Based on the hidden weighted bit function, we propose a family of cryptographically significant Boolean functions. We investigate its algebraic degree and use Schur polynomials to study its algebraic immunity. For a subclass of this family, we deduce a lower bound on its nonlinearity. Moreover, we give an infinite class of balanced functions with very good cryptographic properties: optimum algebraic degree, optimum algebraic immunity, high nonlinearity (higher than the Carlet-Feng function and the function proposed by [25]) and a good behavior against fast algebraic attacks. These functions seem to have the best cryptographic properties among all currently known functions.
CITATION STYLE
Wang, Q., Tan, C. H., & Foo, T. (2014). A family of cryptographically significant boolean functions based on the hidden weighted bit function. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8565, pp. 293–310). Springer Verlag. https://doi.org/10.1007/978-3-319-12160-4_19
Mendeley helps you to discover research relevant for your work.