The FAIR principles provide a framework for enabling proper access and reusability of scientific data, and implementing them is a key goal of the European Open Science Cloud (EOSC). However, providing access to sensitive or confidential data while preserving privacy/confidentiality and usability for researchers is still an open question. Existing solutions like safe rooms, safe pods, or data safe havens are often challenging for the development of reproducible research and seem counter-intuitive when dealing with open science and FAIR principles. The SIESTA project aims to provide a set of tools, services, and methodologies for the effective sharing of sensitive data in the EOSC, following a cloud-based model and approach. SIESTA will provide user-friendly tools with the aim of fostering the uptake of sensitive data sharing and processing in the EOSC. The project will deliver trusted cloud-based environments for the management and sharing of sensitive data that are built in a reproducible way, together with a set of services and tools to ease the secure sharing of sensitive data in the EOSC through state-of-the-art anonymization techniques. The overall objective is to enhance the EOSC Exchange services by delivering a set of cloud-based trusted environments for the analysis of sensitive data in the EOSC demonstrating the feasibility of the FAIR principles over them.