{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T09:27:16Z","timestamp":1768901236842,"version":"3.49.0"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032018540","type":"print"},{"value":"9783032018557","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[[2025]]},"DOI":"10.1007\/978-3-032-01855-7_9","type":"book-chapter","created":{"date-parts":[[2025,8,16]],"date-time":"2025-08-16T19:41:21Z","timestamp":1755373281000},"page":"253-283","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Highway to\u00a0Hull: An Algorithm for\u00a0Solving the\u00a0General Matrix Code Equivalence Problem"],"prefix":"10.1007","author":[{"given":"Alain","family":"Couvreur","sequence":"first","affiliation":[]},{"given":"Christophe","family":"Levrat","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,17]]},"reference":[{"key":"9_CR1","unstructured":"Baldi, M., et al.: LESS (Linear Equivalence Signature Scheme). NIST, Post\u2013Quantum Cryptography : Additional Digital Signature Schemes (2023). https:\/\/www.less-project.com\/"},{"key":"9_CR2","doi-asserted-by":"crossref","unstructured":"Beullens, W.: Not enough LESS: An improved algorithm for solving code equivalence problems over FQ. In: Dunkelman, O., Jacobson, Jr., M.J., O\u2019Flynn, C. (eds.) Selected Areas in Cryptography, pp. 387\u2013403. Springer International Publishing, Cham (2021)","DOI":"10.1007\/978-3-030-81652-0_15"},{"key":"9_CR3","doi-asserted-by":"crossref","unstructured":"Beullens, W.: Graph-theoretic algorithms for the alternating trilinear form equivalence problem. In: Handschuh, H., Lysyanskaya, A. (eds.) Advances in Cryptology \u2013 CRYPTO 2023, pp. 101\u2013126. Springer Nature Switzerland, Cham (2023)","DOI":"10.1007\/978-3-031-38548-3_4"},{"key":"9_CR4","unstructured":"Bl\u00e4ser, M., Duong, D.H., Narayanan, A.K., Plantard, T., Qiao, Y., Sipasseuth, A., Tang, G.: ALTEQ. NIST, Post\u2013Quantum Cryptography : Additional Digital Signature Schemes (2023). https:\/\/csrc.nist.gov\/csrc\/media\/Projects\/pqc-dig-sig\/documents\/round-1\/spec-files\/ALTEQ-Spec-web.pdf"},{"key":"9_CR5","unstructured":"Bos, J.W., et al.: Hawk: a signature scheme inspired by the lattice isomorphism problem. NIST, Post\u2013Quantum Cryptography\u00a0: Additional Digital Signature Schemes (2023). https:\/\/hawk-sign.info\/"},{"key":"9_CR6","doi-asserted-by":"crossref","unstructured":"Bouillaguet, C., Fouque, P.A., V\u00e9ber, A.: Graph-theoretic algorithms for the \u201cIsomorphism of Polynomials\u201d problem. In: Johansson, T., Nguyen, P.Q. (eds.) Advances in Cryptology \u2013 EUROCRYPT 2013, pp. 211\u2013227. Springer Berlin Heidelberg, Berlin, Heidelberg (2013)","DOI":"10.1007\/978-3-642-38348-9_13"},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"Brooksbank, P.A., Wilson, J.B., O\u2019Brien, E.A.: Testing isomorphism of graded algebras. Trans. Amer. Math. Soc. 372(11), 8067\u20138090 (2019)","DOI":"10.1090\/tran\/7884"},{"key":"9_CR8","unstructured":"Caldero, P., Germoni, J.: Nouvelles histoires h\u00e9donistes de groupes et de g\u00e9om\u00e9tries. Math\u00e9matiques en devenir, Calvage et Mounet (2018). https:\/\/hal.science\/hal-02161089"},{"key":"9_CR9","unstructured":"Chou, T., et al.: MEDS (Matrix Equivalence Digital Signature Scheme). NIST, Post\u2013Quantum Cryptography : Additional Digital Signature Schemes (2023). https:\/\/www.meds-pqc.org\/"},{"key":"9_CR10","doi-asserted-by":"crossref","unstructured":"Chou, T., et al.: Take your MEDS: digital signatures from matrix code equivalence. In: El Mrabet, N., De Feo, L., Duquesne, S. (eds.) Progress in Cryptology - AFRICACRYPT 2023, pp. 28\u201352. Springer Nature Switzerland, Cham (2023)","DOI":"10.1007\/978-3-031-37679-5_2"},{"key":"9_CR11","unstructured":"Couvreur, A., Debris-Alazard, T., Gaborit, P.: On the hardness of code equivalence problems in rank metric (2020). https:\/\/hal.archives-ouvertes.fr\/hal-02997801, preprint"},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"Dixon, J.D., Panario, D.: The degree of the splitting field of a random polynomial over a finite field. Electron. J. Comb., R70\u2013R70 (2004)","DOI":"10.37236\/1823"},{"key":"9_CR13","doi-asserted-by":"crossref","unstructured":"von\u00a0zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, 3rd edn. (2013)","DOI":"10.1017\/CBO9781139856065"},{"key":"9_CR14","doi-asserted-by":"crossref","unstructured":"Grochow, J., Qiao, Y.: On the complexity of isomorphism problems for tensors, groups, and polynomials I: tensor isomorphism-completeness. SIAM J. Comput. 52(2), 568\u2013617 (2023)","DOI":"10.1137\/21M1441110"},{"key":"9_CR15","doi-asserted-by":"crossref","unstructured":"Grove, L.C.: Classical Groups and Geometric Algebra, vol.