The avalanche and propagation characteristics from Haar perspective with extended linear and Bent Haar conditions - Siddiqi, Mohammad Umar; Rafiq, Hashum M. (International Journal of Computer Science and Information Security (IJCSIS), 2016)
The avalanche and propagation characteristics are considered as two of the most significant and desired cryptographic criteria. These properties serve as crucial defining characteristics for block cipher systems in terms of their ability in providing diffusion property of the system. The two specific criteria in this case are the strict-avalanche-criterion (SAC) and propagation-criterion (PC) with their related extensions and generalizations. These criteria are measured using the Autocorrelation function as a tool and have been linked to the Walsh spectral domain as well. The contribution of this paper is on the representational view of these criteria from the Haar domain perspective. The paper derives the general Haar spectral definition of the SAC, PC, and the related extension defined as the global avalanche characteristics (GAC). The derivations are carried out for both single order SAC and PC including higher related orders ( SAC(k) and PC(k) resp.). The Haar general definition is deduced based on the Boolean function (BF)derivatives and their connection to the Autocorrelation function. This Haar generalization gives rise to further derivations on the Haar spectral properties of both classes of Linear and Bent BFs. The paper then presents the extensions on Haar spectral conditions for the said two classes of BFs in terms of the products of their spectra and the spectra of their shifted versions.