Abstract
The problem of key management in a communications network is of primary importance. A key distribution pattern is an incidence structure which provides a secure method of distributing keys in a large network reducing storage requirements. It is of interest to find explicit constructions for key distribution patterns. In O'Keefe [5–7], examples are shown using the finite circle geometries (Minkowski, Laguerre and inversive planes); in Quinn [12], examples are constructed from conics in finite projective and affine planes. In this paper, we construct some examples using the finite tangent-circle structures, introduced in Quattrocchi and Rinaldi [10] and we give a comparison of the storage requirements.
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References
R. Blom, An optimal class of symmetric key generation system, Advances in Cryptology: Proceedings of Eurocrypt 84, Lecture Notes in Computer Science, Vol. 209 Springer-Verlag, Berlin (1985) pp. 335–338.
P. Quattrocchi and M. Meschiari, Una classificazione delle strutture di incidenza associate associate a insiemi di sostituzioni strettamente 3-transitivi finiti, Atti Sem. Mat. Fis. Univ. Modena, Vol. 24 (1975) pp. 123–141.
C. J. Mitchell, Combinatorial Techniques for Key Storage Reduction in Secure Networks, Technical memo, Hewlett-Packard Laboratories, Bristol (1988).
C. J. Mitchell and F. C. Piper, Key storage in secure networks, Discrete Applied Mathematics, Vol. 21 (1988) pp. 215–228.
C. M. O'Keefe, Key distribution patterns using Minkowski planes, Designs Codes and Cryptography, Vol. 5 (1995) pp. 261–267.
C. M. O'Keefe, Applications of finite geometries to information security, Austral. J. Comb. Theory, Vol. 7 (1993) pp. 215–228.
C. M. O'Keefe, A comparison of key distribution patterns constructed from circle geometries, Advances in Cryptology, AUSCRYPT '92 (Gold Coast 1992) Lecture Notes in Computer Science, Vol. 718, Springer, Berlin (1993) pp. 517–527.
P. Quattrocchi, Sugli insiemi di permutazioni strettamente 3-transitivi finiti, Atti Sem. Mat. Fis. Univ. Modena, Vol. 24 (1975) pp. 279–289.
P. Quattrocchi, Insiemi planari di permutazioni, Atti Sem. Mat. Fis. Univ. Modena, Vol. 36 (1988) pp. 141–151.
P. Quattrocchi and G. Rinaldi, Finite tangent-circle structures, In Proceedings of the International Conference on Incidence Geometries and Combinatorial structures, Vol. 2 (1988) pp. 349–357.
K. A. S. Quinn, Combinatorial structures with applications to information theory, Ph.D. Thesis, RHBNC, University of London (1991).
K. A. S. Quinn, Some construction for key distribution patterns, Designs, Codes and Cryptography, Vol. 4 (1994) pp. 177–191.
B. Qvist, Some remarks concerning curves of the second degree in a finite plane, Ann. Acad. Sci. Fenn., Vol. 134 (1952) pp. 1–27.
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Rinaldi, G. Key Distribution Patterns Using Tangent Circle Structures. Designs, Codes and Cryptography 31, 289–300 (2004). https://doi.org/10.1023/B:DESI.0000015889.12620.21
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DOI: https://doi.org/10.1023/B:DESI.0000015889.12620.21