Linear codes from perfect nonlinear mappings and their secret sharing schemes

IEEE Transactions on Information Theory

Volumn 51, Issue 6, 2005, Pages 2089-2102

  Carlet, Claude ^a,b   Ding, Cunsheng ^c   Yuan, Jin ^c  

^a INRIA   (France)

^b University of Paris   (France)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Cryptography; Linear codes; Perfect nonlinear functions; Planar functions; Secret sharing schemes

Indexed keywords

CRYPTOGRAPHY; ERROR CORRECTION; MATRIX ALGEBRA; OPTIMIZATION; SET THEORY;

LINEAR CODES; PERFECT NONLINEAR FUNCTIONS; PLANAR FUNCTIONS; SECRET SHARING SCHEMES;

CODES (SYMBOLS);

EID: 20544467493     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.847722     Document Type: Article

References (23)

1. R. J. Anderson, C. Ding, T. Helleseth, and T. Kløve, "How to build robust shared control systems," Des., Codes Cryptogr., vol. 15, pp. 111-124, 1998.
2. G. R. Blakley, "Safeguarding cryptographic keys," in Proc. Nat. Computer Conf., vol. 48, New York, Jun. 1979, pp. 313-317.
3. A. E. Brouwer. Bounds on the Minimum Distance of Linear Codes. [Online]. Available: http://www.win.tue.nl/aeb/voorlincod.html
4. m), and cross correlation of maximum-length sequences," SIAM J. Discr. Math., vol. 13, pp. 105-137, 2000.
5. C. Carlet, P. Charpin, and V. Zinoviev, "Codes, bent functions and permutations suitable for DES-like cryptosystems," Des., Codes Cryptogr., vol. 15, pp. 125-156, 1998.
6. C. Carlet and C. Ding, "Highly nonlinear mappings," J. Complexity, vol. 20, no. 2, pp. 205-244, 2004.
7. P. Charpin, A. Tietäväinen, and V. Zinoviev, "On the minimum distances of nonbinary cyclic codes," Des., Codes Cryptogr., vol. 17, pp. 81-85, 1999.
8. R. S. Coulter and R. W. Mathews, "Planar functions and planes of Lenz-Barlotti class II, " Des., Codes Cryptogr., vol. 10, pp. 167-184, 1997.
9. P. Delsarte, "On subfield subcodes of modified Reed-Solomon codes," IEEE Trans. Inf. Theory, vol. IT-21, no. 5, pp. 575-576, Sep. 1975.
10. C. Ding, T. Helleseth, T. Kløve, and X. Wang, "A general construction of Cartesian anthentication codes," Discr. Math., to be published.
11. C. Ding, D. Kohel, and S. Ling, "Secret sharing with a class of ternary codes," Theor. Comp. Sci., vol. 246, pp. 285-298, 2000.
12. C. Ding and J. Yuan, "Covering and secret sharing with linear codes," in Discrete Mathematics and Theoretical Computer Science (Lecture Notes in Computer Science), C. S. Calude, M. J. Dinneen, and V. Vajnovszki, Eds. Heidelberg, Germany: Springer-Verlag, 2003, vol. 2731, pp. 11-25.
13. C. Ding and J. Yuan, "A new family of skew Paley-Hadamard difference sets," J. Comb. Theory A, to be published.
14. T. Kasami, "Weight distribution formula for some classes of cyclic codes," Coordinated Sci. Lab., University of Illinois at Urbana-Champaign, Urbana, IL, Tech. Rep. R-285 (AD 632574), 1966.
15. R. Lidl and H. Niederreiter, Finite Fields. Cambridge, U.K.: Cambridge Univ. Press, 1997.
16. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1978.
17. J. L. Massey, "Minimal codewords and secret sharing," in Proc. 6th Joint Swedish-Russian Workshop on Information Theory, Mölle, Sweden, Aug. 1993, pp. 276-279.
18. J. L. Massey, "Some applications of coding theory in cryptography," in Codes and Ciphers: Cryptography and Coding IV. Esses, U.K.: Formara Ltd, 1995, pp. 33-47.
19. R. J. McEliece and D. V. Sarwate, "On sharing secrets and Reed-Solomon codes," Commun. ACM, vol. 24, pp. 583-584, 1981.
20. J. Pieprzyk and X. M. Zhang, "Ideal secret sharing schemes from MDS codes," in Proc. 5th Int. Conf. Information Security and Cryptology (ICISC 2002), Seoul, Korea, Nov. 2002, pp. 269-279.
21. A. Renvall and C. Ding, "The access structure of some secret-sharing schemes," in Information Security and Privacy (Lecture Notes in Computer Science). Heidelberg, Germany: Springer-Verlag, 1996, vol. 1172, pp. 67-78.
22. A. Shamir, "How to share a secret," Commun. ACM, vol. 22, pp. 612-613, Dec. 1979.
23. J. Yuan and C. Ding, "Secret sharing schemes from two-weight codes," in Proc. The Bose Centenary Symp. Discrete Mathematics and Applications, Kolkata, India, Dec. 2002, pp. 1-7.