The paper presents an overview of quasi-cyclic alternant codes and their structural analysis regarding the classification of automorphisms. We also have detailed methods for recovering the structure of a given code. The attractiveness of the family of considered codes lies in their cryptographic applications and, as in theory, in reducing the key length of post-quantum code-based schemes. In addition, this method of constructing codes is universal and can be used to obtain subfield subcodes of quasicyclic algebraic-geometric codes associated with an arbitrary curve with a known group of automorphisms. However, as a result of constructing quasi-cyclic alternant codes, it becomes possible to reduce the key security of the source code to a code with smaller parameters, which may not be resistant to a structural attack.
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- Title Construction of quasi-cyclic alternant codes and their application in code-based cryptography
- Headline Construction of quasi-cyclic alternant codes and their application in code-based cryptography
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 65
- Date:
- DOI 10.17223/20710410/65/5
Keywords
quasi-cyclic codes, alternant codes, invariant codes, algebraic-geometric code, function fields, automorphism group of a codeAuthors
References
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Construction of quasi-cyclic alternant codes and their application in code-based cryptography | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2024. № 65. DOI: 10.17223/20710410/65/5
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