Abstract
A general construction of APN polynomial functions of the form \(c_{30}x^3+c_{03}x^{3q}+\sum \nolimits _{i=0}^2\sum \nolimits _{j=0}^2c_{ij}x^{i+qj}\) over a finite field \(\mathbb {F}_{q^2}\) of odd characteristic is proposed, and some variants of this construction are also presented. As a consequence, new APN polynomial functions such as ones over \(\mathbb {F}_{3^{2m}}\) and \(\mathbb {F}_{11^2}\) which are CCZ-inequivalent to known APN functions are obtained.
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Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved both the quality and presentation of this paper. The work of this paper was supported by the National Basic Research Programme under Grant 2013CB834203, the National Natural Science Foundation of China (Grants 61070172 and 11201214), and the Strategic Priority Research Program of Chinese Academy of Sciences under Grant XDA06010702.
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Zha, Z., Hu, L., Sun, S. et al. New constructions of APN polynomial functions in odd characteristic. AAECC 25, 249–263 (2014). https://doi.org/10.1007/s00200-014-0227-2
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DOI: https://doi.org/10.1007/s00200-014-0227-2