In this paper, we design a new lattice-based linearly homomorphic signature scheme over . The existing schemes are all constructed based on hash-and-sign lattice-based signature framework, where the implementation of preimage sampling function is Gaussian sampling, and the use of trapdoor basis needs a larger dimension . Hence, they cannot resist potential side-channel attacks and have larger sizes of public key and signature. Under Fiat–Shamir with aborting signature framework and general SIS problem restricted condition , we use uniform sampling of filtering technology to design the scheme, and then, our scheme has a smaller public key size and signature size than the existing schemes and it can resist side-channel attacks.

中文翻译：

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上基于格的线性同态签名方案

在本文中，我们设计了一种基于的新的基于格的线性同态签名方案。现有方案都是基于基于哈希和符号格的签名框架构建的，其中原像采样功能的实现是高斯采样，而陷门的使用需要更大的维度。。因此，它们无法抵抗潜在的边信道攻击，并且具有更大的公共密钥和签名。在菲亚特-沙米尔（Fiat–Shamir）下具有中止签名框架和常规SIS问题受限条件的情况，我们使用统一的过滤技术采样来设计该方案，然后，与现有方案相比，该方案的公钥大小和签名大小较小，并且可以抵抗边信道攻击。