{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T18:10:40Z","timestamp":1771611040844,"version":"3.50.1"},"publisher-location":"Cham","reference-count":46,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031464942","type":"print"},{"value":"9783031464959","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-46495-9_2","type":"book-chapter","created":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T06:02:56Z","timestamp":1698386576000},"page":"14-34","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fast Gao-Like Decoding of\u00a0Horizontally Interleaved Linearized Reed\u2013Solomon Codes"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2217-9753","authenticated-orcid":false,"given":"Felicitas","family":"H\u00f6rmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7767-1513","authenticated-orcid":false,"given":"Hannes","family":"Bartz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,28]]},"reference":[{"key":"2_CR1","unstructured":"Aguilar Melchor, C., et al.: Hamming Quasi-Cyclic (HQC) (2023). http:\/\/pqc-hqc.org\/download.php?file=hqc-specification_2023-04-30.pdf"},{"key":"2_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/978-3-031-17234-2_3","volume-title":"Post-Quantum Cryptography","author":"C Aguilar-Melchor","year":"2022","unstructured":"Aguilar-Melchor, C., Aragon, N., Dyseryn, V., Gaborit, P., Z\u00e9mor, G.: LRPC codes with multiple syndromes: near ideal-size KEMs without ideals. In: Cheon, J.H., Johansson, T. (eds.) PQCrypto 2022. LNCS, vol. 13512, pp. 45\u201368. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-17234-2_3"},{"key":"2_CR3","doi-asserted-by":"publisher","unstructured":"Alagic, G., et al.: Status report on the third round of the NIST post-quantum cryptography standardization process (2022). https:\/\/doi.org\/10.6028\/NIST.IR.8413-upd1","DOI":"10.6028\/NIST.IR.8413-upd1"},{"key":"2_CR4","unstructured":"Aragon, N., et al.: BIKE: bit flipping key encapsulation (2022). https:\/\/bikesuite.org\/files\/v5.0\/BIKE_Spec.2022.10.10.1.pdf"},{"key":"2_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"728","DOI":"10.1007\/978-3-030-17659-4_25","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"N Aragon","year":"2019","unstructured":"Aragon, N., Blazy, O., Gaborit, P., Hauteville, A., Z\u00e9mor, G.: Durandal: a rank metric based signature scheme. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 728\u2013758. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17659-4_25"},{"key":"2_CR6","doi-asserted-by":"crossref","unstructured":"Aragon, N., Dyseryn, V., Gaborit, P., Loidreau, P., Renner, J., Wachter-Zeh, A.: LowMS: a new rank metric code-based KEM without ideal structure. Cryptology ePrint Archive, Paper 2022\/1596 (2022)","DOI":"10.1007\/s10623-023-01330-5"},{"key":"2_CR7","doi-asserted-by":"crossref","unstructured":"Aragon, N., Gaborit, P., Hauteville, A., Tillich, J.P.: A new algorithm for solving the rank syndrome decoding problem. In: IEEE International Symposium on Information Theory (ISIT), pp. 2421\u20132425 (2018)","DOI":"10.1109\/ISIT.2018.8437464"},{"key":"2_CR8","unstructured":"Avanzi, R., et al.: CRYSTALS-Kyber: algorithm specifications and supporting documentation (Version 3.02) (2021). https:\/\/pq-crystals.org\/kyber\/data\/kyber-specification-round3-20210804.pdf"},{"key":"2_CR9","unstructured":"Azarderakhsh, R., et al.: Supersingular isogeny key encapsulation (2022). https:\/\/sike.org\/files\/SIDH-spec.pdf"},{"key":"2_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1007\/978-3-030-81293-5_23","volume-title":"Post-Quantum Cryptography","author":"M Bardet","year":"2021","unstructured":"Bardet, M., Briaud, P.: An algebraic approach to the rank support learning problem. In: Cheon, J.H., Tillich, J.-P. (eds.) PQCrypto 2021 2021. LNCS, vol. 12841, pp. 442\u2013462. