Computational bounds on hierarchical data processing with applications to information security

We introduce hierarchical data processing (HDP) problems, a class of computations over a collection of values associated with a set of n elements, based on a directed acyclic graph (DAG). We present an Ω(log n) lower bound on various computational cost measures for HDP problems and we develop an efficient randomized DAG scheme for HDP problems. We apply our results to data authentication through cryptographic hashing and multicast key distribution using key-graphs. We show that both problems involve HDP and prove logarithmic lower bounds on their computational and communication costs. Using our new DAG scheme, we present a new efficient authenticated dictionary and a new skip-list version with expected search complexity 1.25 log₂ n + O(1).