Efficient Distributed Third-Party Data Authentication for Tree Hierarchies

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 n data items. When a user U has a subset of n´ of those n data items and needs to verify their integrity, U is provided by D with a number of IV items that U uses to verify its data´s integrity. The model forbids U from receiving any information about the n-n´ data items that the user is not authorized to access, and assumes that D has no signature authority (it stores only pre-signed IVs). Most of the published work in this area uses the Merkle tree or variants thereof, and typically requires D to store a linear or close to linear (in n) number s(n) of IV items that are pre-signed by the trusted authority. Moreover, most of the existing schemes impose on D a non-constant amount of computation work t(n) (typically logarithmic in n) in order to provide U with the IV items that enable U to verify the integrity of its data; we call h(n) the number of such IV items. The h(n) values found in the literature are non-constant, i.e., they actually do depend on the number of data items. The main contribution of this paper is to achieve linear s(n), constant h(n) and constant or logarithmic t(n) when the n data items are organized in a tree hierarchy T, and the user´s subset of n´ items form a subtree T´. The cases of T´ considered are when T´ is (i) rooted at a node v and of depth k below v; and (ii) reachable in k hops from v going both up and down in T.