Abstract
In a first part of the paper, we recall some known open questions on the nonlinearity of Boolean and vectorial functions and on the APN-ness of vectorial functions. All of them have been extensively searched and seem quite difficult. We also indicate related less well-known open questions. In the second part of the paper, we introduce four new open problems (leading to several related sub-problems) and the results which lead to them. Addressing these problems may be less difficult since they have not been much worked on.
Keywords
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By that, we mean a criterion related to those attacks on the cryptosystem viewed as a black box, by opposition to the attacks exploiting leaks, like side channel attacks.
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- 3.
Unless the nonlinearity of the CF function becomes much worse for values of \(n\) which are too large for allowing its computation.
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Acknowledgement
We wish to thank Lilya Budaghyan, Faruk Gologlu and Sihem Mesnager for useful information.
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Carlet, C. (2015). Open Questions on Nonlinearity and on APN Functions. In: Koç, Ç., Mesnager, S., Savaş, E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science(), vol 9061. Springer, Cham. https://doi.org/10.1007/978-3-319-16277-5_5
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