{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T16:24:52Z","timestamp":1767975892955,"version":"3.49.0"},"publisher-location":"New York, NY, USA","reference-count":30,"publisher":"ACM","license":[{"start":{"date-parts":[[2014,7,23]],"date-time":"2014-07-23T00:00:00Z","timestamp":1406073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["HPAC ANR-11-BS02-013"],"award-info":[{"award-number":["HPAC ANR-11-BS02-013"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2014,7,23]]},"DOI":"10.1145\/2608628.2608669","type":"proceedings-article","created":{"date-parts":[[2014,7,1]],"date-time":"2014-07-01T14:23:03Z","timestamp":1404224583000},"page":"170-177","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Sub-cubic change of ordering for Gr\u00f6bner basis"],"prefix":"10.1145","author":[{"given":"Jean-Charles","family":"Faug\u00e8re","sequence":"first","affiliation":[{"name":"INRIA, Paris Rocquencourt Sorbonne Universit\u00e9s UPMC Univ. Paris, France"}]},{"given":"Pierrick","family":"Gaudry","sequence":"additional","affiliation":[{"name":"CNRS, INRIA Universit\u00e9 de Lorraine Caramel Project, LORIA, Nancy, France"}]},{"given":"Louise","family":"Huot","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s UPMC Univ., Paris, France"}]},{"given":"Gu\u00e9na\u00ebl","family":"Renault","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s UPMC Univ., Paris, France"}]}],"member":"320","published-online":{"date-parts":[[2014,7,23]]},"reference":[{"key":"e_1_3_2_1_1_1","first-page":"1","volume-title":"The Effective Methods in Algebraic Geometry Conference, Mega 2005","author":"Bardet M.","year":"2005","unstructured":"M. Bardet , J.-C. Faug\u00e8re , B. Salvy , and B. Yang . Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems. In P. Gianni, editor , The Effective Methods in Algebraic Geometry Conference, Mega 2005 , pages 1 -- 14 , May 2005 . M. Bardet, J.-C. Faug\u00e8re, B. Salvy, and B. Yang. Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems. In P. Gianni, editor, The Effective Methods in Algebraic Geometry Conference, Mega 2005, pages 1--14, May 2005."},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-87-05517-7"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/190347.190382"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"issue":"4","key":"e_1_3_2_1_5_1","first-page":"239","article-title":"Fast algorithms for zero-dimensional polynomial systems using duality. Applicable Algebra in Engineering","volume":"14","author":"Bostan A.","year":"2003","unstructured":"A. Bostan , B. Salvy , and E. Schost . Fast algorithms for zero-dimensional polynomial systems using duality. Applicable Algebra in Engineering , Communication and Computing , 14 ( 4 ): 239 -- 272 , 2003 . A. Bostan, B. Salvy, and E. Schost. Fast algorithms for zero-dimensional polynomial systems using duality. Applicable Algebra in Engineering, Communication and Computing, 14(4):239--272, 2003.","journal-title":"Communication and Computing"},{"key":"e_1_3_2_1_6_1","volume-title":"ICMS'2002","author":"Dumas J.-G.","year":"2002","unstructured":"J.-G. Dumas , T. Gautier , M. Giesbrecht , P. Giorgi , B. Hovinen , E. Kaltofen , B. D. Saunders , W. J. Turner , and G. Villard . LinBox: A generic library for exact linear algebra. In A. M. Cohen, X.-S. Gao, and N. Takayama, editors , ICMS'2002 , Proceedings of the 2002 International Congress of Mathematical Software, Beijing, China, pages 40--50. World Scientific Pub., August 2002. J.-G. Dumas, T. Gautier, M. Giesbrecht, P. Giorgi, B. Hovinen, E. Kaltofen, B. D. Saunders, W. J. Turner, and G. Villard. LinBox: A generic library for exact linear algebra. In A. M. Cohen, X.-S. Gao, and N. Takayama, editors, ICMS'2002, Proceedings of the 2002 International Congress of Mathematical Software, Beijing, China, pages 40--50. World Scientific Pub., August 2002."},{"key":"e_1_3_2_1_7_1","volume-title":"Commutative Algebra with a View Toward Algebraic Geometry","author":"Eisenbud D.","year":"1995","unstructured":"D. Eisenbud . Commutative Algebra with a View Toward Algebraic Geometry . Springer , 1995 . D. Eisenbud. Commutative Algebra with a View Toward Algebraic Geometry. Springer, 1995."},{"key":"e_1_3_2_1_8_1","volume-title":"Polynomial systems solving by fast linear algebra","author":"Faug\u00e8re J.-C.","year":"2013","unstructured":"J.-C. Faug\u00e8re , P. Gaudry , L. Huot , and G. Renault . Polynomial systems solving by fast linear algebra , 2013 . http:\/\/arxiv.org\/abs\/1304.6039. J.-C. Faug\u00e8re, P. Gaudry, L. Huot, and G. Renault. Polynomial systems solving by fast linear algebra, 2013. http:\/\/arxiv.org\/abs\/1304.6039."},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/780506.780516"},{"key":"e_1_3_2_1_10_1","first-page":"1 9158","volume-title":"Journal of Cryptology","author":"Faug\u00e8re J.-C.","year":"2013","unstructured":"J.-C. Faug\u00e8re , P. Gaudry , L. Huot , and G. Renault . Using symmetries in the index calculus for elliptic curves discrete logarithm . Journal of Cryptology , pages 1 -- 41 , 2013 . doi 10.1007\/s00145-013- 9158 - 9155 . J.-C. Faug\u00e8re, P. Gaudry, L. Huot, and G. Renault. Using symmetries in the index calculus for elliptic curves discrete logarithm. Journal of Cryptology, pages 1--41, 2013. doi 10.1007\/s00145-013-9158-5."},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1051"},{"key":"e_1_3_2_1_12_1","volume-title":"Symmetrized summation polynomials: Using small order torsion points to speed up elliptic curve index calculus","author":"Faug\u00e8re J.-C.","year":"2014","unstructured":"J.