Abstract
We compute the Walsh spectrum of a new quadratic APN function, x 3 + Tr(x 9), 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 x 3 + Tr(x 9) 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.
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Bracken, C., Byrne, E., Markin, N., McGuire, G. (2007). On the Walsh Spectrum of a New APN Function. In: Galbraith, S.D. (eds) Cryptography and Coding. Cryptography and Coding 2007. Lecture Notes in Computer Science, vol 4887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77272-9_6
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DOI: https://doi.org/10.1007/978-3-540-77272-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77271-2
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