Results on Algebraic Immunity for Cryptographically Significant Boolean Functions
Results on Algebraic Immunity for Cryptographically Significant Boolean Functions
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DOI：
10.1007/978-3-540-30556-9_9
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发表时间：
2004-12
期刊：
影响因子：
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通讯作者：
Deepak Kumar Dalai;K. Gupta;S. Maitra
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文献类型：
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作者：
Deepak Kumar Dalai;K. Gupta;S. Maitra
近年来，代数攻击在密码学领域受到了广泛的关注。已经观察到，被解释为GF（2）上的多元多项式的布尔函数f在用作密码原语时不应该具有低次倍数。本文证明了高非线性度是抵抗代数攻击的必要条件，并解释了布尔函数的沃尔什谱值与其代数免疫性（抵抗代数攻击）之间的关系。接下来，我们提出了线性无关零化子的计数结果。我们还研究了某些类别的高度非线性弹性布尔函数的代数免疫。
Recently algebraic attack has received a lot of attention in cryptographic literature. It has been observed that a Boolean functionf, interpreted as a multivariate polynomial overGF(2), should not have low degree multiples when used as a cryptographic primitive. In this paper we show that high nonlinearity is a necessary condition to resist algebraic attack and explain how the Walsh spectra values are related to the algebraic immunity (resistance against algebraic attack) of a Boolean function. Next we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity.