Geodesic
On the parameters of a McEliece-type cryptosystem on~$D$-codes based on binary Reed~--- Muller codes
Prikladnaâ diskretnaâ matematika, no. 1 (2025), pp. 7-35

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The characteristics of a McEliece-type code cryptosystem on a special sum of tensor products of base codes, called $D$-code, are investigated. Binary Reed — Muller codes were chosen as the base codes. Previously, conditions were found for these $D$-codes, under which the corresponding cryptosystem is resistant to known structural attacks based on the Schur — Hadamard product. However, when using a decoder operating within half the code distance, a McEliece-type system on $D$-codes provides security comparable to the strength of the classical McEliece cryptosystem on Goppa codes, with a significantly larger key size. In this paper, two probabilistic decoders for $D$-codes are constructed. In the case of using these decoders, parameters of some $D$-codes have been found that provide comparable resistance to information set decoding type attacks, while having a smaller key size than in the classical system. However, the presence of a non-negligible decoding failure rate currently limits the scope of application of the $D$-code cryptosystem to ephemeral session key encapsulation mechanisms (IND-CPA KEM).
Mots-clés : $D$-codes
Keywords: McEliece scheme, key encapsulation mechanism. 
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     author = {Yu. V. Kosolapov and E. A. Lelyuk},
     title = {On the parameters of a {McEliece-type} cryptosystem on~$D$-codes based on binary {Reed~---} {Muller} codes},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {7--35},
     publisher = {mathdoc},
     number = {1},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2025_1_a1/}
}
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Yu. V. Kosolapov; E. A. Lelyuk. On the parameters of a McEliece-type cryptosystem on~$D$-codes based on binary Reed~--- Muller codes. Prikladnaâ diskretnaâ matematika, no. 1 (2025), pp. 7-35. http://geodesic.mathdoc.fr/item/PDM_2025_1_a1/