Abstract
A broadcast encryption system allows a center to communicate securely over a broadcast channel with selected sets of users. Each time the set of privileged users changes, the center enacts a protocol to establish a new broadcast key that only the privileged users can obtain, and subsequent transmissions by the center are encrypted using the new broadcast key. We study the inherent trade-off between the number of establishment keys held by each user and the number of transmissions needed to establish a new broadcast key. For every given upper bound on the number of establishment keys held by each user, we prove a lower bound on the number of transmissions needed to establish a new broadcast key. We show that these bounds are essentially tight, by describing broadcast encryption systems that come close to these bounds.
The author's research was supported in part by the National Science Foundation operating grants CCR-9304722 and NCR-9416101.
This author's research was done while a graduate student in the Mathematics Department, University of California at Berkeley.
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
R. Blom, An optimal class of symmetric key generation systems, “Advances in Cryptology-EUROCRYPT '84”, Lecture Notes in Computer Science 209 (1984), 335–338.
C. Blundo, A. Cresti, Space requirements for broadcast encryption, “Advances in Cryptology-EUROCRYPT '94”, Lecture Notes in Computer Science 950 (1995), pp 287–298.
C. Blundo, A. De Santis, A. Herzberg, S. Kutten, U. Vaccaro and M. Yung, Perfectly secure key distribution in dynamic conferences, “Advances in Cryptology — CRYPTO '92”, Lecture Notes in Computer Science 740 (1993), pp 471–486.
C. Blundo, L. A. Frota Mattos, D. R. Stinson, Trade-offs between communication and storage in unconditionally secure schemes for broadcast encryption and interactive key distribution, “Advances in Cryptology-CRYPTO '96”, Lecture Notes in Computer Science 1109 (1996), pp 387–400.
B. Bollobás, On generalized graphs, Acta Math. Acad. Sci. Hungar., 16 (1965), pp 447–452.
P. Erdös, R. Rado, Intersection theorems for systems of sets, Journal London Math. Soc, 35 (1960), pp 85–90.
A. Fiat, M. Naor, Broadcast encryption, “Advances in Cryptology-CRYPTO '93”, Lecture Notes in Computer Science 773 (1994), pp 480–491.
D. Lubell, A short proof of Sperner's lemma, J. Combinatorial Theory, 1 (1966), p 299.
L. D. Meshalkin, A generalization of Sperner's lemma on the number of subsets of a finite set (English translation), Theory of Probab. and its Applns., 8 (1964), pp 204–205.
E. Sperner, Ein Satz über Untermengen einer endlichen Menge, Math. Zeitschrift, 27 (1928), pp 544–548.
D. R. Stinson, On some methods for unconditionally secure key distribution and broadcast encryption, Designs, Codes and Cryptography, 12 (1997), pp 215–243.
D. R. Stinson and T. van Trung, Some new results on key distribution patterns and broadcast encryption, submitted for publication.
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge, 1992.
K. Yamamoto, Logarithmic order of free distributive lattices, J. Math. Soc. Japan, 6 (1954), pp 343–353.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Luby, M., Staddon, J. (1998). Combinatorial bounds for broadcast encryption. In: Nyberg, K. (eds) Advances in Cryptology — EUROCRYPT'98. EUROCRYPT 1998. Lecture Notes in Computer Science, vol 1403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054150
Download citation
DOI: https://doi.org/10.1007/BFb0054150
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64518-4
Online ISBN: 978-3-540-69795-4
eBook Packages: Springer Book Archive