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ON THE PARAMETERS OF A McELIECE-TYPE CRYPTOSYSTEM ON D-CODES BASED ON BINARY REED — MULLER CODES

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Bibliographic Details
Title: ON THE PARAMETERS OF A McELIECE-TYPE CRYPTOSYSTEM ON D-CODES BASED ON BINARY REED — MULLER CODES
Authors: Yu. V. Kosolapov, E. A. Lelyuk
Source: Prikladnaya Diskretnaya Matematika. :7-35
Publisher Information: Tomsk State University, 2025.
Publication Year: 2025
Description: 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).
Document Type: Article
ISSN: 2311-2263
2071-0410
DOI: 10.17223/20710410/67/1
Accession Number: edsair.doi...........6d09ff0ff5bc28570d931d2a9751fe36
Database: OpenAIRE
Description
Abstract: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).
ISSN:23112263
20710410
DOI:10.17223/20710410/67/1