String commitment scheme with low output locality

Abstract

Commitment schemes are important tools for various protocols. However, no scheme with output locality have been proposed yet. Low output locality is a property of functions that every output bit to depend on a small number of input bits. In this paper, we construct a commitment scheme having low output locality from a modified lattice-based hash function for the first time. We also prove that our scheme satisfies the binding property by using the collision resistance of the lattice-based hash functions and the hiding property by using a modified version of the leftover hash lemma, respectively.