On the Walsh Spectrum of a New APN Function

We compute the Walsh spectrum of a new quadratic APN function, x3 +Tr(x9), showing that its Walsh transform is 3-valued for odd n, and is 5-valued for even n. Therefore, the distribution of the values of the Walsh transform of x3 + Tr(x9) is the same as that of the APN Gold functions. Moreover, for odd n the function is AB, which gives an alternative proof of the APN property of the function.

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

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

[3]  Claude Carlet,et al.  An infinite class of quadratic APN functions which are not equivalent to power mappings , 2006, 2006 IEEE International Symposium on Information Theory.

[4]  Claude Carlet,et al.  Constructing new APN functions from known ones , 2009, Finite Fields Their Appl..

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

[6]  Claude Carlet,et al.  Two Classes of Quadratic APN Binomials Inequivalent to Power Functions , 2008, IEEE Transactions on Information Theory.

[7]  Alexander Pott,et al.  A new APN function which is not equivalent to a power mapping , 2005, IEEE Transactions on Information Theory.

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

[9]  Claude Carlet,et al.  Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems , 1998, Des. Codes Cryptogr..

[10]  Anne Canteaut,et al.  Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences , 2000, SIAM J. Discret. Math..

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

[12]  Claude Carlet,et al.  New classes of almost bent and almost perfect nonlinear polynomials , 2006, IEEE Transactions on Information Theory.