At present, in lattice-based linearly homomorphic signature schemes, especially under the standard model, there are very few schemes with tight security. This paper constructs the first lattice-based linearly homomorphic signature scheme that achieves tight security against existential unforgeability under chosen-message attacks (EUF-CMA) in the standard model. Furthermore, among existing schemes, the scheme proposed in this paper also offers certain advantages in terms of public key size, signature length, and computational cost.

翻译：目前，在基于格的线性同态签名方案中，尤其是在标准模型下，具有紧致安全的方案非常少。本文构造了首个在标准模型下能够针对选择消息攻击下的存在性不可伪造性（EUF-CMA）达成紧致安全的基于格的线性同态签名方案。此外，在现有方案中，本文所提方案在公钥大小、签名长度和计算成本方面也具有一定的优势。