Authenticating Spatial Queries on Blockchain Systems

In many blockchain networks, light nodes (e.g. mobile clients) with few computational resources must rely on more powerful full nodes to retrieve transactions from the chain. However, in this untrusted environment a malicious full node could deliver altered or incomplete information, requiring query authentication techniques to ensure the integrity of the results. To this aim, we study an authentication mechanism for spatial information (i.e. data representing the location, size, and shape of objects in a geographical coordinate system). We assume that light nodes issue range queries to obtain data from a single block. To enable authentication, we propose to construct a Merkle R-tree for each block and embed its root into the corresponding header, so that full nodes can exploit it to fetch information and construct a proof of integrity for lightweight clients. We also develop a new algorithm based on sorting and partitioning for constructing Merkle R-trees from a set of spatial transactions and employ space-filling curves to preserve the locality of elements. We examine its theoretical complexity, evaluate it experimentally on a real data set and compare it against other popular construction strategies. Results show that, as queries become more selective, trees generated with our solution improve query performance and reduce verification times with respect to other approaches. Moreover, we observe that the overhead induced by the tree construction is negligible if compared to the average inter-block time of popular blockchain protocols such as Bitcoin and Ethereum.