Forward-Secure Linearly Homomorphic Signature Scheme in the Standard Model and Its Application

Linearly homomorphic signatures (LHSs) are widely used in scenarios such as network coding and the Internet of Things, but their security faces the serious threat of key leakage. To address this issue, this paper introduces a forward secure mechanism into LHSs, aiming to construct a linearly homomorphic signature (LHS) scheme that can resist the risk of key leakage. By combining the binary tree minimal cover set mechanism with lattice-based extension algorithms, we construct an LHS scheme that supports time-period key updates. We prove its forward secure unforgeability under the standard model (SM) by reducing it to the Short Integer Solution (SIS) problem. To the best of our knowledge, this scheme is the first provably secure lattice-based forward secure linearly homomorphic signature (FSLHS) scheme in the SM, filling a theoretical gap in existing research. Furthermore, we apply this scheme to a smart grid data acquisition system and verify its practicality through concrete performance analysis.