Deep Singh
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India.

Bibhuti Bhusan Mohanta
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India.

Amit Paul
Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India.

Jatinder Kumar
Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India.

Rajwinder Singh
Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India.

DOI https://doi.org/10.33889/IJMEMS.2024.9.6.074

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Abstract

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.

Keywords- 2q-Walsh-Hadamard transform (2q-WHT), 2q-Nega Cross-Correlation (2q-NCC), 2q-Nega auto-correlation (2q-NAC), 2q-Bent functions, 2q-Nega-Hadamard transform (2q-NHT).

Citation

Singh, D., Mohanta, B. B. Paul, A., Kumar, J., & Singh, R. (2024). Some Cryptographic Properties of Functions Based on their 2q-Nega-Hadamard Transform. International Journal of Mathematical, Engineering and Management Sciences, 9(6), 1382-1393. https://doi.org/10.33889/IJMEMS.2024.9.6.074.