A survey of some recent results on bent functions

Lecture Notes in Computer Science

Volumn 3486, Issue , 2005, Pages 1-29

  Dobbertin, Hans ^a   Leander, Gregor ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTER SOFTWARE; FUNCTIONS;

BENT FUNCTIONS; TRACE EXPANSIONS;

SOFTWARE ENGINEERING;

EID: 24944578285     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11423461_1     Document Type: Conference Paper

References (27)

1. A. Braeken, C. Wolf, B. Preneel, A Randomised Algorithm for Checking the Normality of Cryptographic Boolean Functions, 3rd International Conference on Theoretical Computer Science 2004, J. Levy, E. W. Mayr, and J. C. Mitchell (eds.), Kluwer, pp. 51-66, 2004.
2. A. Braeken, M. Daum, G. Leander, C. Wolf An Algorithm for Checking Total Non-Normality, Preprint 2004.
3. A. Canteaut, private communication, June 2004.
4. A. Canteaut, M. Daum, H. Dobbertin, G. Leander, Normal and Non-Normal Bent Functions, Proceedings of the Workshop on Coding and Cryptography (WCC 2003), Versailles, France, March 2003, pp. 91-100.
5. A. Canteaut, M. Daum, H. Dobbertin, G. Leander, Finding Non-Normal Bent Functions, special issue on Coding and Cryptography, Discrete Applied Mathematics, to appear.
6. C. Carlet, A construction of bent functions. Finite Fields and Applications, London Mathematical Society, Lecture Series 233, Cambridge University Press, pp. 47-58, 1996.
7. C. Carlet, On cryptographic complexity of boolean functions, Finite Fields with Applications to Coding Theory, Cryptography and Related Areas (Proceedings of Fq6), pages 53-69, Springer-Verlag, 2002.
8. C.Carlet Codes de Reed-Muller, codes de Kerdock et de Preparata. PhD thesis, Université Paris 6, 1990.
9. C. Carlet. On the secondary constructions of resilient and bent functions. Proceedings of the Workshop on Coding, Cryptography and Combinatorics 2003, published by BirkHauser Verlag, 2004.
10. C.Carlet, H.Dobbertin, G.Leander, Normal Extensions of Bent Functions, IEEE Transactions on Information Theory, vol. 50, no. 11, November 2004
11. M. Daum, H. Dobbertin, G. Leander, An algorithm for checking normality of Boolean functions, Proceedings of the Workshop on Coding and Cryptography (WCC 2003), Versailles, France, March 2003, pp. 133-142.
12. J.F. Dillon, Elementary Hadamard Difference sets, PhD thesis, University of Maryland, 1974.
13. Dillon, J.F., Elementary Hadamard difference sets, Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing, Boca Raton, Florida, Congressus Numerantium No. XIV, Utilitas Math., Winnipeg, Manitoba, 1975, 237-249.
14. J.F. Dillon and H. Dobbertin, New Cyclic Difference Sets with Singer Parameters, Finite Fields And Applications, 2004, pp. 342-389.
15. H. Dobbertin, G. Leander, A. Canteaut, C. Carlet, P. Felke, P. Gaborit, Construction of Bent Functions via Niho Power Functions, submitted.
16. H. Dobbertin, Construction of bent functions and highly nonlinear balanced Boolean functions, in "Fast Software Encryption", Lecture Notes on Computer Science, vol. 1008, Bart Preneel (ed.), Springer Verlag, 1995, 61-74.
17. H. Dobbertin, Uniformly representable permutation polynomials, in the Proceedings of "Sequences and their applications-SETA '01", T. Helleseth, P.V. Kumar and K. Yang (eds.), Springer Verlag, 2002, 1-22.
18. H. Dobbertin, P. Felke, T. Helleseth and P. Rosendahl, Niho type cross-correlation functions via Dickson polynomials and Kloosterman sums, IEEE Transactions on Information Theory, submitted.
19. S. Dubuc-Camus, Etude des fonctions Booléennes dégénérées et sans corrélation, PhD thesis, Université de Caen, 1998.
20. H. Hollmann, Q. Xiang, On binary cyclic codes with few weights, in the Proceedings of the Fifth Conference on Finite Fields and Their Applications, Augsburg, Germany, 1999, D. Jungnickel, H. Niederreiter (eds.), Springer Verlag, 251-275.
21. S. Gangopadhyay, S. Maitra, personal communication.
22. G. Lachaud, J. Wolfmann The Weights of the Orthogonals of the Extended Quadratic Binary Goppa, IEEE Transactions on Information Theory, Vol. 36, No 3, pages 686-692, May 1990
23. G. Leander, Monomial Bent Functions, submitted, 2004.
24. G. Leander, Non Normal Bent Functions, Monomial and Binomial Bent Functions, Ph.D. Thesis, Ruhr University Bochum, 2004.
25. Y. Niho, Multivalued cross-correlation functions between two maximal linear recursive sequences, Ph.D. Thesis, University of Southern California (1972).
26. K. Nyberg, Perfect non-linear S-boxes, in "Advances in Cryptology - Eurocrypt '91", vol. 547, Lecture Notes in Computer Science, Springer Verlag, 1991, 378-386.
27. O.S. Rothaus, On "bent" functions, Journal of Combinatorial Theory, Ser. A, 20 (1976), 300-305.