Big data and AI did not succeed in preventing Covid-19, but they can be very useful in the fight against it and even for avoiding confinements and other restrictions on rights which it brings about. AI can be extremely useful for integrating, structuring and extracting an enormous quantity and variety of big data information and knowledge for biomedical research. It is also useful for improving civic and health assistance and information, telemedicine and the best assignment of human resources and materials. Even more threatening for privacy could be the development of apps, electronic biological passports, geolocation systems, and the traceability and monitoring of people in the fight against Covid-19, particularly if the Asian model is followed. However, it seems that this not being followed in the EU. There is an analysis of the applicable legal set of rules, the legal legitimation of the various data processing systems, and the need for a legal basis of quality, especially in the case of apps and searches. And besides the legal basis and legitimation, the necessary guarantees of these mass processing systems are considered, particularly of the apps. The impetus of law means that it is indeed technologically possible to maximise the efficiency of the fight against Covid-19 and to maximise all our rights.