## 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.

Short URL: ia.cr/2012/212

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