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-81293-5_23"},{"issue":"8","key":"2_CR11","doi-asserted-by":"publisher","first-page":"5026","DOI":"10.1109\/TIT.2021.3067318","volume":"67","author":"H Bartz","year":"2021","unstructured":"Bartz, H., Jerkovits, T., Puchinger, S., Rosenkilde, J.: Fast decoding of codes in the rank, subspace, and sum-rank metric. IEEE Trans. Inf. Theory 67(8), 5026\u20135050 (2021)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2_CR12","doi-asserted-by":"crossref","unstructured":"Bartz, H., Puchinger, S.: Decoding of interleaved linearized Reed-Solomon codes with applications to network coding. In: IEEE International Symposium on Information Theory (ISIT), pp. 160\u2013165 (2021)","DOI":"10.1109\/ISIT45174.2021.9517834"},{"key":"2_CR13","unstructured":"Bartz, H., Puchinger, S.: Fast decoding of interleaved linearized Reed-Solomon codes and variants. IEEE Trans. Inf. Theory (2023, submitted). https:\/\/arxiv.org\/abs\/2201.01339v3"},{"key":"2_CR14","unstructured":"Bernstein, D.J., et al.: Classic McEliece: conservative code-based cryptography: cryptosystem specification (2022). https:\/\/classic.mceliece.org\/mceliece-spec-20221023.pdf"},{"issue":"9","key":"2_CR15","doi-asserted-by":"publisher","first-page":"1991","DOI":"10.1007\/s10623-020-00789-w","volume":"88","author":"D Boucher","year":"2020","unstructured":"Boucher, D.: An algorithm for decoding skew Reed-Solomon codes with respect to the skew metric. Des. Codes Crypt. 88(9), 1991\u20132005 (2020)","journal-title":"Des. Codes Crypt."},{"key":"2_CR16","unstructured":"Caruso, X.: Residues of skew rational functions and linearized Goppa codes. arXiv preprint arXiv:1908.08430v1 (2019)"},{"key":"2_CR17","unstructured":"Castryck, W., Decru, T.: An efficient key recovery attack on SIDH. Cryptology ePrint Archive, Paper 2022\/975 (2022)"},{"key":"2_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1007\/3-540-46416-6_41","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201991","author":"EM Gabidulin","year":"1991","unstructured":"Gabidulin, E.M., Paramonov, A.V., Tretjakov, O.V.: Ideals over a non-commutative ring and their application in cryptology. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 482\u2013489. Springer, Heidelberg (1991). https:\/\/doi.org\/10.1007\/3-540-46416-6_41"},{"key":"2_CR19","doi-asserted-by":"crossref","unstructured":"Gabidulin, E.M., Rashwan, H., Honary, B.: On improving security of GPT cryptosystems. In: IEEE International Symposium on Information Theory, pp. 1110\u20131114 (2009)","DOI":"10.1109\/ISIT.2009.5206029"},{"key":"2_CR20","series-title":"The Springer International Series in Engineering and Computer Science","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/978-1-4757-3789-9_5","volume-title":"Communications, Information and Network Security","author":"S Gao","year":"2003","unstructured":"Gao, S.: A new algorithm for decoding Reed-Solomon codes. In: Bhargava, V.K., Poor, H.V., Tarokh, V., Yoon, S. (eds.) Communications, Information and Network Security. The Springer International Series in Engineering and Computer Science, vol. 712, pp. 55\u201368. Springer, Boston (2003). https:\/\/doi.org\/10.1007\/978-1-4757-3789-9_5"},{"key":"2_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-031-29689-5_1","volume-title":"Code-Based Cryptography","author":"F H\u00f6rmann","year":"2023","unstructured":"H\u00f6rmann, F., Bartz, H., Horlemann, A.L.: Distinguishing and recovering generalized linearized Reed-Solomon codes. In: Deneuville, J.C. (ed.) CBCrypto 2022. LNCS, vol. 13839, pp. 1\u201320. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-29689-5_1"},{"key":"2_CR22","doi-asserted-by":"crossref","unstructured":"H\u00f6rmann, F., Bartz, H., Puchinger, S.: Error-erasure decoding of linearized Reed-Solomon codes in the sum-rank metric. In: IEEE International Symposium on Information Theory (ISIT), pp. 7\u201312 (2022)","DOI":"10.1109\/ISIT50566.2022.9834742"},{"key":"2_CR23","doi-asserted-by":"crossref","unstructured":"H\u00f6rmann, F., Bartz, H., Puchinger, S.: Syndrome-based error-erasure decoding of interleaved linearized Reed-Solomon codes. IEEE Trans. Inf. Theory (2023, submitted)","DOI":"10.1109\/ISIT50566.2022.9834742"},{"key":"2_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/978-3-031-29689-5_6","volume-title":"Code-Based Cryptography","author":"T Jerkovits","year":"2023","unstructured":"Jerkovits, T., H\u00f6rmann, F., Bartz, H.: On decoding high-order interleaved sum-rank-metric codes. In: Deneuville, J.C. (ed.) CBCrypto 2022. LNCS, vol. 13839, pp. 90\u2013109. