Two Indicators of Cross-Correlation for the Functions from Zqn to Z2q

Deep Singh, Harsh Mishra, Vitsoto Luho, Amit Paul
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引用次数: 0

Abstract

Boolean functions play an important role in the design of secure cryptosystems and code division multiple access (CDMA) communication. Several possible generalizations of Boolean functions have been obtained in recent years. In this paper, we analyze the properties of functions from  in terms of their Walsh-Hadamard transform (WHT). We provide a relationship between cross-correlation and the WHT of these functions. Also, we present a necessary and sufficient condition for the functions to have complementary autocorrelation. The Parseval’s identity for the current setup of these functions is obtained. Further, we obtained the modulus indicator (MI) and the sum-of-squares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.
从 Zqn 到 Z2q 函数的两个交叉相关指标
布尔函数在安全密码系统和码分多址(CDMA)通信设计中发挥着重要作用。近年来,人们对布尔函数进行了一些可能的概括。在本文中,我们从函数的沃尔什-哈达玛德变换(WHT)角度分析了函数的性质。我们提供了这些函数的交叉相关和 WHT 之间的关系。此外,我们还提出了函数具有互补自相关性的必要条件和充分条件。我们还得到了这些函数当前设置的 Parseval 特性。此外,我们还得到了当前设置下两个函数间交叉相关的模量指标(MI)和平方和模量指标(SSMI)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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