改进的基于奇偶校验码的McEliece变型方案

McEliece公钥加密体制是基于编码理论的公钥密码体制，其安全性可以归约到一般线性码译码问题，可以抵抗量子攻击。提出了一种改进的基于准循环中密度奇偶校验（QC-MDPC）码和准循环低密度奇偶校验（QC-LDPC）码的McEliece变型方案。主要改进是将QC-LDPC码和QC-MDPC码的奇偶校验矩阵结合作为私钥，生成两者的级联码字应用于McEliece变型方案，并且给出了改进的译码算法。分析表明在80 bit安全参数下该体制密钥量小且实现的复杂度低，能抵抗最近提出的分别针对QC-MDPC和QC-LDPC体制的密钥恢复攻击。

Improved McEliece variant scheme based on parity-check codes

McEliece public-key crypto system is a public-key cryptosystem based on coding theory. Its security can be reduced to the general linear code decoding problem and it can resist quantum attack. This paper proposed an improved Mc-Eliece variant scheme based on quasi-cyclic medium density parity check(QC-MDPC) code and quasi-cyclic low density parity check(QC-LDPC) code. The main improvement was that it combined the parity check matrices of QC-LDPC code and QC- MDPC code as a private key, and applied the concatenated codewords generated to the McEliece variant scheme, then gave an improved decoding algorithm. The analysis shows that under the 80 bit security parameter, it has small system key and low-implement complexity. In addition, this system can resist the recently proposed key recovery attacks on QC-MDPC and QC-LDPC respectively.