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.
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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).
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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.
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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
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DOI: https://doi.org/10.1007/s11227-026-08821-x
Facts Only
* Multi-party digital signatures are fundamental for trust in distributed systems.
* The scheme is based on a chain collaborative signing protocol using NTRU lattice cryptography.
* The protocol achieves linear communication complexity.
* A sequential chain propagation protocol replaces all-to-all broadcast with unidirectional neighbor interactions.
* Signers obtain an identity-based NTRU secret key via trapdoor sampling.
* A lightweight two-step verification process supports asynchronous third-party validation.
* The scheme is proven existentially unforgeable under chosen-message attacks in the random oracle model.
* Security relies on the hardness of the NTRU Shortest Vector Problem.
* The analysis shows linear scaling to thousands of participants with lower communication overhead than broadcast-based protocols.
* The scheme is suited for sequential authorization scenarios such as blockchain smart contracts, supply chain provenance, and IoT attestation chains.
Executive Summary
Full Take
The work successfully bridges the gap between multi-party authentication requirements and post-quantum cryptography by introducing a structure that optimizes communication efficiency through a chaining mechanism. The shift from broadcast to unidirectional neighbor interaction is a crucial structural decision, directly addressing the inherent inefficiency of previous protocols. The introduction of identity-based key management using trapdoor sampling manages the complexity of participant keys, which is essential for practical deployment in large systems. The mathematical guarantee of unforgeability under the random oracle model grounds the scheme in established lattice security, though this places a strong dependency on the assumed hardness of SVP for real-world trust. The implication is that complex distributed consensus and signing can be made feasible within resource-constrained, sequential environments, moving multi-party interaction from an exponential complexity problem to a linear one. The main pattern observed is the focus on architectural innovation—chaining—to achieve cryptographic goals rather than incremental algorithmic improvements alone.
What are the limitations of assuming the hardness of SVP remains sufficient for long-term quantum resistance against more advanced lattice attacks? How can the sequential nature of the chain protocol be leveraged to enhance resilience against denial-of-service attacks in a dynamic system setting? Does the focus on sequential scenarios inherently limit the applicability of this framework to fully concurrent, non-sequential multi-party tasks?