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arXiv · 1903.05350

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

Zilong Wang·Jinjin Chai·Guang Gong
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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 $\mathbb{F}_p$ ($p \geq 2$ is a prime). %with prime $p$. 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 $\mathbb{F}_p$ 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.

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Zilong Wang, Jinjin Chai, Guang Gong. 2019-03-13. The Fourier Spectral Characterization for the Correlation-Immune Functions over Fp. https://arxiv.org/abs/1903.05350

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