A bimodal lattice-based linearly homomorphic signature for chain-based implicit data storage scheme

As the demand for cross-domain collaborative verification grows in fields such as healthcare and industrial Internet of Things, achieving secure and efficient verification of heterogeneous data has become a critical challenge. Traditional linear homomorphic signature schemes face a dilemma: if multi-modal data is merged into a single signature, although the integrity is preserved, it leads to inefficiencies as the entire dataset must be reconstructed and re-signed upon local updates, making it susceptible to padding rule attacks; if signed independently, the cross-domain logical associations are disrupted, allowing attackers to conduct combinatorial fraud by substituting signatures from individual domains. To address these challenges, this paper proposes an innovative solution. Firstly, based on the lattice intersection method and the Chinese Remainder Theorem, a Bimodal Linearly Homomorphic Signature Scheme (BLHS) is designed: by constructing a bimodal lattice structure using coprime moduli, two types of heterogeneous data are embedded into interlocked algebraic spaces, generating short signatures that satisfy cross-domain constraints. The security of this scheme is reduced to the computational hardness of the Short Integer Solution (SIS) problem, strictly proving its unforgeability, and achieving weak context hiding to ensure the privacy of original data during linear combination operations. Secondly, with the rapid development of distributed technologies such as the Internet of Things and blockchain, the long-term storage of massive amounts of interrelated data faces dual challenges of space efficiency and cross-domain verification. Traditional data storage methods exhibit linear growth in storage overhead with respect to data length. To address the space efficiency bottleneck in long-term data storage, based on the proposed BLHS scheme, a Chain-based Implicit Data Storage Scheme (CIDSS) is introduced. The core idea of this scheme is to compress a data sequence into a single end signature for storage through chain-based recursive binding and implicit encoding, thereby achieving constant-level space complexity. The term "chain-based" refers to the use of NTRU equations over polynomial rings to recursively bind the current signature to the generation process of subsequent data blocks, forming an unforgeable dependency chain. The term "implicit" refers to storing only the end signature and recovering the complete historical data layer by layer through reverse solving of the NTRU equation. Theoretical analysis indicates that the scheme trades computational burden for storage efficiency, reducing the traditional explicit storage's O(k) space overhead to a constant level, making it suitable for long-term data archiving and verification scenarios in resource-constrained environments.