{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:57:58Z","timestamp":1772283478878,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":10,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642420009","type":"print"},{"value":"9783642420016","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-42001-6_7","type":"book-chapter","created":{"date-parts":[[2013,11,21]],"date-time":"2013-11-21T04:25:02Z","timestamp":1385007902000},"page":"94-107","source":"Crossref","is-referenced-by-count":9,"title":["Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Gr\u00f6bner Basis Methods \u2013 An Experimental Study"],"prefix":"10.1007","author":[{"given":"Michael","family":"Shantz","sequence":"first","affiliation":[]},{"given":"Edlyn","family":"Teske","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"7_CR1","first-page":"177","volume":"3","author":"L. Bettale","year":"2009","unstructured":"Bettale, L., Faug\u00e8re, J.-C., Perret, L.: Hybrid approach for solving multivariate systems over finite fields. J. Math. Crypt.\u00a03, 177\u2013197 (2009)","journal-title":"J. Math. Crypt."},{"key":"7_CR2","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1145\/321662.321666","volume":"18","author":"G. Collins","year":"1971","unstructured":"Collins, G.: The calculation of multivariate polynomial resultants. Journal of the Association of Computing Machinery\u00a018, 515\u2013522 (1971)","journal-title":"Journal of the Association of Computing Machinery"},{"issue":"1","key":"7_CR3","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1112\/S0010437X10005075","volume":"147","author":"C. Diem","year":"2011","unstructured":"Diem, C.: On the discrete logarithm problem in elliptic curves. Compositio Mathematica\u00a0147(1), 75\u2013104 (2011)","journal-title":"Compositio Mathematica"},{"key":"7_CR4","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0022-4049(99)00005-5","volume":"139","author":"J.-C. Faug\u00e8re","year":"1999","unstructured":"Faug\u00e8re, J.-C.: A new efficient algorithm for computing Gr\u00f6bner bases (F4). Journal of Pure and Applied Algebra\u00a0139, 61\u201388 (1999)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"7_CR5","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), pp. 75\u201383. ACM Press (2002)","DOI":"10.1145\/780506.780516"},{"key":"7_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/978-3-642-29011-4_4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"J.-C. Faug\u00e8re","year":"2012","unstructured":"Faug\u00e8re, J.-C., Perret, L., Petit, C., Renault, G.: Improving the complexity of index calculus algorithms in elliptic curves over binary fields. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol.\u00a07237, pp. 27\u201344. Springer, Heidelberg (2012)"},{"issue":"12","key":"7_CR7","doi-asserted-by":"publisher","first-page":"1690","DOI":"10.1016\/j.jsc.2008.08.005","volume":"44","author":"P. Gaudry","year":"2009","unstructured":"Gaudry, P.: Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem. J. Symbolic Computation\u00a044(12), 1690\u20131702 (2009)","journal-title":"J. Symbolic Computation"},{"key":"7_CR8","unstructured":"Bettale, L.: Hybrid approach for solving multivariate polynomial systems over finite fields, \n                    \n                      http:\/\/www-polsys.lip6.fr\/~bettale\/hybrid"},{"key":"7_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/978-3-642-34961-4_28","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"C. Petit","year":"2012","unstructured":"Petit, C., Quisquater, J.-J.: On polynomial systems arising from a Weil descent. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol.\u00a07658, pp. 451\u2013466. Springer, Heidelberg (2012)"},{"key":"7_CR10","unstructured":"Semaev, I.: Summation polynomials and the discrete logarithm problem on elliptic curves, Cryptology ePrint Archive Report 2004\/031 (2004), \n                    \n                      http:\/\/eprint.iacr.org\/2004\/031\/"}],"container-title":["Lecture Notes in Computer Science","\u2018"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-42001-6_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T13:00:09Z","timestamp":1558702809000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-42001-6_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642420009","9783642420016"],"references-count":10,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-42001-6_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}