Mirror sites approach has been proposed recently for reducing the access delay and providing load balancing in network servers. In the mirror site approach a file, such as a multimedia book, is replicated and dispersed over multiple servers and can be requested in parallel. However, to limit the bandwidth waste, each server maintains not the entire file but only a portion of it. Current solutions to provide parallel access to multiple servers are based on breaking the file into b “pieces” using Forward Error Correction (FEC) codes or their variants. In such techniques, any k = b pieces are necessary and sufficient to construct the file. Thus, protection of the file from unauthorized access has to be based on encryption. As a result, as the degree of parallelism increases a trade off occurs between the security overhead and access delay.In this work, we propose new file dispersal and access control protocols to reduce the security overhead significantly. Our protocols are based on the combinatorial techniques, which break a file into small pieces in a similar way to FEC code. Thus, at least k pieces are necessary to construct the file. However, in contrast with the previous approaches, not every k pieces are sufficient. Capitalizing on this property this work presents secure dispersal and access protocols that aim to minimize the overhead at the servers.