Authenticated dictionaries allow users to send lookup requests to an untrusted server and get authenticated answers. Persistent authenticated dictionaries (PADs) add queries against historical versions. We consider a variety of different trust models for PADs and we present several extensions, including support for aggregation and a rich query language, as well as hiding information about the order in which PADs were constructed. We consider variations on treelike data structures as well as a design that improves efficiency by speculative future predictions. We improve on prior constructions and feature two designs that can authenticate historical queries with constant storage per update and several designs that can return constant-sized authentication results.

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Authenticated dictionaries are a widely discussed paradigm to enable verifiable integrity for data storage on untrusted servers, such as today’s widely used “cloud computing ” resources, allowing a server to provide a “proof, ” typically in the form of a slice through a cryptographic data structure, that the results of any given query are the correct answer, including that the absence of a query result is correct. Persistent authenticated dictionaries (PADs) further allow queries against older versions of the structure. This research presents implementations of a variety of different PAD algorithms, some based on Merkle tree-style data structures and others based on individually signed “tuple ” statements (with and without RSA accumulators). We present system throughput benchmarks, presenting costs in terms of time, storage, and bandwidth as well as considering how much money would be required given standard cloud computing costs. We conclude that Merkle tree PADs are preferable in cases with frequent updates, while tuple-based PADs are preferable with higher query rates. For Merkle tree PADs, red-black trees outperform treaps and skiplists. Applying Sarnak-Tarjan’s versioned node strategy, with a cache of old hashes at every node, to red-black trees yields the fastest Merkle tree PAD implementation, notably using half the memory of the more commonly used applicative path copying strategy. For tuple PADs, although we designed and implemented an algorithm using RSA accumulators that offers constant update size, constant storage per update, constant proof size, and sublinear computation per update, we found that RSA accumulators are so expensive that they are never worthwhile. We find that other optimizations in the literature for tuple PADs are more cost-effective.

When distributed clients query or update shared data, eventual consistency can provide better availability than strong consistency models. However, programming and implementing such systems can be difficult unless we establish a reasonable consistency model, i.e. some minimal guarantees that programmers can understand and systems can provide effectively. To this end, we propose a novel consistency model based on eventually consistent transactions. Unlike serializable transactions, eventually consistent transactions are ordered by two order relations (visibility and arbitration) rather than a single order relation. To demonstrate that eventually consistent transactions can be effectively implemented, we establish a handful of simple operational rules for managing replicas, versions and updates, based on graphs called revision diagrams. We prove that these rules are sufficient to guarantee correct implementation of eventually consistent transactions. Finally, we present two operational models (single server and server pool) of systems that provide eventually consistent transactions. 1.

We present I/O-efficient fully persistent B-Trees that support range searches at any version in O(logB n + t/B) I/Os and updates at any version in O(logB n + log2 B) amortized I/Os, using space O(m/B) disk blocks. By n we denote the number of elements in the accessed version, by m the total number of updates, by t the size of the query’s output, and by B the disk block size. The result improves the previous fully persistent B-Trees of Lanka and Mays by a factor of O(logB m) for the range query complexity and O(logB n) for the update complexity. To achieve the result, we first present a new B-Tree implementation that supports searches and updates in O(logB n) I/Os, using O(n/B) blocks of space. Moreover, every update makes in the worst case a constant number of modifications to the data structure. We make these B-Trees fully persistent using an I/O-efficient method for full persistence that is inspired by the nodesplitting method of Driscoll et al. The method we present is interesting in its own right and can be applied to any external memory pointer based data structure with maximum in-degree din bounded by a constant and out-degree bounded by O(B), where every node occupies a constant number of blocks on disk. The I/O-overhead per modification to the ephemeral structure is O(din log2 B) amortized I/Os, and the space overhead is O(din/B) amortized blocks. Access to a field of an ephemeral block is supported in O(log2 din) worst case I/Os. 1