The Fourier Spectral Characterization for the Correlation-Immune Functions over Fp

03/13/2019

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by   Zilong Wang, et al.

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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 F_p (p ≥ 2 is a prime). 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 F_p is mth-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.