Oblivious data structures: applications to cryptography

We introduce the notion of oblivious data structure, motivated by the use of data structuresin cryptography. Informally, an oblivious data structure yields no knowledge about the sequence of operations that have been applied to it other than the final result of the operations. In particular we define Oblivious Tree, a data structure very similar to 2-3 Tree, but with the additional property that the only information conveyed by an Oblivious Tree is the set of values stored at its leaves. This property is achieved through the use of randomization by the update algorithms. We use the Oblivious Tree data structure to solve the privacy problem for incremental digital signatures raised by Bellare, Goldreich and Goldwasser. An incremental signing algorithm is private if the digital signature it outputs does not give any information on the sequence of edit operations that have been applied to produce the final document. We show how the incremental signature scheme of Bellare, Goldreich and Goldwassercan be made achieve privacy using Oblivious Trees instead of 2-3 Trees.