Abstract
In this paper, we give some relationship between the nonlinearity of rational functions over \( \mathbb{F}_{2^n } \) and the number of points of associated hyperelliptic curve. Using this, we get a lower bound on nonlinearity of rational-typed vector Boolean functions over \( \mathbb{F}_{2^n } \) . While the previous works give us a lower bound on nonlinearity only for special-typed monomials, our result gives us general bound applicable for all rational fuctions defined over \( \mathbb{F}_{2^n } \) . As an application of our results, we get a lower bound on nonlinearity of n × kn S-boxes.
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© 1999 Springer-Verlag Berlin Heidelberg
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Cheon, J.H., Chee, S., Park, C. (1999). S-boxes with Controllable Nonlinearity. In: Stern, J. (eds) Advances in Cryptology — EUROCRYPT ’99. EUROCRYPT 1999. Lecture Notes in Computer Science, vol 1592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48910-X_20
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DOI: https://doi.org/10.1007/3-540-48910-X_20
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