Thanks to new regulations like GDPR, Personal Data Management Systems (PDMS) have become a reality. This decentralized way of managing personal data provides a de facto protection against massive attacks on central servers. But, when performing distributed computations, this raises the question of how to preserve individuals' trust on their PDMS? And how to guarantee the integrity of the final result? This paper proposes a secure computing framework capitalizing on the use of Trusted Execution Environments at the edge of the network to tackle these questions.