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https://doi.org/10.1016/j.ipl.2012.08.004
Title: | A note on the algebraic immunity of the Maiorana-McFarland class of bent functions | Authors: | Wang, Q. Tan, C.H. |
Keywords: | Algebraic immunity Bent function Cryptography Nonlinearity |
Issue Date: | 30-Nov-2012 | Citation: | Wang, Q., Tan, C.H. (2012-11-30). A note on the algebraic immunity of the Maiorana-McFarland class of bent functions. Information Processing Letters 112 (22) : 869-871. ScholarBank@NUS Repository. https://doi.org/10.1016/j.ipl.2012.08.004 | Abstract: | In Gupta et al. (2011) [5], the authors proved that the algebraic immunity of a subclass of Maiorana-McFarland functions is at most ⌈n/4⌈+2 and claimed that this bound is tight. The main theorem of the upper bound is correct. However, their proof is incomplete and the bound is not tight. We will prove a more general theorem of a much larger subclass of Maiorana-McFarland functions and find that its algebraic immunity cannot achieve the optimum value. However, we find an 8-variable Maiorana-McFarland function which is not in that larger subclass of Maiorana-McFarland functions achieving the optimum algebraic immunity (this is the first time that a nontrivial Maiorana-McFarland function with the optimum algebraic immunity is given). Hence, this shows that there exist the Maiorana-McFarland functions achieving the optimum algebraic immunity. © 2012 Elsevier B.V. All rights reserved. | Source Title: | Information Processing Letters | URI: | http://scholarbank.nus.edu.sg/handle/10635/116197 | ISSN: | 00200190 | DOI: | 10.1016/j.ipl.2012.08.004 |
Appears in Collections: | Staff Publications |
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