Loidreau码基密码体制的两个改进
Two modifications for Loidreau's code-based cryptosystem
摘要：
本文对Loidreau的码基密码体制提出了两种改进。Loidreau密码系统是一种基于秩度量码的密码系统，它是在McEliece环境下利用Gabidulin码构造的。最近提出了一种多项式时间密钥恢复攻击，在某些情况下，打破Loidreau的密码系统。为了防止这种攻击，我们建议使用子码来伪装修改\Rmnum{1}中的秘密代码。在修改\Rmnum{2}中，我们选择一个比$\mathbb{F}_q$低列秩的随机矩阵与秘密矩阵混合。根据我们的分析，这两个修改都可以抵抗现有的结构攻击。此外，我们采用了系统的生成矩阵的公钥码，以减少公钥的大小。除了对结构攻击有更强的抵抗能力和更紧凑的公钥表示外，我们的修改还具有更大的信息传输速率。
英文摘要：
This paper presents two modifications for Loidreau's code-based cryptosystem. Loidreau's cryptosystem is a rank metric code-based cryptosystem constructed by using Gabidulin codes in the McEliece setting. Recently a polynomial-time key recovery attack was proposed to break Loidreau's cryptosystem in some cases. To prevent this attack, we propose the use of subcodes to disguise the secret codes in Modification \Rmnum{1}. In Modification \Rmnum{2}, we choose a random matrix of low column rank over $\mathbb{F}_q$ to mix with the secret matrix. According to our analysis, these two modifications can both resist the existing structural attacks. Additionally, we adopt the systematic generator matrix of the public code to make a reduction in the public-key size. In additon to stronger resistance against structural attacks and more compact representation of public keys, our modifications also have larger information transmission rates.
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