Abstract
The aim of this paper is to construct boolean functions \(f:\{0,1\}^n\longrightarrow\{0,1\}^m\), for which the graph gr(f) = {(x,f(x)),x ∈ {0,1}n} ⊆ {0,1}n + m has maximal algebraic immunity. This research is motivated by the need for appropriate boolean functions serving as building blocks of symmetric ciphers. Such functions should have large algebraic immunity for preventing vulnerability of the cipher against algebraic attacks. We completely solve the problem of constructing explicitely defined single-output functions for which the graph has maximal algebraic immunity. Concerning multi-output functions, we present an efficient algorithm, based on matroid union, which computes for given m,n,d the table of a function \(h:\{0,1\}^n\longrightarrow\{0,1\}^m\) for which the algebraic immunity of the graph is greater than d. To the best of our knowledge, this is the first systematic method for constructing multi-output functions of high algebraic immunity.
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Armknecht, F., Krause, M. (2006). Constructing Single- and Multi-output Boolean Functions with Maximal Algebraic Immunity. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_16
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DOI: https://doi.org/10.1007/11787006_16
Publisher Name: Springer, Berlin, Heidelberg
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