A Survey of Some Recent Results on Bent Functions

We report about recent results and methods in the study of bent functions. Here we focus on normality and trace expansions of bent functions.

[1]  Claude Carlet,et al.  Normal extensions of bent functions , 2004, IEEE Transactions on Information Theory.

[2]  Anne Canteaut,et al.  Construction of bent functions via Niho power functions , 2006, J. Comb. Theory, Ser. A.

[3]  Hans Dobbertin,et al.  New cyclic difference sets with Singer parameters , 2004, Finite Fields Their Appl..

[4]  G. Lachaud,et al.  The weights of the orthogonals of the extended quadratic binary Goppa codes , 1990, IEEE Trans. Inf. Theory.

[5]  Bart Preneel,et al.  A Randomised Algorithm for Checking the Normality of Cryptographic Boolean Functions , 2004, IFIP TCS.

[6]  C. Carlet.  On Cryptographic Complexity of Boolean Functions , 2002 .

[7]  H. Hollmann,et al.  On Binary Cyclic Codes With Few Weights , 2001 .

[8]  Claude Carlet.  Codes de reed-muller, codes de kerdock et de preparata , 1990 .

[9]  O. S. Rothaus,et al.  On "Bent" Functions , 1976, J. Comb. Theory, Ser. A.

[10]  C. Carlet.  On the Secondary Constructions of Resilient and Bent Functions , 2004 .

[11]  Hans Dobbertin.  Uniformly Representable Permutation Polynomials , 2001, SETA.

[12]  Hans Dobbertin,et al.  Construction of Bent Functions and Balanced Boolean Functions with High Nonlinearity , 1994, FSE.

[13]  Kaisa Nyberg,et al.  Perfect Nonlinear S-Boxes , 1991, EUROCRYPT.

[14]  Yoji Niho.  Multi-Valued Cross-Correlation Functions between Two Maximal Linear Recursive Sequences , 1972 .

[15]  J. Dillon.  Elementary Hadamard Difference Sets , 1974 .

[16]  Claude Carlet,et al.  A construction of bent function , 1996 .