The lattice cryptosystem is considered to be able to resist the attacks of quantum computers. Lattice-based Public Key Encryption (PKE) schemes have attracted the interest of many researchers. In lattice-based cryptography, Learning With Errors (LWE) problem is a hard problem usually used to construct PKE scheme. To ensure the correctness of decryption, LWE-based schemes have a large ciphertext size. This makes these encryption schemes not practical enough when the communication bandwidth is limited. We propose a new variant of LWE, named Learning With Modulus (LWM) and prove that the new problem can be reduced from LWE problem. The proof idea of our reduction is similar to the reduction of LWR problem. We also construct a new PKE scheme based on the proposed LWM and LWE, which has small ciphertext size. For a 128 bits plaintext, the ciphertext size of our scheme is 53.57% of Lindner–Peikert’s (LP) scheme under the same security level. We use python to test the performance of our scheme. The results show that our scheme is only about 0.015 ms slower than LP in the decryption. The performance of our scheme for generating keys and encrypting messages is similar to LP.

晶格密码系统被认为能够抵抗量子计算机的攻击。基于格的公钥加密（PKE）方案吸引了许多研究人员的兴趣。在基于格的​​密码学中，带错误学习（LWE）问题是通常用于构造PKE方案的难题。为了确保解密的正确性，基于LWE的方案具有较大的密文大小。当通信带宽受到限制时，这使得这些加密方案不够实用。我们提出了一种LWE的新变种，称为学习模量（LWM），并证明可以从LWE问题中减少新问题。我们减少的证明思想类似于减少LWR问题。我们还基于拟议的LWM和LWE构建了一种新的PKE方案，该方案具有较小的密文大小。对于128位纯文本，在相同的安全级别下，我们的方案的密文大小为Lindner–Peikert（LP）方案的53.57％。我们使用python测试我们方案的性能。结果表明，我们的方案在解密方面仅比LP慢约0.015毫秒。我们用于生成密钥和加密消息的方案的性能类似于LP。