Low-rank parity-check codes over Galois rings
Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain fi...
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Gespeichert in:
| Autor*in: |
Renner, Julian [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Designs, codes and cryptography - Springer US, 1991, 89(2020), 2 vom: 13. Dez., Seite 351-386 |
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| Übergeordnetes Werk: |
volume:89 ; year:2020 ; number:2 ; day:13 ; month:12 ; pages:351-386 |
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| DOI / URN: |
10.1007/s10623-020-00825-9 |
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| 520 | |a Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. | ||
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10.1007/s10623-020-00825-9 doi (DE-627)OLC2123459984 (DE-He213)s10623-020-00825-9-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Renner, Julian verfasserin aut Low-rank parity-check codes over Galois rings 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. Galois rings Low-rank parity-check codes Rank-metric codes Algebraic coding theory Neri, Alessandro (orcid)0000-0002-2020-1040 aut Puchinger, Sven aut Enthalten in Designs, codes and cryptography Springer US, 1991 89(2020), 2 vom: 13. Dez., Seite 351-386 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:89 year:2020 number:2 day:13 month:12 pages:351-386 https://doi.org/10.1007/s10623-020-00825-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 89 2020 2 13 12 351-386 |
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10.1007/s10623-020-00825-9 doi (DE-627)OLC2123459984 (DE-He213)s10623-020-00825-9-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Renner, Julian verfasserin aut Low-rank parity-check codes over Galois rings 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. Galois rings Low-rank parity-check codes Rank-metric codes Algebraic coding theory Neri, Alessandro (orcid)0000-0002-2020-1040 aut Puchinger, Sven aut Enthalten in Designs, codes and cryptography Springer US, 1991 89(2020), 2 vom: 13. Dez., Seite 351-386 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:89 year:2020 number:2 day:13 month:12 pages:351-386 https://doi.org/10.1007/s10623-020-00825-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 89 2020 2 13 12 351-386 |
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10.1007/s10623-020-00825-9 doi (DE-627)OLC2123459984 (DE-He213)s10623-020-00825-9-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Renner, Julian verfasserin aut Low-rank parity-check codes over Galois rings 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. Galois rings Low-rank parity-check codes Rank-metric codes Algebraic coding theory Neri, Alessandro (orcid)0000-0002-2020-1040 aut Puchinger, Sven aut Enthalten in Designs, codes and cryptography Springer US, 1991 89(2020), 2 vom: 13. Dez., Seite 351-386 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:89 year:2020 number:2 day:13 month:12 pages:351-386 https://doi.org/10.1007/s10623-020-00825-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 89 2020 2 13 12 351-386 |
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10.1007/s10623-020-00825-9 doi (DE-627)OLC2123459984 (DE-He213)s10623-020-00825-9-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Renner, Julian verfasserin aut Low-rank parity-check codes over Galois rings 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. Galois rings Low-rank parity-check codes Rank-metric codes Algebraic coding theory Neri, Alessandro (orcid)0000-0002-2020-1040 aut Puchinger, Sven aut Enthalten in Designs, codes and cryptography Springer US, 1991 89(2020), 2 vom: 13. Dez., Seite 351-386 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:89 year:2020 number:2 day:13 month:12 pages:351-386 https://doi.org/10.1007/s10623-020-00825-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 89 2020 2 13 12 351-386 |
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Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. © The Author(s) 2020 |
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Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. © The Author(s) 2020 |
| abstract_unstemmed |
Abstract Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above. © The Author(s) 2020 |
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Low-rank parity-check codes over Galois rings |
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https://doi.org/10.1007/s10623-020-00825-9 |
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Neri, Alessandro Puchinger, Sven |
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