{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T14:03:34Z","timestamp":1760623414352,"version":"3.44.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T00:00:00Z","timestamp":1741651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T00:00:00Z","timestamp":1741651200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"CyTeD Program Grant","award":["522RT0131","522RT0131"],"award-info":[{"award-number":["522RT0131","522RT0131"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s10623-025-01610-2","type":"journal-article","created":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T05:41:28Z","timestamp":1741671688000},"page":"2561-2589","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Admissible parameters for the Crossbred algorithm and semi-regular sequences over finite fields"],"prefix":"10.1007","volume":"93","author":[{"given":"John","family":"Baena","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Cabarcas","sequence":"additional","affiliation":[]},{"given":"Sharwan K.","family":"Tiwari","sequence":"additional","affiliation":[]},{"given":"Javier","family":"Verbel","sequence":"additional","affiliation":[]},{"given":"Luis","family":"Villota","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,11]]},"reference":[{"unstructured":"Bardet M., Faug\u00e8re J.-C., Salvy B., Yang B.-Y.: Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems. In: MEGA 2005\u20148th International Symposium on Effective Methods in Algebraic Geometry, pp. 1\u201317 (2005).","key":"1610_CR1"},{"unstructured":"Bardet M.: \u00c9tude des syst\u00e8mes alg\u00e9briques surd\u00e9termin\u00e9s. Applications aux codes cor- recteurs et \u00e0 la cryptographie. PhD thesis, Universit\u00e9 de Paris 6 - Pierre et Marie Curie (2004).","key":"1610_CR2"},{"issue":"1","key":"1610_CR3","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.jco.2012.07.001","volume":"29","author":"M Bardet","year":"2013","unstructured":"Bardet M., Faug\u00e8re J.-C., Salvy B., Spaenlehauer P.-J.: On the complexity of solving quadratic Boolean systems. J. Complex. 29(1), 53\u201375 (2013).","journal-title":"J. Complex."},{"doi-asserted-by":"crossref","unstructured":"Bellini E., Makarim R.H., Sanna C., Verbel J.A.: An estimator for the hardness of the MQ problem. In: Batina L., Daemen J. (eds.) AFRICACRYPT 22, volume 2022 of LNCS, pp. 323\u2013347. Springer, Berlin (July 2022).","key":"1610_CR4","DOI":"10.1007\/978-3-031-17433-9_14"},{"unstructured":"Benadjila R., Feneuil T., Rivain M.: MQ on my mind: post-quantum signatures from the non-structured multivariate quadratic problem. Cryptology ePrint Archive, Paper 2023\/1719 (2023). https:\/\/eprint.iacr.org\/2023\/1719.","key":"1610_CR5"},{"unstructured":"Beullens W., Chen M.-S., Ding J., Gong B., Kannwischer M.J., Patarin J., Peng B.-Y., Schmidt D., Shih C.-J., Tao C., Yang B.-Y.: UOV: specifications (2023). https:\/\/csrc.nist.gov\/csrc\/media\/Projects\/pqc-dig-sig\/documents\/round-1\/spec-files\/UOV-spec-web.pdf.","key":"1610_CR6"},{"doi-asserted-by":"crossref","unstructured":"Beullens W.: MAYO: practical post-quantum signatures from oil-and-vinegar maps. In: AlTawy R., H\u00fclsing A. (eds.) SAC 2021, volume 13203 of LNCS, pp 355\u2013376. Springer, Heidelberg (September\/October 2022).","key":"1610_CR7","DOI":"10.1007\/978-3-030-99277-4_17"},{"doi-asserted-by":"crossref","unstructured":"Chen M.-S., H\u00fclsing A., Rijneveld J., Samardjiska S., Schwabe P.: From 5-pass MQ-based identification to MQ-based signatures. In: Cheon J.H., Takagi T. (eds.) ASIACRYPT\u00a02016, Part\u00a0II, volume 10032 of LNCS, pp. 135\u2013165. Springer, Heidelberg (2016).","key":"1610_CR8","DOI":"10.1007\/978-3-662-53890-6_5"},{"unstructured":"Chen M.-S., H\u00fclsing A., Rijneveld J., Samardjiska S., Schwabe P.: MQDSS specifications (2020). http:\/\/mqdss.org\/specification.html.","key":"1610_CR9"},{"key":"1610_CR10","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1007\/3-540-45539-6_27","volume-title":"Advances in Cryptology\u2013EUROCRYPT 2000","author":"N Courtois","year":"2000","unstructured":"Courtois N., Klimov A., Patarin J., Shamir A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel B. (ed.) Advances in Cryptology\u2013EUROCRYPT 2000, pp. 392\u2013407. Springer, Berlin (2000)."},{"key":"1610_CR11","first-page":"193","volume-title":"Multivariate Public Key Cryptography","author":"J Ding","year":"2009","unstructured":"Ding J., Yang B.-Y.: Multivariate Public Key Cryptography, pp. 193\u2013241. Springer, Berlin (2009)."