The Fourier restriction problem, for instance to the sphere, is a long-standing and influential problem in harmonic analysis. In this talk, we consider an analogous question in a discrete setting, namely the restriction of the Fourier transform to the binary cube. This line of research originates in part from a paper by Kane-Tao (2017), in which they studied additive energy. We provide a complete characterization of the regularities and discuss several interesting applications. This is joint work with Tonći Crmarić (University of Split) and Vjekoslav Kovač (University of Zagreb).