Low-rank parity-check codes over Galois rings

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 ring...

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Vydané v:	Designs, codes, and cryptography Ročník 89; číslo 2; s. 351 - 386
Hlavní autori:	Renner, Julian, Neri, Alessandro, Puchinger, Sven
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.02.2021 Springer Nature B.V
Predmet:	Algorithms Binary system Codes Coding and Information Theory Computer Science Cryptography Cryptology Decoding Discrete Mathematics in Computer Science Fields (mathematics) Parity Rings (mathematics) Upper bounds Rank-metric codes Algebraic coding theory 11T71 Low-rank parity-check codes Galois rings
ISSN:	0925-1022, 1573-7586, 1573-7586
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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.
AbstractList	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. 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.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. 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.
Author	Neri, Alessandro Puchinger, Sven Renner, Julian
Author_xml	– sequence: 1 givenname: Julian surname: Renner fullname: Renner, Julian organization: Institute for Communications Engineering, Technical University of Munich (TUM) – sequence: 2 givenname: Alessandro orcidid: 0000-0002-2020-1040 surname: Neri fullname: Neri, Alessandro email: alessandro.neri@tum.de organization: Institute for Communications Engineering, Technical University of Munich (TUM) – sequence: 3 givenname: Sven surname: Puchinger fullname: Puchinger, Sven organization: Department of Applied Mathematics and Computer Science, Technical University of Denmark (DTU)
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Cites_doi	10.1016/S0019-9958(78)90461-8 10.1109/TIT.2019.2933535 10.1109/TIT.2017.2778726 10.1109/TIT.2019.2933520 10.1109/TIT.2010.2068750 10.1016/S0019-9958(75)80001-5 10.1016/0097-3165(78)90015-8 10.1016/S0019-9958(72)90223-9 10.1109/WCNC.2018.8377229 10.1109/TIT.2014.2346079 10.37236/1489 10.1002/dac.3256 10.1109/TIT.2011.2165816 10.1109/18.75248 10.1109/TIT.2015.2451623 10.1109/REDUNDANCY48165.2019.9003356 10.1109/TIT.2008.928291 10.1109/18.312154 10.1109/TIT.2013.2274264 10.1109/ISIT44484.2020.9174384 10.1017/CBO9781139856065
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Keywords	Rank-metric codes Algebraic coding theory 11T71 Low-rank parity-check codes Galois rings
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References	DelsartePBilinear forms over a finite field, with applications to coding theoryJ. Comb. Theory Ser. A197825322624151461810.1016/0097-3165(78)90015-8 McDonaldBRFinite rings with identity1974New YorkMarcel Dekker Incorporated0294.16012 RothRMMaximum-rank array codes and their application to crisscross error correctionIEEE Trans. Inf. Theory1991372328336109374710.1109/18.75248 GabidulinEMTheory of codes with maximum rank distanceProblemy Peredachi Inf.19852113167915290585.94013 FengCNóbregaRWKschischangFRSilvaDCommunication over finite-chain-ring matrix channelsIEEE Trans. Inf. Theory2014601058995917326500210.1109/TIT.2014.2346079 BlakeIFCodes over integer residue ringsInf. Control197529429530043460710.1016/S0019-9958(75)80001-5 Von Zur GathenJGerhardJModern Computer Algebra2013CambridgeCambridge University Press10.1017/CBO9781139856065 GorlaERavagnaniAAn algebraic framework for end-to-end physical-layer network codingIEEE Trans. Inf. Theory201764644804495380975410.1109/TIT.2017.2778726 BlakeIFCodes over certain ringsInf. Control197220439640432344010.1016/S0019-9958(72)90223-9 Storjohann A.: Algorithms for matrix canonical forms. Ph.D. thesis, ETH Zurich (2000). NazerBGastparMCompute-and-forward: harnessing interference through structured codesIEEE Trans. Inf. Theory2011571064636486288224010.1109/TIT.2011.2165816 