29-06-2022
Constructing more quadratic APN functions with the QAM method
Published in: Cryptography and Communications | Issue 6/2022
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Abstract
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for ease of study by others. In this paper, we recall how to construct new QAMs from a known one. Based on these results and on others on smaller fields, we make two conjectures: that the total number of CCZ-inequivalent quadratic APN functions on \(\mathbb {F}_{2^{8}}\) exceeds 50000, and that the full list of quadratic APN functions could be obtained by modifying only a small number of entries of the QAM, though such a search remains computationally infeasible at this stage. Finally, we propose a new model which can handle the last two columns together and avoid some redundant computation.