Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Cryptography |
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| Online Access: | https://www.mdpi.com/2410-387X/5/4/33 |
| _version_ | 1827673276128690176 |
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| author | Johann-Philipp Thiers Jürgen Freudenberger |
| author_facet | Johann-Philipp Thiers Jürgen Freudenberger |
| author_sort | Johann-Philipp Thiers |
| collection | DOAJ |
| description | The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes. |
| first_indexed | 2024-03-10T04:21:50Z |
| format | Article |
| id | doaj.art-5614071f74e247adae86ca3d32321c60 |
| institution | Directory Open Access Journal |
| issn | 2410-387X |
| language | English |
| last_indexed | 2024-03-10T04:21:50Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Cryptography |
| spelling | doaj.art-5614071f74e247adae86ca3d32321c602023-11-23T07:47:40ZengMDPI AGCryptography2410-387X2021-11-01543310.3390/cryptography5040033Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based CryptographyJohann-Philipp Thiers0Jürgen Freudenberger1Institute for System Dynamics (ISD), HTWG Konstanz, University of Applied Sciences, 78462 Konstanz, GermanyInstitute for System Dynamics (ISD), HTWG Konstanz, University of Applied Sciences, 78462 Konstanz, GermanyThe code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.https://www.mdpi.com/2410-387X/5/4/33public-key cryptographyMcEliece cryptosystemNiederreiter cryptosystemmaximum distance separable codesconcatenated codes |
| spellingShingle | Johann-Philipp Thiers Jürgen Freudenberger Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography Cryptography public-key cryptography McEliece cryptosystem Niederreiter cryptosystem maximum distance separable codes concatenated codes |
| title | Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography |
| title_full | Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography |
| title_fullStr | Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography |
| title_full_unstemmed | Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography |
| title_short | Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography |
| title_sort | generalized concatenated codes over gaussian and eisenstein integers for code based cryptography |
| topic | public-key cryptography McEliece cryptosystem Niederreiter cryptosystem maximum distance separable codes concatenated codes |
| url | https://www.mdpi.com/2410-387X/5/4/33 |
| work_keys_str_mv | AT johannphilippthiers generalizedconcatenatedcodesovergaussianandeisensteinintegersforcodebasedcryptography AT jurgenfreudenberger generalizedconcatenatedcodesovergaussianandeisensteinintegersforcodebasedcryptography |