Kiran T., Rajan B.S.: Optimal STBCs from codes over Galois rings. In: IEEE International Conference on Personal Wireless Communications (ICPWC), pp. 120–124 (2005). Renner J., Jerkovits T., Bartz H.: Efficient decoding of interleaved low-rank parity-check codes. In: International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY) (2019). KamcheHTMouahaCRank-metric codes over finite principal ideal rings and applicationsIEEE Trans. Inf. Theory2019651277187735403889510.1109/TIT.2019.2933520 Melchor C.A., et al.: Nist post-quantum cryptography standardization proposal: rank-Ouroboros, LAKE and LOCKER (ROLLO) (2020). TunaliNEHuangYCBoutrosJJNarayananKRLattices over Eisenstein integers for compute-and-forwardIEEE Trans. Inf. Theory2015611053065321340028310.1109/TIT.2015.2451623 SilvaDKschischangFRKoetterRA rank-metric approach to error control in random network codingIEEE Trans. Inf. Theory200854939513967245076210.1109/TIT.2008.928291 Qachchach I.E., Habachi O., Cances J., Meghdadi V.: Efficient multi-source network coding using low rank parity check code. In: IEEE Wireless Communications and Networking Conference (WCNC) (2018). BiniGFlaminiFFinite commutative rings and their applications2012New YorkSpringer Science & Business Media1095.13032 Renner J., Puchinger S., Wachter-Zeh A., Hollanti C., Freij-Hollanti R.: Low-rank parity-check codes over the ring of integers modulo a prime power. In: IEEE International Symposium on Information Theory (ISIT), conference version of this paper. arXiv:2001.04800 (2020). SpiegelECodes over Zm, revisitedInf. Control197837110010410.1016/S0019-9958(78)90461-8 WilsonMPNarayananKPfisterHDSprintsonAJoint physical layer coding and network coding for bidirectional relayingIEEE Trans. Inf. Theory2010561156415654280859910.1109/TIT.2010.2068750 YazbekAKEL QachchachICancesJPMeghdadiVLow rank parity check codes and their application in power line communications smart grid networksInt. J. Commun. Syst.20173012e325610.1002/dac.3256 Aragon N., Gaborit P., Hauteville A., Ruatta O., Zémor G.: Low rank parity check codes: New decoding algorithms and applications to cryptography. arXiv:1904.00357 (2019). HammonsARKumarPVCalderbankARSloaneNJSoléPThe Z4-linearity of Kerdock, Preparata, Goethals, and related codesIEEE Trans. Inf. Theory199440230131910.1109/18.312154 HonoldTLandjevILinear codes over finite chain ringsElectr. J. Comb.20007R11R11174133310.37236/1489 Gaborit P., Murat G., Ruatta O., Zémor G.: Low rank parity check codes and their application to cryptography. In: Proceedings of the Workshop on Coding and Cryptography WCC. vol. 2013 (2013). ConstantinescuIHeiseWA metric for codes over residue class ringsProblemy Peredachi Inf.1997333222814763680977.94055 FengCSilvaDKschischangFRAn algebraic approach to physical-layer network codingIEEE Trans. Inf. Theory2013591175767596312466110.1109/TIT.2013.2274264 E Gorla (825_CR11) 2017; 64 G Bini (825_CR2) 2012 C Feng (825_CR7) 2014; 60 825_CR15 AK Yazbek (825_CR29) 2017; 30 I Constantinescu (825_CR5) 1997; 33 825_CR10 825_CR1 EM Gabidulin (825_CR9) 1985; 21 RM Roth (825_CR22) 1991; 37 825_CR17 IF Blake (825_CR3) 1972; 20 825_CR19 AR Hammons (825_CR12) 1994; 40 E Spiegel (825_CR24) 1978; 37 C Feng (825_CR8) 2013; 59 D Silva (825_CR23) 2008; 54 J Von Zur Gathen (825_CR27) 2013 T Honold (825_CR13) 2000; 7 825_CR25 B Nazer (825_CR18) 2011; 57 825_CR20 HT Kamche (825_CR14) 2019; 65 BR McDonald (825_CR16) 1974 825_CR21 P Delsarte (825_CR6) 1978; 25 IF Blake (825_CR4) 1975; 29 NE Tunali (825_CR26) 2015; 61 MP Wilson (825_CR28) 2010; 56
