Governments across the world are evaluating means to move out of COVID-19 lockdown gradually. Until researchers find a vaccine, the most effective solution appears to be infection-chain investigations, to notify encounters of infected people to self-isolate and get tested. However, those solutions raise many valid privacy concerns. The collected information, while essential for investigations to be carried out properly, can lead to mass surveillance. To protect our collective freedom, it is crucial to put in place insurances that the data will not be accessed unlawfully and that the usage is restricted to its intended use. These insurances will maintain a democratically agreed balance between the need for data on the one hand and civic rights on the other. Exposure investigations face many efficiency challenges. Automatically tracing citizens with their mobile phones has been technically limited for years to address rightful privacy concerns. The NHS is currently recruiting 18,000 contact tracers, but manual tracing is highly intrusive, can't scale, and is unlikely to identify all contacts adequately. Both automatic and manual tracing techniques are complementary and need a secure collaboration service to maximise the global impact of cluster investigation while preserving people's privacy. Secretarium has built a secure solution, currently used in financial services, that enables individual institutions to collaborate whilst keeping their respective confidential data private. We use the latest cryptography and hardware security technologies to guarantee that private data is never disclosed, as it remains encrypted even during processing. This is highly innovative because it is easy to secure data in storage and in transit using traditional encryption techniques, but it is very hard to keep it secure while being processed by a computer programme. We started adapting our technology for COVID-19 infection investigation in March, and are preparing collaboration tools to efficiently investigate infection clusters while preventing mass-surveillance. For example, this will enable infection cluster investigators to get in touch with patients without having to know their identity. By improving privacy in this way, it will give the general population more confidence and trust to use the system without fearing that their personal data is going to be misused.