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-29689-5_6"},{"issue":"2","key":"2_CR25","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1016\/0021-8693(88)90063-4","volume":"119","author":"TY Lam","year":"1988","unstructured":"Lam, T.Y., Leroy, A.: Vandermonde and Wronskian matrices over division rings. J. Algebra 119(2), 308\u2013336 (1988)","journal-title":"J. Algebra"},{"key":"2_CR26","doi-asserted-by":"crossref","unstructured":"Le Gall, F.: Powers of tensors and fast matrix multiplication. In: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, pp. 296\u2013303 (2014)","DOI":"10.1145\/2608628.2608664"},{"key":"2_CR27","unstructured":"Loidreau, P.: An evolution of GPT cryptosystem. In: International Workshop on Algebraic and Combinatorial Coding Theory (ACCT) (2016)"},{"key":"2_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1007\/978-3-642-12929-2_11","volume-title":"Post-Quantum Cryptography","author":"P Loidreau","year":"2010","unstructured":"Loidreau, P.: Designing a rank metric based McEliece cryptosystem. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 142\u2013152. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-12929-2_11"},{"key":"2_CR29","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1016\/j.jalgebra.2018.02.005","volume":"504","author":"U Mart\u00ednez-Pe\u00f1as","year":"2018","unstructured":"Mart\u00ednez-Pe\u00f1as, U.: Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring. J. Algebra 504, 587\u2013612 (2018)","journal-title":"J. Algebra"},{"issue":"8","key":"2_CR30","doi-asserted-by":"publisher","first-page":"4785","DOI":"10.1109\/TIT.2019.2912165","volume":"65","author":"U Mart\u00ednez-Pe\u00f1as","year":"2019","unstructured":"Mart\u00ednez-Pe\u00f1as, U., Kschischang, F.R.: Reliable and secure multishot network coding using linearized Reed-Solomon codes. IEEE Trans. Inf. Theory 65(8), 4785\u20134803 (2019)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2_CR31","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1080\/03081087408817070","volume":"2","author":"G Matsaglia","year":"1974","unstructured":"Matsaglia, G., Styan, G.P.H.: Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2(3), 269\u2013292 (1974)","journal-title":"Linear Multilinear Algebra"},{"key":"2_CR32","first-page":"114","volume":"42\u201344","author":"RJ McEliece","year":"1978","unstructured":"McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. Deep Space Netw. Progr. Rep. 42\u201344, 114\u2013116 (1978)","journal-title":"Deep Space Netw. Progr. Rep."},{"issue":"4","key":"2_CR33","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1109\/18.53757","volume":"36","author":"J Metzner","year":"1990","unstructured":"Metzner, J., Kapturowski, E.: A general decoding technique applicable to replicated file disagreement location and concatenated code decoding. IEEE Trans. Inf. Theory 36(4), 911\u2013917 (1990)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2_CR34","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1090\/S0002-9947-1933-1501703-0","volume":"35","author":"O Ore","year":"1933","unstructured":"Ore, O.: On a special class of polynomials. Trans. Am. Math. Soc. 35(3), 559\u2013584 (1933)","journal-title":"Trans. Am. Math. Soc."},{"key":"2_CR35","doi-asserted-by":"crossref","unstructured":"Ore, O.: Theory of non-commutative polynomials. Ann. Math. 480\u2013508 (1933)","DOI":"10.2307\/1968173"},{"key":"2_CR36","doi-asserted-by":"crossref","unstructured":"Puchinger, S., Rosenkilde n\u00e9 Nielsen, J., Li, W., Sidorenko, V.: Row reduction applied to decoding of rank-metric and subspace codes. Des. Codes Crypt. 