References_xml	– reference: NazerBGastparMCompute-and-forward: harnessing interference through structured codesIEEE Trans. Inf. Theory2011571064636486288224010.1109/TIT.2011.2165816 – reference: Storjohann A.: Algorithms for matrix canonical forms. Ph.D. thesis, ETH Zurich (2000). – reference: FengCNóbregaRWKschischangFRSilvaDCommunication over finite-chain-ring matrix channelsIEEE Trans. Inf. Theory2014601058995917326500210.1109/TIT.2014.2346079 – reference: Renner J., Jerkovits T., Bartz H.: Efficient decoding of interleaved low-rank parity-check codes. In: International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY) (2019). – reference: SilvaDKschischangFRKoetterRA rank-metric approach to error control in random network codingIEEE Trans. Inf. Theory200854939513967245076210.1109/TIT.2008.928291 – reference: BlakeIFCodes over certain ringsInf. Control197220439640432344010.1016/S0019-9958(72)90223-9 – reference: BlakeIFCodes over integer residue ringsInf. Control197529429530043460710.1016/S0019-9958(75)80001-5 – reference: Kiran T., Rajan B.S.: Optimal STBCs from codes over Galois rings. In: IEEE International Conference on Personal Wireless Communications (ICPWC), pp. 120–124 (2005). – reference: Melchor C.A., et al.: Nist post-quantum cryptography standardization proposal: rank-Ouroboros, LAKE and LOCKER (ROLLO) (2020). – reference: Von Zur GathenJGerhardJModern Computer Algebra2013CambridgeCambridge University Press10.1017/CBO9781139856065 – reference: GabidulinEMTheory of codes with maximum rank distanceProblemy Peredachi Inf.19852113167915290585.94013 – reference: BiniGFlaminiFFinite commutative rings and their applications2012New YorkSpringer Science & Business Media1095.13032 – reference: HonoldTLandjevILinear codes over finite chain ringsElectr. J. Comb.20007R11R11174133310.37236/1489 – reference: Qachchach I.E., Habachi O., Cances J., Meghdadi V.: Efficient multi-source network coding using low rank parity check code. In: IEEE Wireless Communications and Networking Conference (WCNC) (2018). – reference: KamcheHTMouahaCRank-metric codes over finite principal ideal rings and applicationsIEEE Trans. Inf. Theory2019651277187735403889510.1109/TIT.2019.2933520 – reference: Renner J., Puchinger S., Wachter-Zeh A., Hollanti C., Freij-Hollanti R.: Low-rank parity-check codes over the ring of integers modulo a prime power. In: IEEE International Symposium on Information Theory (ISIT), conference version of this paper. arXiv:2001.04800 (2020). – reference: RothRMMaximum-rank array codes and their application to crisscross error correctionIEEE Trans. Inf. Theory1991372328336109374710.1109/18.75248 – reference: Gaborit P., Murat G., Ruatta O., Zémor G.: Low rank parity check codes and their application to cryptography. In: Proceedings of the Workshop on Coding and Cryptography WCC. vol. 2013 (2013). – reference: YazbekAKEL QachchachICancesJPMeghdadiVLow rank parity check codes and their application in power line communications smart grid networksInt. J. Commun. Syst.20173012e325610.1002/dac.3256 – reference: SpiegelECodes over Zm, revisitedInf. Control197837110010410.1016/S0019-9958(78)90461-8 – reference: WilsonMPNarayananKPfisterHDSprintsonAJoint physical layer coding and network coding for bidirectional relayingIEEE Trans. Inf. Theory2010561156415654280859910.1109/TIT.2010.2068750 – reference: TunaliNEHuangYCBoutrosJJNarayananKRLattices over Eisenstein integers for compute-and-forwardIEEE Trans. Inf. Theory2015611053065321340028310.1109/TIT.2015.2451623 – reference: DelsartePBilinear forms over a finite field, with applications to coding theoryJ. Comb. Theory Ser. A197825322624151461810.1016/0097-3165(78)90015-8 – reference: McDonaldBRFinite rings with identity1974New YorkMarcel Dekker Incorporated0294.16012 – reference: HammonsARKumarPVCalderbankARSloaneNJSoléPThe Z4-linearity of Kerdock, Preparata, Goethals, and related codesIEEE Trans. Inf. Theory199440230131910.1109/18.312154 – reference: GorlaERavagnaniAAn algebraic framework for end-to-end physical-layer network codingIEEE Trans. Inf. Theory201764644804495380975410.1109/TIT.2017.2778726 – reference: