With the increased use of Internet, governments and large companies store and share massive amounts of personal data in such a way that leaves no space for transparency. When a user needs to achieve a simple task like applying for college or a driving license, he needs to visit a lot of institutions and organizations, thus leaving a lot of private data in many places. The same happens when using the Internet. These privacy issues raised by the centralized architectures along with the recent developments in the area of serverless applications demand a decentralized private data layer under user control. We introduce the Private Data System (PDS), a distributed approach which enables self-sovereign storage and sharing of private data. The system is composed of nodes spread across the entire Internet managing local key-value databases. The communication between nodes is achieved through executable choreographies, which are capable of preventing information leakage when executing across different organizations with different regulations in place. The user has full control over his private data and is able to share and revoke access to organizations at any time. Even more, the updates are propagated instantly to all the parties which have access to the data thanks to the system design. Specifically, the processing organizations may retrieve and process the shared information, but are not allowed under any circumstances to store it on long term. PDS offers an alternative to systems that aim to ensure self-sovereignty of specific types of data through blockchain inspired techniques but face various problems, such as low performance. Both approaches propose a distributed database, but with different characteristics. While the blockchain-based systems are built to solve consensus problems, PDS's purpose is to solve the self-sovereignty aspects raised by the privacy laws, rules and principles.