Secret Sharing Schemes with Nice Access Structures

• Autorzy: Ding C. , Salomaa A.
• Języki publikacji: EN

Abstrakty

EN

Secret sharing schemes, introduced by Blakley and Shamir independently in 1979, have a number of applications in security systems. One approach to the construction of secret sharing schemes is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But only well structured linear codes give secret sharing schemes with nice access structures in the sense that every pair of participants plays the same role in the secret sharing. In this paper, we construct a class of good linear codes, and use them to obtain a class of secret sharing schemes with nice access structures.

Słowa kluczowe

EN

secret sharing; linear codes; access structures

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 73, nr 1-2
• Strony: 51--63
• Opis fizyczny: bibliogr. 19 poz.

Twórcy

autor

Ding C.

autor

Salomaa A.

• Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China,

Bibliografia

• [1] R.J. Anderson, C. Ding, T. Helleseth, T. Kløve: How to build robust shared control systems. Designs, Codes and Cryptography, 15 (1998), 111-124.
• [2] A. Ashikhmin, A. Barg, G. Cohen, L. Huguet: Variations on minimal codewords in linear codes. Proc. Of AAECC 1995, LNCS 948, Springer, Berlin, 1995, 96-105.
• [3] A. Ashikhmin, A. Barg: Minimal vectors in linear codes. IEEE Trans. Information Theory, 44, 5 (1998), 2010-2017.
• [4] G.R. Blakley: Safeguarding cryptographic keys. Proc. NCC AFIPS, 1979, 313-317.
• [5] C. Carlet, C. Ding, J. Yuan: Linear codes from highly nonlinear functions and their secret sharing schemes. IEEE Trans. Information Theory, 51, 6 (2005), 2089-2102.
• [6] C. Ding, D. Kohel, S. Ling: Secret sharing with a class of ternary codes. Theoretical Computer Science, 246 (2000), 285-298.
• [7] C. Ding, J. Yuan: Covering and secret sharing with linear codes. Discrete Mathematics and Theoretical Computer Science, LNCS 2731, Springer, Heidelberg, 2003, 11-25.
• [8] E.D. Karnin, J.W. Greene, M.E. Hellman: On secret sharing systems. IEEE Trans. Information Theory, 29 (1983), 35-41.
• [9] L. Lidl, H. Niederreiter: Finite Fields. Cambridge University Press, Cambridge, 1997.
• [10] F.J. Macwilliams, N.J.A. Sloane: The Theory of Error Correcting Codes. North-Holland, Amsterdam, 1978.
• [11] J.L. Massey: Minimal codewords and secret sharing, Proc. 6th Joint Swedish-Russian Workshop on Information Theory, August 22-27, 1993, 276-279.
• [12] J.L. Massey: Some applications of coding theory. Cryptography, Codes and Ciphers: Cryptography and Coding IV, Formara Ltd, Esses, England, 1995, 33-47.
• [13] R.J. McEliece, D.V. Sarwate: On sharing secrets and Reed-Solomon codes. Comm. ACM, 24 (1981), 583-584.
• [14] C. Moreno, O. Moreno: Exponential sums and Goppa Codes. Proc. of the American Mathematical Society, 111 (1991), 523-531.
• [15] K. Okada, K. Kurosawa: MDS secret sharing scheme secure against cheaters. IEEE Trans. Inform. Theory, 46, 3 (2000), 1078-1081.
• [16] J. Pieprzyk, X.M. Zhang: Ideal Threshold Schemes from MDS Codes. Information Security and Cryptology - Proc. of ICISC 2002, LNCS 2587, Springer, Berlin, 2003, 269-279.
• [17] A. Renvall, C. Ding: The access structure of some secret-sharing schemes. Information Security and Privacy, LNCS 1172, Springer, Berlin, 1996, 67-78.
• [18] A. Shamir: How to share a secret. Comm. ACM, 22 (1979), 612-613.
• [19] J. Yuan, C. Ding: Secret sharing schemes from two-weight codes. Discrete Mathematics, to appear.