The correlation-immune functions serve as an important metric for measuring resistance of a cryptosystem against correlation attacks. Existing literature emphasize on matrices, orthogonal arrays and Walsh-Hadamard spectra to characterize the correlation-immune functions over \(\phantom {\dot {i}\!}\mathbb {F}_{p}\) (p ≥ 2 is a prime). Recently, Wang and Gong investigated the Fourier spectral characterization over the complex field for correlation-immune Boolean functions. In this paper, the discrete Fourier transform (DFT) of non-binary functions was studied. It was shown that a function f over \(\phantom {\dot {i}\!}\mathbb {F}_{p}\) is m th-order correlation-immune if and only if its Fourier spectrum vanishes at a specific location under any permutation of variables. Moreover, if f is a symmetric function, f is correlation-immune if and only if its Fourier spectrum vanishes at only one location.

中文翻译：

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Fp $ \ phantom {\ dot {i} \！} \ mathbb {F} _ {p} $上相关免疫函数的傅里叶光谱表征

免疫相关功能是衡量密码系统抵抗相关攻击的重要指标。现有文献强调在基质上，正交阵列和沃尔什-哈达玛光谱来表征相关免疫功能上\（\幻象{\点{I} \！} \ mathbb {F} _ {P} \） （p ≥2是素数）。最近，Wang和Gong研究了相关免疫布尔函数在复数场上的傅立叶光谱表征。本文研究了非二元函数的离散傅里叶变换（DFT）。结果表明，一个函数˚F超过\（\幻象{\点{I} \！} \ mathbb {F} _ {P} \）是米当且仅当其傅立叶谱在变量的任何排列下的特定位置消失时，三阶相关免疫。而且，如果f是一个对称函数，则当且仅当它的傅立叶谱仅在一个位置消失时，f才是相关免疫的。