Cryptology ePrint Archive: Report 2012/210

On the Existence of Boolean Functions with Optimal Resistance against Fast Algebraic Attacks

Yusong Du, and Fangguo Zhang

Abstract: It has been pointed out that an $n$-variable Boolean function $f$ has optimal resistance against fast algebraic attacks if and only if there does not exist a nonzero $n$-variable Boolean function $g$ of degree lower than $\frac{n}{2}$ such that $fg=h$ and $\mathrm{deg}(g)+\mathrm{deg}(h)<n$. In this corresponding, we show that there does not exist an $n$-variable Boolean function with optimal resistance against fast algebraic attacks for most values of $n$.

Category / Keywords: stream ciphers, fast algebraic attacks, Boolean functions

Date: received 16 Apr 2012, last revised 16 Apr 2012

Contact author: yusongdu at hotmail com

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Version: 20120422:224034 (All versions of this report)

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