Quantum Safe Lattice-Based Single Round Online Collaborative Multi-Signature Scheme for Blockchain-Enabled IoT Applications

Multi-signature protocols allow a group of signers to collectively generate a single signature for a shared message. In the context of a decentralized blockchain, multi-signature schemes play a pivotal role in reducing the signature size. Recently, several multi-signature methods have emerged in the literature, some operating in discrete-log settings and others in lattice settings. However, many of the existing lattice-based multi-signature schemes incur high computation costs and online round complexity. Traditional public key-based multi-signature schemes are susceptible to quantum threats, and they are computationally intensive as well. A lattice-based multi-signature can provide robust security, which often falls short in terms of efficiency when it comes to round complexity. In this article, we aim to introduce a single-round lattice-based multi-signature scheme specifically designed for decentralized public blockchains. What sets the proposed scheme apart is its ability to function without the need for trapdoor commitments or sample pre-images, which are common features in existing lattice-based signature methods. Furthermore, we explore some potential applications in a generic Internet of Things (IoT) environment and their integration of the proposed scheme with the blockchain technology. The security of the proposed scheme is based on lattice-hard problems, like Ring-SIS (Shortest Integer Solution) and Ring-LWE (Learning with Errors).