Linearly Homomorphic Signature with Tight Security on Lattice

Constructing efficient, tightly secure short signature schemes based on lattices has remained a significant challenge in cryptographic theory. In their ASIACRYPT 2016 paper, Boyen and Li raised an open problem: how to construct a tightly or almost-tightly secure homomorphic signature scheme in the standard model under the Short Integer Solution (SIS) hardness assumption. Under the same assumption, this paper presents the first lattice-based short signature scheme that achieves adaptive security and provides a proof of its almost-tight security. Furthermore, the proposed scheme retains the potential to be further refined into a tightly secure signature scheme.