Masking-based domain extenders for UOWHFs: bounds and constructions

We study the class of masking-based domain extenders for universal one-way hash functions (UOWHFs). Our first contribution is to show that any correct masking-based domain extender for UOWHF which invokes the compression UOWHF s times must use at least lceillog₂srceil masks. As a consequence, we obtain the key expansion optimality of several known algorithms among the class of all masking-based domain extending algorithms. Our second contribution is to present a new parallel domain extender for UOWHF. The new algorithm achieves asymptotically optimal speedup over the sequential algorithm and the key expansion is almost everywhere optimal, i.e., it is optimal for almost all possible number of invocations of the compression UOWHF