In this paper, we put forward a brand-new idea of masking the algebraic structure of linear codes used in code-based cryptography. Specially, we introduce the so-called semilinear transformations in coding theory, make a thorough study on their algebraic properties and then creatively apply them to the construction of code-based cryptosystems. Note that $\mathbb{F}_{q^m}$ can be viewed as an $\mathbb{F}_q$-linear space of dimension $m$, a semilinear transformation $\varphi$ is therefore defined to be an $\mathbb{F}_q$-linear transformation over $\mathbb{F}_{q^m}$. Then we impose this transformation to a linear code $\mathcal{C}$ over $\mathbb{F}_{q^m}$. Apparently $\varphi(\mathcal{C})$ forms an $\mathbb{F}_q$-linear space, but generally does not preserve the $\mathbb{F}_{q^m}$-linearity according to our analysis. Inspired by this observation, a new technique for masking the structure of linear codes is developed in this paper. Meanwhile, we endow the secret code with the so-called partial cyclic structure to make a reduction in public-key size. Compared to some other code-based cryptosystems, our proposal admits a much more compact representation of public keys. For instance, 1058 bytes are enough to reach the security of 256 bits, almost 1000 times smaller than that of the Classic McEliece entering the third round of the NIST PQC project.

翻译：在本文中, 我们提出了一个全新的概念, 遮盖代码加密中所用线性代码的代数结构的代数结构。 特别是, 我们引入了所谓的半线性变换, 对其代数属性进行彻底研究, 然后创造性地将其应用到基于代码的代数加密系统的构建中。 请注意, $\ mathbb{ F ⁇ q}$ 可以被看成一个$\ mathb{ F ⁇ q$- 线性空间, 以基于代码的代数表示 $_ mom, 一个半线性变换 $\ varphie 。 因此, 定义半线性变换 $\ mathb{ F ⁇ q$ $- 线性变换一个$\ mindline yalal 转换 。 然后, 我们将这种变换成基于代码的线性代码 $\mathbbb{F\\\ } $ 。 。 Q\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\