An optimal strategy for comparing file copies

We study the problem of identifying corrupted pages between two remotely located copies of a file in a distributed system. An efficient deterministic algorithm is presented to identify up to any given number of differing pages. The algorithm requires a single exchange of messages and is based on the structure of the Reed-Solomon code. In order to identify up to f corrupted pages, 2f signatures are transmitted. The algorithm requires less communication costs than previously proposed solutions. In fact, we prove that our algorithm is optimal, in the sense that no other algorithm is guaranteed to identify with probability 1 the corrupted pages by exchanging less information