Third-party grid-data integrity verification

In the third-party model for the distribution of data, the trusted data creator or owner provides an untrusted distributor D with integrity verification (IV ) items that are stored at D in addition to the data itself. When a user U requests data from D, the user is provided by D with that data and a (hopefully small) number of IV items that make it possible for U to verify the integrity of the data received. Most of the published work in this area uses the Merkle tree or variants thereof. For the problem of 2-dimensional range queries, the best published solutions require D to store O(n log n) IV items for a database of n items, and allow a user U to be sent only O(log n) of those IV s for the purpose of verifying the integrity of the data it receives from D (regardless of the size of U's query rectangle). For data that is modeled as a 2-dimensional grid (such as GIS and image data), this paper shows that better bounds are possible: The number of IV s stored at D (and the time it takes to compute them) can be brought down to O(n), and the number of IV s sent to U for verification can be brought down to practically a constant. More precisely, for data modeled as an m x m2-dimensional grid of n = m2 cells, and with requests from users taking the form of arbitrary rectangular ranges, our solution stores O(n) IV items (generated in O(n) time) at D and requires only O(log(log* n)) IV items to be provided to U for the verification of its rectangular range; this is essentially constant because log(log* n) is less than 2 even for huge values of n. Moreover, in our scheme, D can find these IV items also in O(log(log* n)) (hence practically constant) time.