},{"unstructured":"Duarte J.D.: On the complexity and admissible parameters of the crossbred algorithm in $${\\mathbb{F}}_{q\\ge 2}$$. Cryptology ePrint Archive, Paper 2023\/1664 (2023). https:\/\/eprint.iacr.org\/2023\/1664.","key":"1610_CR12"},{"doi-asserted-by":"crossref","unstructured":"Faug\u00e8re J.C.: A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero (F5). In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ISSAC \u201902, pp. 75\u201383, New York, NY, USA, 2002. Association for Computing Machinery.","key":"1610_CR13","DOI":"10.1145\/780506.780516"},{"issue":"1","key":"1610_CR14","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0022-4049(99)00005-5","volume":"139","author":"JC Faug\u00e8re","year":"1999","unstructured":"Faug\u00e8re J.C.: A new efficient algorithm for computing Gr\u00d6bner bases (F4). J. Pure Appl. Algebra 139(1), 61\u201388 (1999).","journal-title":"J. Pure Appl. Algebra"},{"unstructured":"Information Technology\u00a0Laboratory Computer Security\u00a0Division. Round 1 additional signatures\u2014post-quantum cryptography: Digital signature schemes: Csrc.","key":"1610_CR15"},{"key":"1610_CR16","volume-title":"Number-Theoretic Methods in Cryptology, pp 3\u201321","author":"A Joux","year":"2018","unstructured":"Joux A., Vitse V.: A crossbred algorithm for solving Boolean polynomial systems. In: Kaczorowski J., Pieprzyk J., Pomyka\u0142a J. (eds.) Number-Theoretic Methods in Cryptology, pp 3\u201321. Springer, Cham (2018)."},{"issue":"210","key":"1610_CR17","first-page":"777","volume":"64","author":"E Kaltofen","year":"1995","unstructured":"Kaltofen E.: Analysis of coppersmith\u2019s block Wiedemann algorithm for the parallel solution of sparse linear systems. Math. Comput. 64(210), 777\u2013806 (1995).","journal-title":"Math. Comput."},{"doi-asserted-by":"crossref","unstructured":"Kipnis A., Patarin J., Goubin L.: Unbalanced oil and vinegar signature schemes. EUROCRYPT 1999. LNCS, 1592, 206\u2013222 (1999).","key":"1610_CR18","DOI":"10.1007\/3-540-48910-X_15"},{"doi-asserted-by":"crossref","unstructured":"Kipnis A., Patarin J., Goubin L.: Unbalanced oil and vinegar signature schemes. In: Stern J. (ed) EUROCRYPT\u201999, vol. 1592, pp. 206\u2013222. LNCS. Springer, Heidelberg (1999).","key":"1610_CR19","DOI":"10.1007\/3-540-48910-X_15"},{"doi-asserted-by":"crossref","unstructured":"Nakamura S.: Admissible parameter sets and complexity estimation of crossbred algorithm. Cryptology ePrint Archive, Paper 2023\/1687 (2023). https:\/\/eprint.iacr.org\/2023\/1687.","key":"1610_CR20","DOI":"10.2139\/ssrn.4876774"},{"unstructured":"The\u00a0FLINT Team. FLINT: fast Library for Number Theory, 2023. Version 3.0.0. https:\/\/flintlib.org.","key":"1610_CR21"},{"doi-asserted-by":"crossref","unstructured":"Thomae E., Wolf C.: Solving underdetermined systems of multivariate quadratic equations revisited. In: Fischlin M., Buchmann J., Manulis M. (eds.) Public Key Cryptography\u2014PKC 2012, pp. 156\u2013171. Springer, Berlin (2012).","key":"1610_CR22","DOI":"10.1007\/978-3-642-30057-8_10"},{"doi-asserted-by":"crossref","unstructured":"Vidal D., Ionica S., Delaplace C.: An analysis of the crossbred algorithm for the MQ problem. Cryptology ePrint Archive, Paper 2024\/992 (2024).","key":"1610_CR23","DOI":"10.62056\/ak86cy7qiu"},{"doi-asserted-by":"crossref","unstructured":"Yang B.-Y., Chen O.C.-H., Bernstein D.J., Chen J.-M.: Analysis of QUAD. In: Biryukov A. (ed) FSE 2007, volume 4593 of LNCS, pp. 290\u2013308. Springer, Heidelberg (2007).","key":"1610_CR24","DOI":"10.1007\/978-3-540-74619-5_19"},{"key":"1610_CR25","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/978-3-540-27800-9_24","volume-title":"Information Security and Privacy","author":"B-Y Yang","year":"2004","unstructured":"Yang B.-Y., Chen J.-M.: Theoretical analysis of XL over small fields. In: Wang H., Pieprzyk J., Varadharajan V. (eds.) Information Security and Privacy, pp. 277\u2013288. Springer, Berlin (2004)."},{"unstructured":"Yasuda T., Dahan X., Huang Y.-J., Takagi T., Sakurai K.: MQ challenge: hardness evaluation of solving multivariate quadratic problems. In: NIST Workshop on Cybersecurity in a Post-Quantum World, 2015. Washington, DC. https:\/\/www.mqchallenge.org.","key":"1610_CR26"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01610-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-025-01610-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01610-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T07:34:09Z","timestamp":1757144049000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-025-01610-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,11]]},"references-count":26,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["1610"],"URL":"https:\/\/doi.org\/10.1007\/s10623-025-01610-2","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2025,3,11]]},"assertion":[{"value":"6 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}