Research on the Construction of Plateaued Functions
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摘要: Plateaued函数在密码学及编码等领域有着极其重要的应用，该文提出一种Plateaued函数的直接构造方法，研究了由该方法构造的Plateaued函数的密码学性质，证明了现有的直接构造方法可归约到本构造方法。
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关键词:
- 布尔函数 /
- Plateaued函数 /
- 非线性度 /
- 弹性阶
Abstract: Plateaued functions play a significant role in cryptography, coding theory and so on. In this paper, a new primary construction of plateaued function is given. Some cryptographic properties of the constructed plateaued functions are studied. It is shown that the existing primary constructions of plateaued function can be reduced to the proposed construction.-
Key words:
- Boolean function /
- Plateaued function /
- Nonlinearity /
- Resiliency
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表 1 谱值与根空间维数的关系
${W_f}({{ω}} )$ ${{ω}} $的个数 0 ${2^n} - {2^{n - t}}$ ${2^{(n + t)/2}}$ ${2^{n - t - 1}} + {( - 1)^{f(0)}}{2^{(n - t - 2)/2}}$ $ - {2^{(n + t)/2}}$ ${2^{n - t - 1}} - {( - 1)^{f(0)}}{2^{(n - t - 2)/2}}$ 
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