People living with type 1 diabetes often use several apps and devices that help them collect and analyse data for a better monitoring and management of their disease. When such health related data is analysed in the cloud, one must always carefully consider privacy protection and adhere to laws regulating the use of personal data. In this paper we present our experience at the pilot Vinter competition 2021-22 organised by Vinnova. The competition focused on digital services that handle sensitive diabetes related data. The architecture that we proposed for the competition is discussed in the context of a hypothetical cloud-based service that calculates diabetes self-care metrics under strong privacy preservation. It is based on Fully Homomorphic Encryption (FHE)-a technology that makes computation on encrypted data possible. Our solution promotes safe key management and data life-cycle control. Our benchmarking experiment demonstrates execution times that scale well for the implementation of personalised health services. We argue that this technology has great potentials for AI-based health applications and opens up new markets for third-party providers of such services, and will ultimately promote patient health and a trustworthy digital society.