Linearly Homomorphic Signature with Tight Security on Lattice
Abstract
Constructing cryptographic schemes with tight or almost-tight security has long been one of the central problems in theoretical cryptography. At ASIACRYPT 2016, Boyen and Li posed an open problem: whether it is possible to construct a homomorphic signature scheme with tight or almost-tight security under the Short Integer Solution (SIS) assumption in the standard model. In 2024, Chen achieved the first construction with almost-tight security under a weaker security model. To further achieve tight security in the standard model, this paper introduces a new security model whose security requirements are weaker than those of the standard adaptive model but stronger than the model adopted by Chen. Under this model, we construct a linearly homomorphic signature scheme with tight security.
Keywords
Cite
@article{arxiv.2412.01641,
title = {Linearly Homomorphic Signature with Tight Security on Lattice},
author = {Heng Guo and Fengxia Liu and Kun Tian and Zhiyong Zheng},
journal= {arXiv preprint arXiv:2412.01641},
year = {2026}
}
Comments
30pages, research article