Abstract
The higher order nonlinearity of a Boolean function is a cryptographic criterion, which plays an important role in the design of secure block ciphers and stream ciphers. In this paper, we obtain lower bounds of second-order nonlinearities of two classes of highly nonlinear cubic Boolean functions of the form \(f(x)=tr_1^n(\lambda x^{2^{2r}+2^{r+1}+1}),\) \(\lambda\in\mathbb{F}_{2^n}\setminus\{0\}\), for n = 3r and n = 5r by investigating the lower bounds of the first order nonlinearity of their derivatives.
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© 2013 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Singh, D., Bhaintwal, M. (2013). On Second-Order Nonlinearities of Two Classes of Cubic Boolean Functions. In: Singh, K., Awasthi, A.K. (eds) Quality, Reliability, Security and Robustness in Heterogeneous Networks. QShine 2013. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37949-9_49
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DOI: https://doi.org/10.1007/978-3-642-37949-9_49
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