LPN(Learning Parity With Noise)问题是构造后量子密码方案的基础问题之一。基于LPN构造的密码方案具有计算速度快和抗量子计算攻击的优点，但基于普通LPN构造的密码方案存在密钥空间大这一影响其可用性的缺点。基于结构化的LPN（比如Ring-LPN、 Toepliz-LPN等）构造公钥密码可以降低存储要求，进一步提高方案的效率。因此，利用Ring-LPN的特有优势并结合标签加密构造技术，提出并证明了环上的背包问题，设计了一个基于Ring-LPN且CCA（Chosen-Ciphertext-Attacks）安全的公钥加密方案。与基于普通LPN的同类型密码方案相比较，所提出的方案以环多项式向量为公私钥，在计算上采取快速傅里叶变换，可以大幅提高加解密速率，因此方案具有更小的计算开销和存储开销；与达到相同安全级别的LPN方案相比，所需的样本数更少，密文扩展率更小。同时，方案的CCA安全性在标准模型下归约到了Ring-LPN假设。
The LPN problem is one of the basic problems to construct post-quantum cryptographic schemes, due to its simple operations and resistance to quantum attacks. However, large part of LPN based cryptographic schemes suffer from large key size which limits their availability. Fortunately, the structured LPN (such as Ring-LPN, Toepliz-LPN, etc.) based public-key cryptography can reduce storage requirements and further improve the efficiency. Therefore, we take advantage of the Ring-LPN and the tag-based encryption technology, propose and prove the knapsack problems on the ring, and then present a Ring-LPN based public key encryption scheme which is provably CCA secure. Concretely, our scheme has less computational cost and storage overhead when compared with those of previously proposed LPN based cryptographic schemes, fewer samples are required and ciphertext expansion rate are smaller than LPN based schemes which achieve the same security level. At the same time, the CCA security of the scheme is reduced to the Ring-LPN Assumption in the standard model.