Paper 2024/1786 Original: eprint.iacr.org/2024/1786 ↗

Black-Box Timed Commitments from Time-Lock Puzzles

Abstract

A Timed Commitment (TC) with time parameter $t$ is hiding for time at most $t$, that is, commitments can be force-opened by any third party within time $t$. In addition to various cryptographic assumptions, the security of all known TC schemes relies on the sequentiality assumption of repeated squarings in hidden-order groups. The repeated squaring assumption is therefore a security bottleneck. In this work, we give a black-box construction of TCs from any time-lock puzzle (TLP) by additionally relying on one-way permutations and collision-resistant hashing. Currently, TLPs are known from (a) the specific repeated squaring assumption, (b) the general (necessary) assumption on the existence of worst-case non-parallelizing languages and indistinguishability obfuscation, and (c) any iteratively sequential function and the hardness of the circular small-secret LWE problem. The latter admits a plausibly post-quantum secure instantiation. Hence, thanks to the generality of our transform, we get i) the first TC whose timed security is based on the the existence of non-parallelizing languages and ii) the first TC that is plausibly post-quantum secure. We first define quasi publicly-verifiable TLPs (QPV-TLPs) and construct them from any standard TLP in a black-box manner without relying on any additional assumptions. Then, we devise a black-box commit-and-prove system to transform any QPV-TLPs into a TC.