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Constructing even-variable RSBFs with higher nonlinearity, optimal AI and almost optimal FAI

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Abstract

In cryptography, rotation symmetric Boolean functions (RSBFs) have very significant research value. In this paper, based on the knowledge of integer splitting, a new class of even-variable RSBFs with optimal algebraic immunity (AI) was constructed. The new functions have a nonlinearity of \(2^{n-1}-\left( {\begin{array}{c}n-1\\ k\end{array}}\right) +2^{k-3}(k-3)(k-2) \), which is the highest among all existing RSBFs with optimal AI as well as existing nonlinearity. The algebraic degree of our new construction is as well the highest. Additionally, the results indicate that within the computing capacity of computer, the new class of even-variable RSBFs have almost optimal fast algebraic immunity (FAI).

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (No. 61103244), the Science and Technology Planning Project of Guangdong Province (No. 190827105555406, 2019B010116001), the Natural Science Foundation of Guangdong Province (No. 2020A1515010899), the Key Scientific Research Project of Universities in Guangdong Province (No. 2020ZDZX3028), and the Guangdong Special Cultivation Funds for College Students’ Scientific and Technological Innovation (No. pdjh2020b0224).

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Correspondence to Yindong Chen.

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Chen, Y., Ruan, J. & He, X. Constructing even-variable RSBFs with higher nonlinearity, optimal AI and almost optimal FAI. J. Appl. Math. Comput. 68, 1669–1683 (2022). https://doi.org/10.1007/s12190-021-01584-z

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  • DOI: https://doi.org/10.1007/s12190-021-01584-z

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