Abstract
Using a random deal of cards to players and a computatio-nally unlimited eavesdropper, all players wish to share a common one-bit secret key which is information-theoretically secure from the eavesdrop-per. This can be done by the so-called key set protocol. In this paper we give a necessary and sufficient condition for a key set protocol to be “optimal,” that is, to succeed always in sharing a one-bit secret key.
Chapter PDF
References
T. Asano, “An O(n log log n) time algorithm for constructing a graph of maximum connectivity with prescribed degrees”, J. Comput. and Syst. Sci., vol. 51, pp. 503–510, 1995.
M. J. Fischer, M. S. Paterson, and C. Rackofi, “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 eficient 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.
S. L. Hakimi, “On realizability of a set of integers as degrees of the vertices of a linear graph. I,” J. SIAM Appl. Math., vol. 10, no. 3, pp. 496–506, 1962.
F. Harary, “Graph Theory,” Addison-Wesley, Reading, Mass., 1969.
T. Mizuki, “Sharing unconditionally secure secret keys,” Ph.D. Thesis, Tohoku University, Sendai, 2000.
T. Mizuki, H. Shizuya, and T. Nishizeki, “Dealing necessary and sufficient 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.
E. F. Schmeichel and S. L. Hakimi, “On planar graphical degree sequences,” SIAM J. Appl. Math., vol. 32, no. 3, pp. 598–609, 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mizuki, T., Shizuya, H., Nishizeki, T. (2000). Characterization of Optimal Key Set Protocols. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds) Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics. TCS 2000. Lecture Notes in Computer Science, vol 1872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44929-9_21
Download citation
DOI: https://doi.org/10.1007/3-540-44929-9_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67823-6
Online ISBN: 978-3-540-44929-4
eBook Packages: Springer Book Archive