ConstantinescuIHeiseWA metric for codes over residue class ringsProblemy Peredachi Inf.1997333222814763680977.94055 – reference: Aragon N., Gaborit P., Hauteville A., Ruatta O., Zémor G.: Low rank parity check codes: New decoding algorithms and applications to cryptography. arXiv:1904.00357 (2019). – reference: FengCSilvaDKschischangFRAn algebraic approach to physical-layer network codingIEEE Trans. Inf. Theory2013591175767596312466110.1109/TIT.2013.2274264 – volume: 37 start-page: 100 issue: 1 year: 1978 ident: 825_CR24 publication-title: Inf. Control doi: 10.1016/S0019-9958(78)90461-8 – ident: 825_CR1 doi: 10.1109/TIT.2019.2933535 – volume-title: Finite commutative rings and their applications year: 2012 ident: 825_CR2 – volume: 64 start-page: 4480 issue: 6 year: 2017 ident: 825_CR11 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2017.2778726 – ident: 825_CR10 – volume: 65 start-page: 7718 issue: 12 year: 2019 ident: 825_CR14 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2019.2933520 – volume: 56 start-page: 5641 issue: 11 year: 2010 ident: 825_CR28 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2010.2068750 – volume: 29 start-page: 295 issue: 4 year: 1975 ident: 825_CR4 publication-title: Inf. Control doi: 10.1016/S0019-9958(75)80001-5 – volume: 25 start-page: 226 issue: 3 year: 1978 ident: 825_CR6 publication-title: J. Comb. Theory Ser. A doi: 10.1016/0097-3165(78)90015-8 – volume: 20 start-page: 396 issue: 4 year: 1972 ident: 825_CR3 publication-title: Inf. Control doi: 10.1016/S0019-9958(72)90223-9 – ident: 825_CR19 doi: 10.1109/WCNC.2018.8377229 – volume: 60 start-page: 5899 issue: 10 year: 2014 ident: 825_CR7 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2014.2346079 – volume: 33 start-page: 22 issue: 3 year: 1997 ident: 825_CR5 publication-title: Problemy Peredachi Inf. – ident: 825_CR25 – volume: 7 start-page: R11 year: 2000 ident: 825_CR13 publication-title: Electr. J. Comb. doi: 10.37236/1489 – volume: 30 start-page: e3256 issue: 12 year: 2017 ident: 825_CR29 publication-title: Int. J. Commun. Syst. doi: 10.1002/dac.3256 – volume-title: Finite rings with identity year: 1974 ident: 825_CR16 – volume: 57 start-page: 6463 issue: 10 year: 2011 ident: 825_CR18 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2011.2165816 – volume: 37 start-page: 328 issue: 2 year: 1991 ident: 825_CR22 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.75248 – ident: 825_CR15 – ident: 825_CR17 – volume: 61 start-page: 5306 issue: 10 year: 2015 ident: 825_CR26 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2015.2451623 – ident: 825_CR20 doi: 10.1109/REDUNDANCY48165.2019.9003356 – volume: 21 start-page: 3 issue: 1 year: 1985 ident: 825_CR9 publication-title: Problemy Peredachi Inf. – volume: 54 start-page: 3951 issue: 9 year: 2008 ident: 825_CR23 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2008.928291 – volume: 40 start-page: 301 issue: 2 year: 1994 ident: 825_CR12 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.312154 – volume: 59 start-page: 7576 issue: 11 year: 2013 ident: 825_CR8 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2013.2274264 – ident: 825_CR21 doi: 10.1109/ISIT44484.2020.9174384 – volume-title: Modern Computer Algebra year: 2013 ident: 825_CR27 doi: 10.1017/CBO9781139856065
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Snippet	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... 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...
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SubjectTerms	Algorithms Binary system Codes Coding and Information Theory Computer Science Cryptography Cryptology Decoding Discrete Mathematics in Computer Science Fields (mathematics) Parity Rings (mathematics) Upper bounds
Title	Low-rank parity-check codes over Galois rings
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