-C. Faug\u00e8re , L. Huot , A. Joux , G. Renault , and V. Vitse . Symmetrized summation polynomials: Using small order torsion points to speed up elliptic curve index calculus , 2014 . To appear in the proceedings of the 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2014). J.-C. Faug\u00e8re, L. Huot, A. Joux, G. Renault, and V. Vitse. Symmetrized summation polynomials: Using small order torsion points to speed up elliptic curve index calculus, 2014. To appear in the proceedings of the 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2014)."},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993886.1993908"},{"key":"e_1_3_2_1_14_1","unstructured":"J.-C. Faug\u00e8re and C. Mou. Sparse FGLM algorithms. http:\/\/hal.inria.fr\/hal-00807540 2013.  J.-C. Faug\u00e8re and C. Mou. Sparse FGLM algorithms. http:\/\/hal.inria.fr\/hal-00807540 2013."},{"key":"e_1_3_2_1_16_1","series-title":"LNCS","first-page":"247","volume-title":"Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Proceedings of AAECC-5","author":"Gianni P.","year":"1989","unstructured":"P. Gianni and T. Mora . Algebraic solution of systems of polynomial equations using Gr\u00f6bner bases . In Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Proceedings of AAECC-5 , volume 356 of LNCS , pages 247 -- 257 . Springer , 1989 . P. Gianni and T. Mora. Algebraic solution of systems of polynomial equations using Gr\u00f6bner bases. In Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Proceedings of AAECC-5, volume 356 of LNCS, pages 247--257. Springer, 1989."},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90032-3"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.5555\/3929.3939"},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/100216.100294"},{"key":"e_1_3_2_1_20_1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/3-540-12868-9_99","volume-title":"Computer Algebra","author":"Lazard D.","year":"1983","unstructured":"D. Lazard . Gr\u00f6bner bases, gaussian elimination and resolution of systems of algebraic equations . In J. van Hulzen, editor, Computer Algebra , volume 162 of Lecture Notes in Computer Science , pages 146 -- 156 . Springer Berlin\/Heidelberg , 1983 . D. Lazard. Gr\u00f6bner bases, gaussian elimination and resolution of systems of algebraic equations. In J. van Hulzen, editor, Computer Algebra, volume 162 of Lecture Notes in Computer Science, pages 146--156. Springer Berlin\/Heidelberg, 1983."},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1969.1054260"},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(02)00297-9"},{"key":"e_1_3_2_1_23_1","volume-title":"USA","author":"Morgan A.","year":"2009","unstructured":"A. Morgan . Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems . Society for Industrial and Applied Mathematics, Philadelphia, PA , USA , 2009 . A. Morgan. Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2009."},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/276698.276862"},{"key":"e_1_3_2_1_25_1","volume-title":"The oakley key determination protocol","author":"Orman H.","year":"1998","unstructured":"H. Orman . The oakley key determination protocol , 1998 . H. Orman. The oakley key determination protocol, 1998."},{"issue":"5","key":"e_1_3_2_1_27_1","first-page":"433","article-title":"Solving zero-dimensional systems through the rational univariate representation. Applicable Algebra in Engineering","volume":"9","author":"Rouillier F.","year":"1999","unstructured":"F. Rouillier . Solving zero-dimensional systems through the rational univariate representation. Applicable Algebra in Engineering , Communication and Computing , 9 ( 5 ): 433 -- 461 , 1999 . F. Rouillier. Solving zero-dimensional systems through the rational univariate representation. Applicable Algebra in Engineering, Communication and Computing, 9(5):433--461, 1999.","journal-title":"Communication and Computing"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/322217.322225"},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02165411"},{"key":"e_1_3_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214056"},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1986.1057137"},{"key":"e_1_3_2_1_32_1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1007\/3-540-09519-5_73","volume-title":"Probabilistic algorithms for sparse polynomials","author":"Zippel R.","year":"1979","unstructured":"R. Zippel . Probabilistic algorithms for sparse polynomials . In E. Ng, editor, Symbolic and Algebraic Computation, volume 72 of Lecture Notes in Computer Science , pages 216 -- 226 . Springer Berlin Heidelberg , 1979 . R. Zippel. Probabilistic algorithms for sparse polynomials. In E. Ng, editor, Symbolic and Algebraic Computation, volume 72 of Lecture Notes in Computer Science, pages 216--226. Springer Berlin Heidelberg, 1979."}],"event":{"name":"ISSAC '14: International Symposium on Symbolic and Algebraic Computation","location":"Kobe Japan","acronym":"ISSAC '14","sponsor":["ACM Association for Computing Machinery","SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"]},"container-title":["Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2608628.2608669","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2608628.2608669","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T18:55:59Z","timestamp":1750272959000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2608628.2608669"}},"subtitle":["a probabilistic approach"],"short-title":[],"issued":{"date-parts":[[2014,7,23]]},"references-count":30,"alternative-id":["10.1145\/2608628.2608669","10.1145\/2608628"],"URL":"https:\/\/doi.org\/10.1145\/2608628.2608669","relation":{},"subject":[],"published":{"date-parts":[[2014,7,23]]},"assertion":[{"value":"2014-07-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}