A Multi-trapdoor Commitment Scheme from the RSA Assumption

Abstract

Gennaro introduced the notion of multi-trapdoor commitments which is a stronger form of trapdoor commitment schemes at CRYPTO 2004. Multi-trapdoor commitments have several cryptographic applications. For example, Gennaro proposed a conversion that makes a non-interactive multi-trapdoor commitment scheme into a non- interactive and reusable non-malleable commitment scheme and a compiler that transforms any proof of knowledge into concurrently non-malleable one. Gennaro gave constructions of multi-trapdoor commitments, but they rely on stronger assumptions, such as the strong RSA assumption, the q-strong Diffie-Hellman assumption.In this paper, we propose a non-interactive multi-trapdoor commitment scheme from the standard RSA assumption. Thus, as a corollary of our result, we obtain a non-interactive and reusable non-malleable commitment scheme from the standard RSA assumption. Our scheme is based on the Hohenberger-Waters signature scheme proposed at CRYPTO 2009. Several non-interactive and reusable non-malleable commitment schemes (in the common reference string model) have been proposed, but all of them rely on stronger assumptions (e.g., strong RSA).