Several distributed storage solutions that do not rely on a central server have been proposed over the last few years. Most of them are deployed on public networks on the internet. However, these solutions often do not provide a mechanism for access rights to enable the users to control who can access a specific file or piece of data. In this article, we propose Mutida (from the Latin word "Aditum" meaning "access"), a protocol that allows the owner of a file to delegate access rights to another user. This access right can then be delegated to a computing node to process the piece of data. The mechanism relies on the encryption of the data, public key/value pair storage to register the access control list and on a function executed locally by the nodes to compute the decryption key. After presenting the mechanism, its advantages and limitations, we show that the proposed mechanism has similar functionalities to Wave, an authorization framework with transitive delegation. However, Wave does not require fully trusted nodes. We implement our approach in a Java software program and evaluate it on the Grid'5000 testbed. We compare our approach to an approach based on a protocol relying on Shamir key reconstruction, which provides similar features.