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

• Published in: International journal of mathematical, engineering and management sciences engineering and management sciences, 2024-12, Vol.9 (6), p.1382-1393
• Main Authors: Singh, Deep, Mohanta, Bibhuti Bhusan, Paul, Amit, Kumar, Jatinder, Singh, Rajwinder
• Format: Article
• Language: English
• Subjects: 2q-bent functions; 2q-nega auto-correlation (2q-nac); 2q-nega cross-correlation (2q-ncc); 2q-nega-hadamard transform (2q-nht); 2q-walsh-hadamard transform (2q-wht)
• ISSN: 2455-7749; 2455-7749
• DOI: 10.33889/IJMEMS.2024.9.6.074

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.