Pre-computed Algebraic Signatures for Fast String Search, Protection Against Incidental Viewing and Corruption of Data in an SDDS

We propose to encode records of a Scalable Distributed Data Structure (SDDS) using precomputed algebraic signatures. The partly pre-computed algebraic signature of a string encodes each symbol into its contribution to the algebraic signature of the string. The cumulative pre-computed algebraic signature encodes each symbol with the signature of the string prefix ending with the symbol. The encoding/decoding according to either scheme occurs at the SDDS clients. For both schemes, and each operation, the overhead is of linear time complexity O (n). It is however slightly higher for the cumulative signature. The schemes protect the SDDS data against incidental viewing by an unauthorized server’s administrator. One may use them also to detect and localize the silent corruption. These features should be of interest to P2P and grid computing. Both schemes provide also fast string search (match) directly on encoded data at the SDDS servers. They appear an alternative to known Karp-Rabin type schemes in our context of a search in a file or a database. Both accelerate the string search with respect to the fast already use of the algebraic signatures on the original data. Moreover, both appear typically the fastest in the context, among any string search algorithms we are aware of. The cumulative signature provides the fastest searches. For the string of l symbols in a field of n symbols, the complexity is almost O (1) for prefix search, and O (n – l) for the string search. The string manipulation capabilities of our schemes should be by themselves of interest to applications.