Security, along with justice and freedom, is an objective pursued by modern constitutions that are threatened in the digital age, which is increasingly technologically complex. The guarantee of citizens and organizations security is as a real challenge for the contemporary State, in the task of combating the risks and crime that lurk in the cyberspace. The Rule of Law has serious difficulties to act in the digital space through its traditional public powers. From this perspective, the presentation synthesizes the central elements of digital security in the digitalization process, in particular of public administrations, as well as the legal categories of Public Law affected by the guarantee of cybersecurity. Some individual and collective security risks in cyberspace are also covered, such as threats to digital identity and legal security on the Internet, as well as the protection of essential services and critical infrastructures.