Cryptology ePrint Archive: Report 2012/212
Perfect Algebraic Immune Functions
Meicheng Liu and Yin Zhang and Dongdai Lin
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 the Carlet-Feng functions
on $2^s+1$ variables and the modified Carlet-Feng functions on $2^s$
variables are shown to be perfect algebraic immune functions.
Furthermore, it is shown that a perfect algebraic immune function
behaves good against probabilistic algebraic attacks as well.
Category / Keywords: Boolean functions, Algebraic immunity, Fast algebraic attacks, Probabilistic algebraic attacks
Date: received 17 Apr 2012, last revised 8 Aug 2012
Contact author: meicheng liu at gmail com
Available format(s): PDF | BibTeX Citation
Note: The proof of the "only if" direction of Theorem 8 has been corrected.
Version: 20120808:132312 (All versions of this report)
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