A Certificateless Aggregate G+G Signature Scheme with Intersection Method for Efficiency Improvement in Smart Grids

Smart grids (SGs) can greatly improve the efficiency, reliability, and sustainability of traditional grids. In an industrial SG, real-time user-side metering data may be frequently collected for monitoring and controlling electricity consumption. To reduce the burden on SGs, most existing privacy-preserving schemes use aggregated signatures to ensure the integrity of the message and improve communication efficiency. In CRYPTO ’24, Marius et al. proposed an aggregating Falcon signature scheme LaBRADOR, which is a trapdoor-based lattice signature scheme. Currently, there are two types of lattice-based signature schemes: one is a trapdoor-based signature scheme, and the other is a Fiat-Shamir-based signature scheme. There is currently no particularly efficient Fiat-Shamir-based lattice-based aggregate signature scheme. Therefore, we construct an aggregate signature scheme with constant signature size without rejection sampling under the Fiat-Shamir style based on the G+G lattice signature (ASIACRYPT ’23) and the intersection method (EUROCRYPT ’11). In addition, we make our scheme certificateless to resist malicious key generation centers and the key escrow problem, and apply our scheme to SGs. Compared with other schemes, our signature scheme has a smaller aggregated signature size (any number of signatures), less signature time, and is more secure. Finally, we demonstrate that our scheme is existentially unforgeable in the context of adaptive chosen message attacks against type I and type II adversaries in the random oracle model.