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

Authors

  • Deep Singh Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India https://orcid.org/0000-0003-4628-9607
  • Harsh Mishra Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India
  • Vitsoto Luho Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India
  • Amit Paul Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India https://orcid.org/0000-0002-1042-1656

DOI:

https://doi.org/10.37256/cm.5220243489

Keywords:

WHT, cross-correlation, autocorrelation, MI, SSMI

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 Zqn to Z2q 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-ofsquares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.

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Published

2024-03-27

How to Cite

1.
Singh D, Mishra H, Luho V, Paul A. Two Indicators of Cross-Correlation for the Functions from Z<i><sub>q</sub><sup>n</sup></i> to <i>Z<sub>2q</sub></i>. Contemp. Math. [Internet]. 2024 Mar. 27 [cited 2024 Jun. 17];5(2):1122-31. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3489