Abstract
The construction of Boolean functions with an odd number of variables and maximum algebraic immunity is studied in this paper. Starting with any function f obtained by the Carlet–Feng construction, we develop an efficient method to properly modify f in order to provide new functions having maximum algebraic immunity. This new approach, which exploits properties of the punctured Reed–Muller codes, suffices to generate a large number of new functions with maximum algebraic immunity through swapping an arbitrary number of elements between the support of f and its complement.
This work is co–financed by the European Union (European Social Fund) and Greek national funds through the operational program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF). Research funding program THALES: investing in knowledge society through the European Social Fund.
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The authors would like to thank the anonymous reviewers for the helpful comments and suggestions.
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Limniotis, K., Kolokotronis, N. (2016). Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes. In: Pasalic, E., Knudsen, L. (eds) Cryptography and Information Security in the Balkans. BalkanCryptSec 2015. Lecture Notes in Computer Science(), vol 9540. Springer, Cham. https://doi.org/10.1007/978-3-319-29172-7_1
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