On the Cost of Authenticated Data Structures

Authenticated data structures provide a model for data authentication, where answers to queries contain extra information that can produce a cryptographic proof about their validity. In this paper, we study the authentication cost that is associated with this model when authentication is performed through hierarchical cryptographic hashing. We introduce measures that precisely model the computational overhead that is introduced due to authentication. We study the theoretical limitations of the model for authenticated structures that solve the dictionary problem of size n and prove (i) an intrinsic equivalence between authentication through hashing and searching by comparison, (ii) a Ω(log n) lower bound for the authentication cost and (iii) the optimality of tree structures. In view of the logarithmic lower bound, we (i) analyze and study the performance of existing authenticated structures with O(log n) authentication cost and (ii) describe a new authentication scheme based on skip-lists that achieves a performance very close to the theoretically optimal. Through the relation between authentication cost and number of comparisons, we finally get a new skip list version achieving expected performance that is very close to the theoretically optimal with respect to the logarithmic constant. Namely, a search operation takes on average 1.25 log 2 n + O(1) comparisons, which must be compared with the 1.5 log 2 n + O(1) previous best scheme.