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

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.