Topological Lattice Signatures for IoV: Graphic Groups Meets Traceable Ring Schemes

Liao et al. (2023) use lattice-based ring signatures for IoV privacy, while Zhao et al. (2023) propose graphic lattices for asymmetric topology cryptography. This research combines both: vehicle network topologies are encoded as graphic lattices, where ring signatures are generated over their algebraic structure. Traceability emerges from lattice isomorphism checks (e.g., comparing sublattice invariants), avoiding Liao’s "additional information" overhead. The approach could leverage well-rounded lattices (Bastos et al., 2025) for efficient key generation. Unlike conventional schemes, this integrates network topology directly into cryptographic primitives, enabling context-aware security (e.g., detecting rogue nodes via lattice distortion). Impact: A novel IoV security framework where physical topology and cryptographic guarantees are mathematically intertwined.

References:

1. Traceable Ring Signature Scheme in Internet of Vehicles Based on Lattice Cryptography. Wei Liao, Lansheng Han, Peng Chen (2023). 2023 IEEE Intl Conf on Parallel & Distributed Processing with Applications, Big Data & Cloud Computing, Sustainable Computing & Communications, Social Computing & Networking (ISPA/BDCloud/SocialCom/SustainCom).
2. Well-rounded lattices from odd prime degree number fields in the ramified case. Jefferson Luiz Rocha Bastos, Robson Ricardo de Araujo, Trajano Pires da N'obrega Neto, Antonio Aparecido de Andrade (2025). Advances in Geometry.
3. Graphic Groups, Graph Homomorphisms, and Graphic Group Lattices in Asymmetric Topology Cryptography. Meimei Zhao, Hongyu Wang, B. Yao (2023). Entropy.