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Code-Based Cryptography With Generalized Concatenated Codes for Restricted Error Values

  • Code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-ary codes lead to high error correction capabilities. Hence, these codes achieve high work factors for information set decoding attacks. In this work, we adapt this concept to codes for the weight-one error channel, i.e., a binary channel model where at most one bit-error occurs in each block of m bits. We also propose a low complexity decoding algorithm for the proposed codes. Compared to codes over Gaussian and Eisenstein integers, these codes achieve higher minimum Hamming distances for the dual codes of the inner component codes. This property increases the work factor for a structural attack on concatenated codes leading to higher overall security. For comparable security, the key size for the proposed code construction is significantly smaller than for the classic McEliece scheme based on Goppa codes.

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Metadaten
Author:Johann-Philipp ThiersORCiD, Jürgen FreudenbergerORCiDGND
URN:urn:nbn:de:bsz:kon4-opus4-32724
DOI:https://doi.org/10.1109/OJCOMS.2022.3206395
ISSN:2644-125X
Parent Title (English):IEEE Open Journal of the Communications Society
Volume:Vol. 3
Publisher:IEEE
Document Type:Article
Language:English
Year of Publication:2022
Release Date:2022/11/28
Tag:Code-based cryptography; Generalized concatenated codes; McEliece cryptosystem; Public-key cryptography; Restricted error values
First Page:1528
Last Page:1539
Note:
Corresponding author: Jürgen Freudenberger
Institutes:Institut für Systemdynamik - ISD
Open Access?:Ja
Relevance:Peer reviewed Publikation in Master Journal List
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International