Abstract
The focus of this paper is on nonlinear characteristics of cryptographic Boolean functions. First, we introduce the notion of plateaued functions that have many cryptographically desirable properties. Second, we establish a sequence of strengthened inequalities on some of the most important nonlinearity criteria, including nonlinearity, propagation and correlation immunity, and prove that critical cases of the inequalities coincide with characterizations of plateaued functions. We then proceed to prove that plateaued functions include as a proper subset all partially-bent functions that were introduced earlier by Carlet. This settles an open question that arises from previously known results on partially-bent functions. In addition, we construct plateaued, but not partially-bent, functions that have many properties useful in cryptography.
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© 1999 Springer-Verlag Berlin Heidelberg
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Zheng, Y., Zhang, XM. (1999). Plateaued Functions. In: Varadharajan, V., Mu, Y. (eds) Information and Communication Security. ICICS 1999. Lecture Notes in Computer Science, vol 1726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47942-0_24
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DOI: https://doi.org/10.1007/978-3-540-47942-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66682-0
Online ISBN: 978-3-540-47942-0
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