Verifiable Homomorphic Linear Combinations in Multi-Instance Time-Lock Puzzles

TL;DR

This paper introduces new multi-instance time-lock puzzles supporting verifiable homomorphic linear combinations, enabling efficient, scalable, and trustless computation verification across multiple clients and puzzles.

Contribution

The paper presents MH-TLP and MMH-TLP schemes that support verifiable homomorphic linear combinations without relying on asymmetric cryptography or trusted third parties.

Findings

Schemes support efficient verifiable homomorphic linear combinations.

Scalability scales linearly with number of clients and puzzles.

No need for trusted third parties or asymmetric cryptography.

Abstract

Time-Lock Puzzles (TLPs) have been developed to securely transmit sensitive information into the future without relying on a trusted third party. Multi-instance TLP is a scalable variant of TLP that enables a server to efficiently find solutions to different puzzles provided by a client at once. Nevertheless, existing multi-instance TLPs lack support for (verifiable) homomorphic computation. To address this limitation, we introduce the "Multi-Instance partially Homomorphic TLP" (MH-TLP), a multi-instance TLP supporting efficient verifiable homomorphic linear combinations of puzzles belonging to a client. It ensures anyone can verify the correctness of computations and solutions. Building on MH-TLP, we further propose the "Multi-instance Multi-client verifiable partially Homomorphic TLP" (MMH-TLP). It not only supports all the features of MH-TLP but also allows for verifiable homomorphic linear combinations of puzzles from different clients. Our schemes refrain from using asymmetric-key cryptography for verification and, unlike most homomorphic TLPs, do not require a trusted third party. A comprehensive cost analysis demonstrates that our schemes scale linearly with the number of clients and puzzles.