Geodesic
Quasi-cyclic alternant codes and analysis of their security in cryptographic applications
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 147-152 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents an overview of quasi-cyclic alternant codes and their structural analysis regarding the classification of automorphisms. Also, we describe in detail methods for restoring the structure of a given code. The attractiveness of the family of considered codes lies in its 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 alternant codes of quasi-cyclic algebraic-geometric codes associated with an arbitrary curve with a known group of automorphisms. However, as shown in the work, 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.
Mots-clés : quasi-cyclic codes, alternant codes, invariant codes, automorphism group of a code.
Keywords: algebraic-geometric code, function fields 
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     title = {Quasi-cyclic alternant codes and analysis of their security in cryptographic applications},
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A. A. Kuninets. Quasi-cyclic alternant codes and analysis of their security in cryptographic applications. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 147-152. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a37/

[1] Barelli E., On the security of short McEliece keys from algebraic and algebraic geometry codes with automorphisms, University of Paris-Saclay, France, 2018 (in French)

[2] Kuninets A. A., Malygina E. S., “Vychislenie par, ispravlyayuschikh oshibki, dlya algebrogeometricheskogo koda”, Prikladnaya diskretnaya matematika, 2023, no. 63, 65–90 | MR

[3] Malygina E. S., Kuninets A. A., Ratochka V. L. i dr., “Algebrogeometricheskie kody i dekodirovanie na osnove par, ispravlyayuschikh oshibki”, Prikladnaya diskretnaya matematika, 2023, no. 62, 83–105 | MR

[4] Stichtenoth H., “On automorphisms of geometric Goppa codes”, J. Algebra, 130:1 (1990), 113–121 | DOI | MR | Zbl