Distributed Multi-User Secret Sharing

We consider a distributed secret sharing system that consists of dealer, n storage nodes, and m users. Each user is given access to certain subset where it can download the stored data. The dealer wants securely convey specific s j j via for j=1,2, ..., m. More specifically, two secrecy conditions are considered in this multi-user context. weak condition each does not get any information about individual secrets other users, while perfect implies collection all users' secrets. In system, encodes into several shares loads them nodes. Given number nodes we find maximum users be served such construct schemes achieve with secrecy. further define major properties systems; communication complexity defined as total amount data need order reconstruct their secrets; overhead size loaded by normalized Lower bounds on minimum characterized protocols, under parameters, attain lower bound providing Furthermore, again conditions, simultaneously secrecy, thereby demonstrating optimal terms both parameters. It shown how modify proposed protocols balanced load complexity.