Due to the weakness of public key cryptosystems encounter of quantum computers, the need to provide a solution was emerged. The McEliece cryptosystem and its security equivalent, the Niederreiter cryptosystem, which are based on Goppa codes, are one of the solutions, but they are not practical due to their long key length. Several prior attempts to decrease the length of the public key in code-based cryptosystems involved substituting the Goppa code family with other code families. However, these efforts ultimately proved to be insecure. In 2016, the National Institute of Standards and Technology (NIST) called for proposals from around the world to standardize post-quantum cryptography (PQC) schemes to solve this issue. After receiving of various proposals in this field, the Classic McEliece cryptosystem, as well as the Hamming Quasi-Cyclic (HQC) and Bit Flipping Key Encapsulation (BIKE), chosen as code-based encryption category cryptosystems that successfully progressed to the final stage. This article proposes a method for developing a code-based public key cryptography scheme that is both simple and implementable. The proposed scheme has a much shorter public key length compared to the NIST finalist cryptosystems. The key length for the primary parameters of the McEliece cryptosystem (n=1024, k=524, t=50) ranges from 18 to 500 bits. The security of this system is at least as strong as the security of the Niederreiter cryptosystem. The proposed structure is based on the Niederreiter cryptosystem which exhibits a set of highly advantageous properties that make it a suitable candidate for implementation in all extant systems.

翻译：鉴于量子计算机对公钥密码系统构成的威胁，亟需提供一种解决方案。基于Goppa码的McEliece密码系统及其安全等价体Niederreiter密码系统是候选方案之一，但其密钥长度过长导致实用性不足。早期为缩短基于编码密码系统公钥长度所做的尝试中，曾用其他编码族替代Goppa码族，但这些努力最终被证明存在安全隐患。2016年，美国国家标准与技术研究院（NIST）面向全球征集后量子密码（PQC）方案标准化提案。在收到该领域多份提案后，Classic McEliece密码系统、汉明准循环（HQC）以及比特翻转密钥封装（BIKE）作为基于编码的加密类密码系统成功进入最终轮次。本文提出一种兼具简洁性与可实现性的基于编码的公钥密码系统构建方法。与NIST决赛轮密码系统相比，所提方案具有更短的公钥长度。针对McEliece密码系统的主参数（n=1024, k=524, t=50），其密钥长度范围仅为18至500比特。该系统的安全性至少与Niederreiter密码系统相当。本方案基于Niederreiter密码系统构建，具备一系列显著优势特性，使其适合部署于现有所有系统。