82(1\u20132), 389\u2013409 (2017)","DOI":"10.1007\/s10623-016-0257-9"},{"key":"2_CR37","doi-asserted-by":"crossref","unstructured":"Puchinger, S., Renner, J., Rosenkilde, J.: Generic decoding in the sum-rank metric. In: IEEE International Symposium on Information Theory (ISIT), pp. 54\u201359 (2020)","DOI":"10.1109\/ISIT44484.2020.9174497"},{"key":"2_CR38","unstructured":"Puchinger, S., Renner, J., Wachter-Zeh, A.: Decoding high-order interleaved rank-metric codes. arXiv preprint arXiv:1904.08774 (2019)"},{"key":"2_CR39","doi-asserted-by":"crossref","unstructured":"Renner, J., Jerkovits, T., Bartz, H.: Efficient decoding of interleaved low-rank parity-check codes. In: 2019 XVI International Symposium \u201cProblems of Redundancy in Information and Control Systems\u201d (REDUNDANCY), pp. 121\u2013126 (2019)","DOI":"10.1109\/REDUNDANCY48165.2019.9003356"},{"key":"2_CR40","doi-asserted-by":"crossref","unstructured":"Renner, J., Puchinger, S., Wachter-Zeh, A.: Decoding high-order interleaved rank-metric codes. In: IEEE International Symposium on Information Theory (ISIT), pp. 19\u201324 (2021)","DOI":"10.1109\/ISIT45174.2021.9518085"},{"key":"2_CR41","doi-asserted-by":"crossref","unstructured":"Sidorenko, V., Bossert, M.: Decoding interleaved Gabidulin codes and multisequence linearized shift-register synthesis. In: IEEE International Symposium on Information Theory, pp. 1148\u20131152 (2010)","DOI":"10.1109\/ISIT.2010.5513676"},{"issue":"2","key":"2_CR42","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1109\/TIT.2010.2096032","volume":"57","author":"V Sidorenko","year":"2011","unstructured":"Sidorenko, V., Jiang, L., Bossert, M.: Skew-feedback shift-register synthesis and decoding interleaved Gabidulin codes. IEEE Trans. Inf. Theory 57(2), 621\u2013632 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2_CR43","unstructured":"Stein, W.A., et al.: Sage Mathematics Software (Version 9.6). The Sage Development Team (2022). http:\/\/www.sagemath.org"},{"key":"2_CR44","unstructured":"Storjohann, A.: Algorithms for matrix canonical forms. Ph.D. thesis (2000)"},{"key":"2_CR45","unstructured":"Wachter-Zeh, A.: Decoding of block and convolutional codes in rank metric. Ph.D. thesis, Ulm University and University of Rennes 1, Ulm, Germany and Rennes, France (2013)"},{"issue":"1","key":"2_CR46","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10623-012-9659-5","volume":"66","author":"A Wachter-Zeh","year":"2013","unstructured":"Wachter-Zeh, A., Afanassiev, V., Sidorenko, V.: Fast decoding of Gabidulin codes. Des. Codes Crypt. 66(1), 57\u201373 (2013)","journal-title":"Des. Codes Crypt."}],"container-title":["Lecture Notes in Computer Science","Code-Based Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-46495-9_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T20:33:01Z","timestamp":1703449981000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-46495-9_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031464942","9783031464959"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-46495-9_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"28 October 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CBCrypto","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Code-Based Cryptography Workshop","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lyon","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 April 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 April 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cbc2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.cb-crypto.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"23","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"8","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"35% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}