Secure erasure codes with partial decodability

The MDS property (aka the k-out-of-n property) requires that if a file is split into several symbols and subsequently encoded into n coded symbols, each being stored in one storage node of a distributed storage system (DSS), then an user can recover the file by accessing any k nodes. We study the so-called p-decodable μ-secure erasure coding scheme (1 ≤ p ≤ k − μ, 0 ≤ μ < k, p|(k − μ)), which satisfies the MDS property and the following additional properties: (P1) strongly secure up to a threshold: an adversary which eavesdrops at most μ storage nodes gains no information (in Shannon´s sense) about the stored file, (P2) partially decodable: a legitimate user can recover a subset of p file symbols by accessing some μ + p storage nodes.