**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

**Available format(s): **PDF | BibTeX Citation

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

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