Maximally Nonlinear Functions and Bent Functions

We give a construction of bent functions in 2n variables, here n is odd, by using maximally nonlinear functions on GF(2n).

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

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

[3]  Kaisa Nyberg,et al.  Differentially Uniform Mappings for Cryptography , 1994, EUROCRYPT.

[4]  Hans Dobbertin,et al.  Almost Perfect Nonlinear Power Functions on GF(2n): The Welch Case , 1999, IEEE Trans. Inf. Theory.

[5]  Philippe Langevin,et al.  Results on Bent Functions , 1997, J. Comb. Theory, Ser. A.

[6]  Tadao Kasami,et al.  The Weight Enumerators for Several Clauses of Subcodes of the 2nd Order Binary Reed-Muller Codes , 1971, Inf. Control..

[7]  Robert L. McFarland,et al.  A Family of Difference Sets in Non-cyclic Groups , 1973, J. Comb. Theory A.

[8]  Hans Dobbertin,et al.  Almost Perfect Nonlinear Power Functions on GF(2n): The Niho Case , 1999, Inf. Comput..

[9]  Stephen D. Cohen,et al.  A class of exceptional polynomials , 1994 .

[10]  Hans Dobbertin,et al.  One-to-One Highly Nonlinear Power Functions on GF(2n) , 1998, Applicable Algebra in Engineering, Communication and Computing.

[11]  Marie Henderson,et al.  A class of functions and their application in constructing semi-biplanes and association schemes , 1999, Discret. Math..

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

[13]  Claude Carlet,et al.  A Characterization of Binary Bent Functions , 1996, J. Comb. Theory, Ser. A.

[14]  Robert Gold,et al.  Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.) , 1968, IEEE Trans. Inf. Theory.

[15]  Hans Dobbertin.  Another Proof of Kasami's Theorem , 1999, Des. Codes Cryptogr..

[16]  H. Dobbertin.  Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets , 1999 .

[17]  Claude Carlet.  Generalized partial spreads , 1995, IEEE Trans. Inf. Theory.

[18]  Tor Helleseth,et al.  Some Power Mappings with Low Differential Uniformity , 1997, Applicable Algebra in Engineering, Communication and Computing.

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

[20]  Serge Vaudenay,et al.  Links Between Differential and Linear Cryptanalysis , 1994, EUROCRYPT.

[21]  Cunsheng Ding,et al.  On Almost Perfect Nonlinear Permutations , 1994, EUROCRYPT.