Secure distributive storage of decentralized source data: Can interaction help?

We consider the problem of securing a distributed storage system with decentralized data, where some of the nodes are compromised by an eavesdropper. The system is formed of n storage nodes among which k nodes (k <; n) have information sources. The system is required to have the “MDS property”, i.e., to allow any user to recover all the sources by contacting any k nodes. To achieve this goal, the source nodes need to disseminate their data to the other nodes in the system while revealing no information to the eavesdropper. We investigate the role of interaction between the sources in reducing the total required bandwidth. When the sources are independent, we show that interaction does not help and that there always exists an optimal non-interactive scheme.