Characterization and Properties of Bent‐Negabent Functions

JIANG, Niu; Zhao, Min; Zhiyao, Yang; Zhuo, Zepeng; Chen, Guolong

doi:10.1049/cje.2021.00.417

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…The nega-convolution theorem for Boolean functions has been given by Jiang et al (2022). Here, we discuss the generalized nega-convolution theorem for the generalized Boolean function ℎ ∈ ℬ 𝑛 𝑞 .…”

Section: Some Results On Generalized Composition and Convolution Theo...mentioning

confidence: 99%

A Characterization of Generalized Boolean Functions Employed in CDMA Communications

Singh,

Chawla,

Bhogta

et al. 2024

Int. j. math. eng. manag. sci.

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In design of secure cryptosystems and CDMA communications, the negabent functions play a significant role. The generalized Boolean functions have been extensively studied by Schmidt and established several important results in this setup. In this paper, several characteristics of the generalized nega-Hadamard transform (GNT) of generalized Boolean functions like inverse of GNT, generalized nega-cross correlation, generalized nega-Parseval’s identity, relationship between GNT and generalized nega-cross correlation have analyzed. We studied the GNT for the derivative of this setup of functions and established the connection of generalized Walsh-Hadamard transform and GNT of derivatives of these functions. Also, the GNT of composition of vectorial Boolean function and generalized Boolean function is presented. Further, the generalized nega-convolution theorem for generalized Boolean function is obtained.

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Section: Some Results On Generalized Composition and Convolution Theo...mentioning

confidence: 99%

A Characterization of Generalized Boolean Functions Employed in CDMA Communications

Singh,

Chawla,

Bhogta

et al. 2024

Int. j. math. eng. manag. sci.

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Some Cryptographic Properties of Functions Based on their 2q-Nega-Hadamard Transform

Singh,

Mohanta,

Paul

et al. 2024

Int. j. math. eng. manag. sci.

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Negabent functions play a vital role in the field of cryptography and coding theory for designing secure cryptosystems. In this article, we investigate the various properties of 2q-nega-Hadamard transform (2q-NHT) of the functions from Z_q^n to Z_2q with q≥2 is a positive integer. We discuss the 2q-NHT of the derivative of these functions and develop a connection between 2q-walsh-Hadamard transform (2q-WHT) and 2q-NHT for the derivative of these functions. Also, we show that the dual g ̃ of g∈B_(n,q) is 2q-bent if N_g (ϑ)=ω^(g ̃(ϑ)) for all ϑ∈Z_q^n. The 2q-nega convolution transform theorem for the current setup is obtained. Further, we have obtained the 2q-NHT of composition of generalized vectorial function and generalized function.

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Characterization and Properties of Bent‐Negabent Functions

Cited by 2 publications

References 18 publications

A Characterization of Generalized Boolean Functions Employed in CDMA Communications

A Characterization of Generalized Boolean Functions Employed in CDMA Communications

Some Cryptographic Properties of Functions Based on their 2q-Nega-Hadamard Transform

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