Bounds on the efficiency of black-box commitment schemes

Constructions of cryptographic primitives based on general assumptions (e.g., the existence of one-way functions) tend to be less efficient than constructions based on specific (e.g., number-theoretic) assumptions. This has prompted a recent line of research aimed at investigating the best possible efficiency of (black-box) constructions based on general assumptions. Here, we present bounds on the efficiency of statistically-binding commitment schemes constructed using black-box access to one-way permutations; our bounds are tight for the case of perfectly-binding schemes. We present the bounds in an extension of the Impagliazzo-Rudich model; that is, we show that any construction beating our bounds would imply the unconditional existence of a one-way function (from which a commitment scheme could be constructed “from scratch”). Our analysis is the first in the area to pertain directly to an information-theoretic component of the security notion.