Walsh-Hadamard spectrum is widely used in the field of science and technology like classification of cancer cells, image processing, speech processing, signal and image compression etc. In this paper, a genomic analysis using Walsh-Hadamard spectrum and cross-correlation has been done. Transformation of genetic code using Walsh-Hadamard spectrum has been given. We redefine the Walsh-Hadamard spectrum in genomics and analyse the origin of mRNA features by using this spectra. Finally, using Walsh-Hadamard spectrum the overall energy of the mRNA sequence has been evaluated.

Transparency order is considered to be a cryptographically significant property that characterizes the resistance of S-boxes in opposition to differential power analysis attacks. The S-box having low transparency order is more resistant to these attacks. Until now, little attempts have been noticed to examine theoretically the transparency order and its relationship with other cryptographic properties. All constructions associated with transparency order are relying on search algorithms. In this paper, we discuss the new interpretation of bent functions in terms of their transparency order. Using the concept of vector concatenation and correlation characteristics, we find the transparency order of Boolean functions. The notion of complementary transparency order is given. For a pair of Boolean functions, we interpret complementary transparency order by their Walsh-Hadamard transform. We establish a relationship of transparency order with cross-correlation for a pair of Boolean functions. We find a relationship of transparency order with (n − 2)−variable decomposition bent functions. We generalize the bounds on sum-of-squares of autocorrelation in terms of transparency order of Boolean functions using Walsh-Hadamard spectra. Further the transparency order of a function fulfilling the propagation criterion about a linear subspace is evaluated.