Abstract
This paper concerns 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).
In a recent paper st95a, Stinson described a method of constructing key predistribution schemes by combining Mitchell-Piper key distribution patterns with resilient functions; and also presented a construction method for broadcast encryption schemes that combines Fiat-Naor key predistribution schemes with ideal secret sharing schemes. In this paper, we further pursue these two themes, providing several nice applications of these techniques by using combinatorial structures such as orthogonal arrays, perpendicular arrays, Steiner systems and universal hash families.
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References
C. H. Bennett, G. Brassard and J.-M. Robert, Privacy amplification by public discussion, SIAM J. Comput., Vol. 17 (1988) pp. 210-229.
S. Berkovits, How to broadcast a secret, In Advances in Cryptology-EUROCRYPT' 91, Springer-Verlag, Berlin (1992) pp. 536-541.
J. Bierbrauer, Construction of orthogonal arrays, Journal of Statistical Planning and Inference, Vol. 56 (1996) pp. 39-47.
J. Bierbrauer, T. Johansson, G. Kabatianskii and B. Smeets, On families of hash functions via geometric codes and concatenation, In Advances in Cryptology-CRYPTO' 93, Springer-Verlag, Berlin (1994) pp. 331-342.
J. Bierbrauer, K. Gopalakrishnan and D.R. Stinson, Orthogonal arrays, resilient functions, error-correcting codes and linear programming bounds, SIAM J. Discrete Math., Vol. 9 (1996) pp. 424-452.
C. Blundo, A. De Santis, A. Herzberg, S. Kutten, U. Vaccaro and M. Yung, Perfectly secure key distribution for dynamic conferences, In Advances in Cryptology-CRYPTO'92, Springer-Verlag, Berlin (1993) pp. 471-486.
B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich and R. Smolensky, The bit extraction problem or t-resilient functions, In Proc. 26th IEEE Symposium on Foundations of Computer Science(1985) pp. 396- 407.
C. J. Colbourn and J. H. Dinitz, eds., CRC Handbook of Combinatorial Designs, CRC Press, Inc. (1996).
A. Fiat and M. Naor, Broadcast encryption, In Advances in Cryptology-CRYPTO' 93, Springer-Verlag, Berlin (1994) pp. 480-491.
K. Gopalakrishnan and D. R. Stinson, Three characterizations of non-binary correlation-immune and resilient functions, Designs, Codes and Cryptography, Vol. 5 (1995) pp. 241-251.
C. J. Mitchell and F. C. Piper, Key storage in secure networks, Discrete Applied Mathematics, Vol. 21 (1988) pp. 215-228.
A. Shamir, How to share a secret, Communications of the ACM, Vol. 22 (1979) pp. 612-613.
D. R. Stinson, Combinatorial designs and cryptography, In Surveys in Combinatorics, 1993, Cambridge University Press (1993) pp. 257-287.
D. R. Stinson, On some methods for unconditionally secure key distribution and broadcast encryption, Designs, Codes and Cryptography, Vol. 12 (1997), pp. 215-243.
D. R. Stinson and J. L. Massey, An infinite class of counterexamples to a conjecture concerning non-linear resilient functions, Journal of Cryptology, Vol. 8 (1995) pp. 167-173.
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Stinson, D.R., van Trung, T. Some New Results on Key Distribution Patterns and Broadcast Encryption. Designs, Codes and Cryptography 14, 261–279 (1998). https://doi.org/10.1023/A:1008209004667
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DOI: https://doi.org/10.1023/A:1008209004667