A Boolean function f satisfies PC(l) of order k if f(x) direct+ f(x direct+ alpha) is balanced for any alpha such that 1<=W(alpha) <= l even if any k input bits are kept constant, where W(alpha) denotes the Hamming weight of alpha. This paper shows the first design method of suich functions which provides deg(f)>=3. More than that, we show how to design "balanced' such functions. High nonlinearity and large degree are also obtained. Further, we present balanced SAC(k) functions which achieve the maximum degree. Finally, we extend our technique to vector output Booolean functions.
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机译:如果对于任何alpha平衡f(x)direct + f(x direct + alpha),则布尔函数f满足k阶的PC(l),即使任何k个输入位保持恒定,1 <= W(alpha)<= l ,其中W(alpha)表示alpha的汉明权重。本文展示了提供deg(f)> = 3的suich函数的第一种设计方法。不仅如此,我们还展示了如何设计“平衡”这样的函数。还获得了高非线性度和高程度。此外,我们提出了达到最大程度的平衡SAC(k)函数。最后,我们将技术扩展到了矢量输出Booolean功能。
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