Paper 2021/921
Semilinear Transformations in Coding Theory: A New Technique in CodeBased Cryptography
Wenshuo Guo and FangWei Fu
Abstract
This paper presents a new technique for disturbing the algebraic structure of linear codes in codebased cryptography. Specifically, we introduce the socalled semilinear transformations in coding theory and then creatively apply them to the construction of codebased 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 as an $\mathbb{F}_q$linear automorphism of $\mathbb{F}_{q^m}$. Then we impose this transformation to a linear code $\mathcal{C}$ over $\mathbb{F}_{q^m}$. It is clear that $\varphi(\mathcal{C})$ forms an $\mathbb{F}_q$linear space, but generally does not preserve the $\mathbb{F}_{q^m}$linearity any longer. Inspired by this observation, a new technique for masking the structure of linear codes is developed in this paper. Meanwhile, we endow the underlying Gabidulin code with the socalled partial cyclic structure to reduce the publickey size. Compared to some other codebased cryptosystems, our proposal admits a much more compact representation of public keys. For instance, 2592 bytes are enough to achieve the security of 256 bits, almost 403 times smaller than that of Classic McEliece entering the third round of the NIST PQC project.
Metadata
 Available format(s)
  withdrawn 
 Category
 Publickey cryptography
 Publication info
 Published elsewhere. Major revision.https://arxiv.org/
 Keywords
 postquantum cryptographycodebased cryptography
 Contact author(s)
 ws_guo @ mail nankai edu cn
 History
 20211207: withdrawn
 20210709: received
 See all versions
 Short URL
 https://ia.cr/2021/921
 License

CC BY