A Revised Transformation Protocol for Unconditionally Secure Secret Key Exchange
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Abstract
The transformation protocol can allow two players to share an unconditionally secure secret key using a random deal of cards. A sufficient condition on the number of cards for the transformation protocol to succeed was known. However, it has been an open problem to obtain a necessary and sufficient condition. This paper improves the transformation protocol and gives a necessary and sufficient condition for the resulting protocol to succeed.
Keywords
Card games Random deal of cards Secret key exchange Key set protocol Transformation protocolPreview
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References
- 1.Fischer, M.J., Paterson, M.S., Rackoff, C.: Secret bit transmission using a random deal of cards. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 2, pp. 173–181. AMS, Providence (1991) Google Scholar
- 2.Fischer, M.J., Wright, R.N.: Multiparty secret key exchange using a random deal of cards. In: Proceedings of CRYPTO’91. Lecture Notes in Computer Science, vol. 576, pp. 141–155. Springer, Berlin (1992) Google Scholar
- 3.Fischer, M.J., Wright, R.N.: An application of game-theoretic techniques to cryptography. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 13, pp. 99–118. AMS, Providence (1993) Google Scholar
- 4.Fischer, M.J., Wright, R.N.: An efficient protocol for unconditionally secure secret key exchange. In: Proceedings of the 4th Annual Symposium on Discrete Algorithms, pp. 475–483 (1993) Google Scholar
- 5.Fischer, M.J., Wright, R.N.: Bounds on secret key exchange using a random deal of cards. J. Cryptol. 9, 71–99 (1996) MATHCrossRefMathSciNetGoogle Scholar
- 6.Mizuki, T., Nishizeki, T.: Necessary and sufficient numbers of cards for sharing secret keys on hierarchical groups. IEICE Trans. Inf. Syst. E 85-D(2), 333–345 (2002) Google Scholar
- 7.Mizuki, T., Shizuya, H., Nishizeki, T.: Eulerian secret key exchange. In: Proceedings of COCOON’98. Lecture Notes in Computer Science, vol. 1449, pp. 349–360. Springer, Berlin (1998) Google Scholar
- 8.Mizuki, T., Shizuya, H., Nishizeki, T.: Dealing necessary and sufficient numbers of cards for sharing a one-bit secret key. In: Proceedings of EUROCRYPT’99. Lecture Notes in Computer Science, vol. 1592, pp. 389–401. Springer, Berlin (1999) Google Scholar
- 9.Mizuki, T., Shizuya, H., Nishizeki, T.: A complete characterization of a family of key exchange protocols. Int. J. Inf. Secur. 1(2), 131–142 (2002) MATHCrossRefGoogle Scholar
- 10.Mizuki, T., Shizuya, H., Nishizeki, T.: Characterization of optimal key set protocols. Discrete Appl. Math. 131, 213–236 (2003) MATHCrossRefMathSciNetGoogle Scholar
- 11.Mizuki, T., Sui, Z., Shizuya, H., Nishizeki, T.: On the average length of secret key exchange Eulerian circuits. IEICE Trans. Fundam. E 83-A(4), 662–670 (2000) Google Scholar
- 12.Winkler, P.: The advent of cryptology in the game of bridge. Cryptologia 7, 327–332 (1983) CrossRefGoogle Scholar
- 13.Wright, R.N.: Achieving perfect secrecy using correlated random variables. Ph.D. thesis, Yale University, New Haven, CT (1994) Google Scholar
- 14.Yoshikawa, R., Guo, S., Motegi, K., Igarashi, Y.: Construction of secret key exchange spanning trees by random deals of cards on hierarchical structures. IEICE Trans. Fundam. E 84-A(5), 1110–1119 (2001) Google Scholar
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