LAUSR

This is the third special issue of Cryptography and Communications dedicated to Boolean functions and their applications (the previous two appeared in 2016 and 2019 and were associated with the events of BFA 2014 and BFA 2017). Boolean functions (single-output and multi-output ones) are used in the design of stream and block ciphers and in the definition of some important error correcting codes; they are also directly related to some problems on sequences for telecommunications. In June 2018, we invited leading specialists from nine different countries all over the world to Loen, Norway, for the international workshop on Boolean functions and their applications BFA 2018. All speakers have been invited to submit a paper. All the papers sent were thoroughly reviewed and twelve papers, described below, have been accepted after revision. In cryptography, S(ubstitution)-boxes are core components in symmetric ciphers. In order for the algorithm to resist one of the most prominent cryptanalytic techniques, namely differential attacks [13], S-boxes should have a low differential uniformity. APN functions are optimal in this respect. The paper “If a Generalised Butterfly is APN then it Operates on 6 Bits” by Anne Canteaut, Léo Perrin and Shizhu Tian is dedicated to a very important problem on the existence of APN permutations over F22n and it proves that a recently introduced generalised butterfly construction using Gold exponents can never be APN for n > 3. Continuing the work of Budaghyan, Carlet, Helleseth, Li and Sun on finding conditions when a resulting function after changing one value in an APN function is APN itself, Nikolay Kaleyski studies a similar problem for the case of changing two values in the paper “Changing APN Functions at Two Points”. Algebraic attacks are a powerful technique for the cryptanalysis of stream ciphers. The algebraic immunity of Boolean functions quantifies their contribution to the resistance