中文摘要：

在不降低安全性的情况下，对一种简单而高效的公钥密码算法的改进，通过利用矩阵变换的方法对其改进，使其困难性假设容易保证（矩阵一般构成环，且存在零元素，分析比较困难）、加密速度更快（一次可以处理多位）；通过把明文分为两部分后一部分添加2r个字节使其避免了原来随机K带来的格攻击，同时又增加了随机性使得原有方案更安全。并且基于此改进提出了一种签名算法，证明了该签名算法也是安全的。

英文摘要：

Without compromising safety in the case of a simple and efficient public key cryptography algorithm,, by using matrix transformation method for its improvement, making it difficult to ensure easy assumption （general matrix form a ring, and there is zero element analysis more difficult）, the encryption is faster （more than one can handle）, through the latter part of the plaintext is divided into two parts to avoid adding 2r byte random K brings the original lattice attack, while increasing the random original program makes safer. Based on this improved and proposed a signature algorithm proved that the signature algorithm is safe.