{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:42:59Z","timestamp":1775054579837,"version":"3.50.1"},"reference-count":18,"publisher":"Pleiades Publishing Ltd","issue":"2","license":[{"start":{"date-parts":[[2010,3,1]],"date-time":"2010-03-01T00:00:00Z","timestamp":1267401600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2010,3,1]],"date-time":"2010-03-01T00:00:00Z","timestamp":1267401600000},"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":["Program Comput Soft"],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1134\/s0361768810020040","type":"journal-article","created":{"date-parts":[[2010,4,9]],"date-time":"2010-04-09T22:45:17Z","timestamp":1270853117000},"page":"75-82","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Generalization of the F5 algorithm for calculating Gr\u00f6bner bases for polynomial ideals"],"prefix":"10.1134","volume":"36","author":[{"given":"A. I.","family":"Zobnin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2010,4,11]]},"reference":[{"key":"6058_CR1","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1145\/780506.780516","volume-title":"Proc. of ISSAC 2002","author":"J.C. Faug\u00e8re","year":"2002","unstructured":"Faug\u00e8re, J.C., A New Efficient Algorithm for Computing Gr\u00f6bner Bases without Reduction to Zero (F5), Proc. of ISSAC 2002, New York: ACM, 2002, pp. 75\u201383."},{"key":"6058_CR2","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/978-3-540-45146-4_3","volume":"2729","author":"J.C. Faug\u00e8re","year":"2003","unstructured":"Faug\u00e8re, J.C. and Joux, A., Algebraic Cryptanalysis of Hidden Field Equations (HFE) Using Gr\u00f6bner Bases, Lecture Notes in Computer Science, Springer, 2003, vol. 2729, pp. 44\u201360.","journal-title":"Lecture Notes in Computer Science"},{"key":"6058_CR3","doi-asserted-by":"crossref","unstructured":"Kreuzer, M., Algebraic Attacks Galore! Groups-Complexity-Cryptology, 2009, no. 2.","DOI":"10.1515\/GCC.2009.231"},{"key":"6058_CR4","unstructured":"Stegers, T., Faug\u00e8re\u2019s F5 Algorithm Revisited, Diploma Thesis, Department of Mathematics, Technische Universitat Darmstadt, 2005."},{"key":"6058_CR5","doi-asserted-by":"crossref","unstructured":"M\u00f6ller, H.M., Mora, T., and Traverso, C., Gr\u00f6bner Bases Computation Using Syzygies, Proc. of ISSAC, ACM, 1992, pp. 320\u2013328.","DOI":"10.1145\/143242.143343"},{"key":"6058_CR6","unstructured":"Bardet, M., \u00c9tude des Sys\u00e8mes Alg\u00e9briques Surdetermin\u00e9s. Applications aux Codes Correcteurs et \u00e0 la Cryptographie, These de Doctorat."},{"key":"6058_CR7","unstructured":"Bardet, M., Faug\u00e8re, J.-C., and Salvy, B., On the Complexity of Gr\u00f6bner Basis Computation for Semiregular Overdetermined Algebraic Equations, Proc. of the Int. Conf. on Polynomial System Solving (ICPSS), 2003, pp. 71\u201375."},{"key":"6058_CR8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107340954","volume-title":"Solving Polynomial Equation Systems II: Macaulay\u2019s Paradigm and Gr\u00f6bner Technology","author":"T. Mora","year":"2005","unstructured":"Mora, T., Solving Polynomial Equation Systems II: Macaulay\u2019s Paradigm and Gr\u00f6bner Technology, Cambridge: Cambridge Univ. Press, 2005."},{"key":"6058_CR9","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/3-540-12868-9_99","volume":"162","author":"D. Lazard","year":"1983","unstructured":"Lazard, D., Gr\u00f6bner Bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations, Lecture Notes in Computer Science, 1983, vol. 162, pp. 146\u2013156.","journal-title":"Lecture Notes in Computer Science"},{"key":"6058_CR10","unstructured":"Faug\u00e8re, J.-C., Calcul Efficace des Bases de Gr\u00f6bner et Applications. Habilitation \u00e0 Diriger des Recherches, Universite Paris 6, 2007."},{"key":"6058_CR11","unstructured":"Ars, G. and Hashemi, A., Efficient Computation of Syzygies by Faug\u00e8re\u2019s F5 Algorithm, Proc. of Int. Conf. on Mathematical Aspects of Computer and Information Science (MACIS), 2007."},{"key":"6058_CR12","unstructured":"Eder, C., The Algorithmic Behavior of the F5 Algorithm. arXiv:0810.5335. 2008."},{"key":"6058_CR13","unstructured":"Eder, C., On the Criteria of the F5 Algorithm. arXiv:0804.2033. 2008."},{"key":"6058_CR14","doi-asserted-by":"crossref","unstructured":"Eder, C. and Perry, J., F5C: A Variant of Faug\u00e8re\u2019s F5 Algorithm with Reduced Gr\u00f6bner Bases. arXiv:0906. 2967. 2009.","DOI":"10.1016\/j.jsc.2010.06.019"},{"key":"6058_CR15","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.-C. and Rahmany, S., Solving Systems of Polynomial Equations with Symmetries Using SAGBI-Gr\u00f6bner Bases, Proc. of ISSAC-2009, 2009.","DOI":"10.1145\/1576702.1576725"},{"key":"6058_CR16","unstructured":"Segers, A., Algebraic Attacks from a Gr\u00f6bner Basis Perspective, Master\u2019s Thesis, Technische Universiteit Eindhoven, 2004."},{"key":"6058_CR17","volume-title":"Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"D. Cox","year":"1998","unstructured":"Cox, D., Little, J., and O\u2019shea, D., Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, New York: Springer, 1998. Translated under the title Idealy, mnogoobraziya i algoritmy, Moscow: Mir, 2000."},{"key":"6058_CR18","volume-title":"On Efficient Computation of Gr\u00f6bner Bases","author":"J.M. Gash","year":"2008","unstructured":"Gash, J.M., On Efficient Computation of Gr\u00f6bner Bases, Ph. D. Dissertation, Indian University, Bloomington, 2008."}],"container-title":["Programming and Computer Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768810020040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0361768810020040","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768810020040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768810020040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T02:12:26Z","timestamp":1775009546000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0361768810020040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["6058"],"URL":"https:\/\/doi.org\/10.1134\/s0361768810020040","relation":{},"ISSN":["0361-7688","1608-3261"],"issn-type":[{"value":"0361-7688","type":"print"},{"value":"1608-3261","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]},"assertion":[{"value":"1 August 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2010","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}