Practical NTRU lattice

Abstract Multi-party digital signatures are fundamental for trust in distributed systems, yet existing solutions suffer from quadratic communication overhead and vulnerability to quantum attacks. This paper presents a practical chain collaborative signing scheme based on NTRU lattice cryptography that achieves linear communication complexity and post-quantum security. The core innovation is a sequential chain propagation protocol that replaces all-to-all broadcast with unidirectional neighbor interactions. Each signer obtains an identity-based NTRU secret key via trapdoor sampling, enabling efficient authentication with minimal storage. A lightweight two-step verification process supports asynchronous third-party validation. The scheme is proved existentially unforgeable under chosen-message attacks in the random oracle model, assuming the hardness of the NTRU Shortest Vector Problem. Extensive theoretical analysis shows linear scaling to thousands of participants with significantly lower communication overhead than broadcast-based protocols. The scheme is particularly suited for sequential authorization scenarios such as blockchain smart contracts, supply chain provenance, and IoT attestation chains. This work bridges the gap between multi-party authentication and post-quantum cryptography by introducing a chain protocol that simultaneously achieves linear message growth, identity-based key management, and provable existential unforgeability, providing a practical solution for resource-constrained environments requiring ordered collaborative signing. Data Availability No datasets were generated or analysed during the current study. References Li X, Wang H, Chen J, Li S, Sun Y, Su Y (2023) Secure multi-party SM2 signature based on SPDZ protocol. 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IEEE Trans Dependable Secur Comput 22(4):4189–4199. https://doi.org/10.1109/TDSC.2025.3543425 Funding This work was supported by the 2025 China Telecom Quantum Group Collaborative Signature Research and Development Project (grant no. 25VZV1YF5019-001) and by 2025 China Telecom Quantum Group Hardware Technology Department Quantum-Resistant Chip R&D Technology Development Project (grant no. 25VZV1YF5037-001). Author information Authors and Affiliations Contributions Y.L., M.H. and F.L. wrote the main manuscript text, M.H. and C.X. prepared figures and tables. All authors reviewed the manuscript. Corresponding author Ethics declarations Conflict of interest The authors declare no conflict of interest. Ethics approval Not applicable. Additional information Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Rights and permissions Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. About this article Cite this article Li, Y., Huang, M., Long, F. et al. Practical NTRU lattice-based chain collaborative signing scheme. J Supercomput 82, 689 (2026). https://doi.org/10.1007/s11227-026-08821-x Received: Accepted: Published: Version of record: DOI: https://doi.org/10.1007/s11227-026-08821-x