Abstract
A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of input variables is a power of two. Also, for n equal to a power of two, the Carlet-Feng functions on nā+ā1 variables and the modified Carlet-Feng functions on n variables are shown to be perfect algebraic immune functions.
Supported by the National 973 Program of China under Grant 2011CB302400, the National Natural Science Foundation of China under Grants 10971246, 60970152, and 61173134, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant XDA06010701, and the CAS Special Grant for Postgraduate Research, Innovation and Practice.
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Liu, M., Zhang, Y., Lin, D. (2012). Perfect Algebraic Immune Functions. In: Wang, X., Sako, K. (eds) Advances in Cryptology ā ASIACRYPT 2012. ASIACRYPT 2012. Lecture Notes in Computer Science, vol 7658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34961-4_12
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