A New Transform Related to Distance From a Boolean Function
A New Transform Related to Distance From a Boolean Function
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DOI：
10.1109/tit.2016.2536730
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发表时间：
2016-05
影响因子：
2.5
通讯作者：
A. Klapper
中科院分区：
文献类型：
--
作者：
A. Klapper
我们介绍了一种新的变换布尔函数推广的沃尔什-阿达玛变换。对于布尔函数$q$和$f$，$f$的$q$ -变换度量了$f$与由$q$通过变换基得到的函数集的接近程度。这对某些代数攻击的安全性有影响。在本文中，我们得到的期望值和二阶矩（Parseval的方程）的$q$ -变换，导致的概念$q$ -的。我们还开发了一个泊松求和公式，这导致了一个证明，$q$变换是可逆的。
We introduce a new transform on Boolean functions generalizing the Walsh–Hadamard transform. For Boolean functions $q$ and $f$ , the $q$ -transform of $f$ measures the proximity of $f$ to the set of functions obtained from $q$ by change of basis. This has implications for security against certain algebraic attacks. In this paper, we derive the expected value and second moment (Parseval’s equation) of the $q$ -transform, leading to a notion of $q$ -bentness. We also develop a Poisson summation formula, which leads to a proof that the $q$ -transform is invertible.