Abstract
Suppose that there are players in two hierarchical groups and a computationally unlimited eavesdropper. Using a random deal of cards, a player in the higher group wishes to send a one-bit message information-theoretically securely either to all the players in her group or to all the players in the two groups. This can be done by the socalled 2-level key set protocol. In this paper we give a necessary and su.cient condition for the 2-level key set protocol to succeed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. J. Fischer, M. S. Paterson, and C. Racko., “Secret bit transmission using a random deal of cards,” DIMACS Series in Discrete Mathematics and Theoretical Computer Science, AMS, vol. 2, pp. 173–181, 1991.
M. J. Fischer and R. N. Wright, “An application of game-theoretic techniques to cryptography,” DIMACS Series in Discrete Mathematics and Theoretical Computer Science, AMS, vol. 13, pp. 99–118, 1993.
M. J. Fischer and R. N. Wright, “An e.cient protocol for unconditionally secure secret key exchange,” Proc. of the 4th Annual Symposium on Discrete Algorithms, pp. 475–483, 1993.
M. J. Fischer and R. N. Wright, “Bounds on secret key exchange using a random deal of cards,” J. Cryptology, vol. 9, pp. 71–99, 1996.
M. J. Fischer and R. N. Wright, “Multiparty secret key exchange using a random deal of cards,” Proc. CRYPTO’ 91, Lecture Notes in Computer Science, Springer-Verlag, vol. 576, pp. 141–155, 1992.
F. Harary, “Graph Theory,” Addison-Wesley, Reading, Mass., 1969.
T. Mizuki, “Sharing Unconditionally Secure Secret Keys,” Ph.D. Thesis, Tohoku University, Sendai, 2000. Available at http://www.nishizeki.ecei.tohoku.ac.jp/~mizuki/thesis.ps.
T. Mizuki, H. Shizuya, and T. Nishizeki, “Characterization of optimal key set protocols,” Proc. IFIP TCS 2000, Lecture Notes in Computer Science, Springer-Verlag, vol. 1872, pp. 273–285, 2000.
T. Mizuki, H. Shizuya, and T. Nishizeki, “Dealing necessary and su.cient numbers of cards for sharing a one-bit secret key,” Proc. EUROCRYPT’ 99, Lecture Notes in Computer Science, Springer-Verlag, vol. 1592, pp. 389–401, 1999. 197, 199
R. Yoshikawa, S. Guo, K. Motegi, and Y. Igarashi, “Construction of secret key exchange spanning trees by random deals of cards on hierarchical structures,” IEICE Trans. Fundamentals, vol. E84-A, no. 5, pp. 1110–1119, 2001.
R. Yoshikawa, S. Guo, K. Motegi, and Y. Igarashi, “Secret key exchange using random deals of cards on hierarchical structures,” Proc. ISAAC 2000, Lecture Notes in Computer Science, Springer-Verlag, vol. 1969, pp. 290–301, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mizuki, T., Nishizeki, T. (2001). Necessary and Sufficient Numbers of Cards for Sharing Secret Keys on Hierarchical Groups. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_18
Download citation
DOI: https://doi.org/10.1007/3-540-45678-3_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42985-2
Online ISBN: 978-3-540-45678-0
eBook Packages: Springer Book Archive