Spectral Characterization and Analysis of Avalanche in Cryptographic Substitution Boxes using Walsh-Hadamard Transformations

paper presents a novel analytical technique of examining the avalanche characteristics of cryptographic substitution boxes (s-boxes) using the Walsh Hadamard spectral analysis of their Boolean maps. Avalanche is a desirable cryptographic property that is necessary to ensure that a cipher is not susceptible to statistical attacks and small difference between two plaintexts results in a significant random difference between the two corresponding ciphertexts. An analytical model of avalanche characteristics based on spectral analysis is developed which allows us to determine the degree of avalanche achievable in an m n