Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees...

information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. the document processor, matching function and query analyzer are the main components of an information retrieval system. document retrieval system is fundamentally based on: boolean, vector-space, probabilistic, and language models. in this paper, a new methodology for mat...

Given a bijective vectorial Boolean function Z~-1-Z~, define the correlation matrix P as an N x N matrix, N = 2 n-1, whose entries are given as the squares of the correlation coefficients between nonzero linear combinations of the component Boolean functions of F and nonzero linear Boolean functions of the same n variables. Let A denote the number of nonzero entries in P. When F is chosen unifo...

Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary...

This work surveys mathematical aspects of division property, which is a state-of-the-art technique in cryptanalysis symmetric-key algorithms, such as authenticated encryption, block ciphers and stream ciphers. It aims to find integral distinguishers cube attacks, exploit weaknesses the algebraic normal forms output coordinates involved vectorial Boolean functions. Division property can also be ...