\u00a039. American Mathematical Soc. (2002)","DOI":"10.1007\/0-306-47122-1_2"},{"key":"9_CR16","unstructured":"Kerr, M.: Algebra I Lecture Notes. https:\/\/www.math.wustl.edu\/~matkerr\/5031\/index.html"},{"key":"9_CR17","doi-asserted-by":"crossref","unstructured":"Leon, J.: Computing automorphism groups of error-correcting codes. IEEE Trans. Inform. Theory 28(3), 496\u2013511 (1982)","DOI":"10.1109\/TIT.1982.1056498"},{"key":"9_CR18","doi-asserted-by":"publisher","unstructured":"L\u00f3pez, A., Maisner, D., Nart, E., Xarles, X.: Orbits of Galois Invariant n-Sets of P1 under the action of PGL2. Finite Fields Appl. 8(2), 193\u2013206 (2002). https:\/\/doi.org\/10.1006\/ffta.2001.0335","DOI":"10.1006\/ffta.2001.0335"},{"key":"9_CR19","doi-asserted-by":"crossref","unstructured":"Matsumoto, T., Imai, H.: Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In: Advances in Cryptology\u2014 EUROCRYPT\u201988: Workshop on the Theory and Application of Cryptographic Techniques Davos, Switzerland, May 25\u201327, 1988 Proceedings 7, pp. 419\u2013453. Springer (1988)","DOI":"10.1007\/3-540-45961-8_39"},{"key":"9_CR20","doi-asserted-by":"crossref","unstructured":"Narayanan, A.K., Qiao, Y., Tang, G.: Algorithms for matrix code and alternating trilinear form equivalences via new isomorphism invariants. In: Joye, M., Leander, G. (eds.) Advances in Cryptology \u2013 EUROCRYPT 2024, pp. 160\u2013187. Springer Nature Switzerland, Cham (2024)","DOI":"10.1007\/978-3-031-58734-4_6"},{"key":"9_CR21","doi-asserted-by":"publisher","unstructured":"Neiger, V., Pernet, C.: Deterministic computation of the characteristic polynomial in the time of matrix multiplication. J. Complexity 67, 101572 (2021). https:\/\/doi.org\/10.1016\/j.jco.2021.101572","DOI":"10.1016\/j.jco.2021.101572"},{"key":"9_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/3-540-68339-9_4","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201996","author":"J Patarin","year":"1996","unstructured":"Patarin, J.: Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33\u201348. Springer, Heidelberg (1996). https:\/\/doi.org\/10.1007\/3-540-68339-9_4"},{"issue":"3","key":"9_CR23","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1112\/S0024609302001820","volume":"35","author":"M Perret","year":"2003","unstructured":"Perret, M.: On the number of points of some varieties over finite fields. Bull. Lond. Math. Soc. 35(3), 309\u2013320 (2003). https:\/\/doi.org\/10.1112\/S0024609302001820","journal-title":"Bull. Lond. Math. Soc."},{"key":"9_CR24","doi-asserted-by":"crossref","unstructured":"Ran, L., Samardjiska, S.: Rare structures in tensor graphs. In: Chung, K.M., Sasaki, Y. (eds.) Advances in Cryptology \u2013 ASIACRYPT 2024, pp. 66\u201396. Springer Nature Singapore, Singapore (2025)","DOI":"10.1007\/978-981-96-0944-4_3"},{"key":"9_CR25","doi-asserted-by":"crossref","unstructured":"Ran, L., Samardjiska, S., Trimoska, M.: Algebraic algorithm for the alternating trilinear form equivalence problem. In: Esser, A., Santini, P. (eds.) Code-Based Cryptography, pp. 84\u2013103. Springer Nature Switzerland, Cham (2023)","DOI":"10.1007\/978-3-031-46495-9_5"},{"issue":"2","key":"9_CR26","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1137\/S0895480195294027","volume":"10","author":"N Sendrier","year":"1997","unstructured":"Sendrier, N.: On the dimension of the hull. SIAM J. Discrete Math. 10(2), 282\u2013293 (1997). https:\/\/doi.org\/10.1137\/S0895480195294027","journal-title":"SIAM J. Discrete Math."},{"key":"9_CR27","doi-asserted-by":"crossref","unstructured":"Sendrier, N.: Finding the permutation between equivalent linear codes: the support splitting algorithm. IEEE Trans. Inform. Theory 46(4), 1193\u20131203 (2000)","DOI":"10.1109\/18.850662"},{"key":"9_CR28","doi-asserted-by":"crossref","unstructured":"Sendrier, N., Simos, D.E.: The hardness of code equivalence over and its application to code-based cryptography. In: Post-Quantum Cryptography\u00a02013. Lecture Notes Comput. Sci., vol.\u00a07932, pp. 203\u2013216. Springer (2013)","DOI":"10.1007\/978-3-642-38616-9_14"},{"key":"9_CR29","unstructured":"Serre, J.P.: Lettre \u00e0 M. Tsfasman. Ast\u00e9risque 198, 199\u2013200 (1989)"},{"key":"9_CR30","doi-asserted-by":"crossref","unstructured":"Tang, G., Duong, D.H., Joux, A., Plantard, T., Qiao, Y., Susilo, W.: Practical post-quantum signature schemes from isomorphism problems of trilinear forms. In: Dunkelman, O., Dziembowski, S. (eds.) Advances in Cryptology \u2013 EUROCRYPT 2022, pp. 582\u2013612. Springer International Publishing, Cham (2022)","DOI":"10.1007\/978-3-031-07082-2_21"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-01855-7_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T19:21:50Z","timestamp":1768850510000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-01855-7_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783032018540","9783032018557"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-01855-7_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"17 August 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CRYPTO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Cryptology Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santa Barbara, CA","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 August 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 August 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"45","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}