Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a partition requires further work. Whereas prior presentations of this approach focus on specific fingerprinting schemes for specific use-cases, we give a more generic description and analysis in the broader context of set reconciliation. Precisely capturing the design space for fingerprinting schemes allows us to survey for cryptographically secure schemes. Furthermore, we reduce the time complexity of local computations by a logarithmic factor compared to previous publications.