Linearly Homomorphic Signature with Tight Security on Lattice

TL;DR

This paper presents a new security model and constructs a linearly homomorphic signature scheme with tight security in the standard model, advancing cryptographic security guarantees based on lattice assumptions.

Contribution

It introduces a novel security model and achieves the first tight security construction of a homomorphic signature scheme under lattice assumptions in the standard model.

Findings

First tight security scheme under lattice assumptions in the standard model

New security model weaker than standard but stronger than previous work

Achieves almost-tight security in 2024

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.