arXiv subjects

Wen-Feng Qi

Publications and source records attributed to Wen-Feng Qi.

2 recordsLinked to original sources

arXiv2006

Construction and Count of Boolean Functions of an Odd Number of Variables with Maximum Algebraic Immunity

Algebraic immunity has been proposed as an important property of Boolean functions. To resist algebraic attack, a Boolean function should possess high algebraic immunity. It is well known now that the algebraic immunity of an $n$-variable Boolean function is upper bounded by $\left\lceil {\frac{n}{2}} \right\rceil $. In this paper, for an odd integer $n$, we present a construction method which can efficiently generate a Boolean function of $n$ variables with maximum algebraic immunity, and we also show that any such function can be generated by this method. Moreover, the number of such Boolean functions is greater than $2^{2^{n-1}}$.

cs.CR↗

arXiv2006

Further Results on the Distinctness of Decimations of l-sequences

Let $\underline{a}$ be an \textit{l}-sequence generated by a feedback-with-carry shift register with connection integer $q=p^{e}$, where $ p$ is an odd prime and $e\geq 1$. Goresky and Klapper conjectured that when $ p^{e}\notin \{5,9,11,13\}$, all decimations of $\underline{a}$ are cyclically distinct. When $e=1$ and $p>13$, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, we further show that when $e\geq 2$ and$ p^{e}\neq 9$, all decimations of $\underline{a}$ are also cyclically distinct.

cs.CR↗