Cloud Computing is an inevitable trend. In the near future almost every consumer electronics device will be connected to an ecosystem of third-party partners providing payment systems, streamed content, etc. However, a whole field of cloud services still lacks solutions because of security issues. Cloud operators and their end users (individuals, companies, etc.) do not always trust each other. As long as storage is concerned, classical cryptography is an efficient way to get round the problem. But things are different when remote processing of sensitive data is required. As a consequence, without a strong chain of trust between them, end users and cloud operators cannot delegate the processing of their sensitive data to the un-trusted other: cloud operators have full administrator privileges on their computing farms and end users can compromise their local equipment by hardware and software attacks. This lack of trust limits the potential of the cloud computing market.The TRESCCA project aims to lay the foundations of a secure and trustable cloud platform by ensuring strong logical and physical security on the edge devices, using both hardware security and virtualization techniques while considering the whole cloud architecture. The project will propose and demonstrate hardware/software solutions allowing stakeholders to delegate the processing of their sensitive data to a remote processing engine opening up whole new field of cloud services and applications. The approach avoids undesirable paradigm shifts, both in the software and in the hardware by complementing existing legacy solutions by non-intrusive add-ons. Security is a main concern but cost, performance and acceptability will also be considered as key metrics. In order to promote the solutions and to challenge them against security experts, openness will be an important characteristic of the project: as much as possible of the project's outcomes will be public and released under free software licenses.