LAUSR

Many problems in the domains of cryptography, coding theory, sequence theory and circuit theory can be formulated in terms of Boolean functions. The connections between these domains and Boolean functions, and between these domains through Boolean functions, are numerous. The present special issue of the Journal “Cryptography and Communications” is devoted to them. A first example of such connection is with substitution boxes (S-boxes) and their nonlinearity and differential uniformity (including the notion of APNness). These notions come from cryptography, but also play an important role in sequence theory and are closely related to important issues in coding theory. The papers “On APN functions L1(x) + L2(x) with linear L1 and L2” by Irene Villa, “On an algorithm generating 2-to-1 APN functions and its applications to the Big APN problem“, by Valeriya Idrisova and “Cellular Automata Based S-boxes“ by Luca Mariot, Stjepan Picek, Alberto Leporati and Domagoj Jakobovic deal with the generation of vectorial functions having such good features. A second example is with the notions of nonlinearity of Boolean functions and of bent functions, whose definitions come from cryptography as well, but are also connected to coding theory through Kerdock codes and to (bent) sequences. The papers “On the nonlinearity of Boolean functions with restricted input” by Sihem Mesnager, Zhengchun Zhou and Cunsheng Ding and “New classes of p-ary bent functions” by Bimal Mandal, Pantelimon Stănică and Sugata Gangopadhyay study further these notions, with additional constraints and extended to other characteristics. The circuit complexity plays an important role in all applicative domains of Boolean functions. The papers “The Multiplicative Complexity of 6-variable Boolean Functions” by