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Erschienen in:
16.05.2019
The Fourier spectral characterization for the correlation-immune functions over \(\phantom {\dot {i}\!}\mathbb {F}_{p}\)
Erschienen in: Cryptography and Communications | Ausgabe 3/2020
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Abstract
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.