnan - 1996
16	Communication in key distribution schemes - Beimel, Chor - 1996
15	Bounds for resilient functions and orthogonal arrays - Bierbrauer, Gopalakrishnan, et al. - 1994
14	Universally ideal secret sharing schemes - Beimel, Chor - 1994
10	Interaction in key distribution schemes - Beimel, Chor - 1994
10	On key distribution via true broadcasting - Just, Kranakis, et al. - 1994
4	Multiple Key Distribution Maintaining User Anonymity via Broadcast Channels - Blundo, Mattos, et al. - 1994
4	Security of the center in Key Distribution Schemes - Kurosawa, Okada, et al. - 1995
4	Incidence structure for key sharing - Matsumoto - 1995
4	Some constructions for key distribution patterns - Quinn - 1994
2	A Study of Correlation-immune, Resilient and Related Cryptographic Functions - Gopalakrishnan - 1994
2	Tilborg. A broadcast key distribution scheme based on block designs - Korjik, Ivkov, et al. - 1995
2	Applications of Finite Geometries to Information Security - O'Keefe - 1993