{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T04:56:50Z","timestamp":1764997010601},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642552199"},{"type":"electronic","value":"9783642552205"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-642-55220-5_3","type":"book-chapter","created":{"date-parts":[[2014,4,30]],"date-time":"2014-04-30T07:47:50Z","timestamp":1398844070000},"page":"40-57","source":"Crossref","is-referenced-by-count":5,"title":["Symmetrized Summation Polynomials: Using Small Order Torsion Points to Speed Up Elliptic Curve Index Calculus"],"prefix":"10.1007","author":[{"given":"Jean-Charles","family":"Faug\u00e8re","sequence":"first","affiliation":[]},{"given":"Louise","family":"Huot","sequence":"additional","affiliation":[]},{"given":"Antoine","family":"Joux","sequence":"additional","affiliation":[]},{"given":"Gu\u00e9na\u00ebl","family":"Renault","sequence":"additional","affiliation":[]},{"given":"Vanessa","family":"Vitse","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"#cr-split#-3_CR1.1","doi-asserted-by":"crossref","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput.\u00a024(3-4), 235-265 (1997)","DOI":"10.1006\/jsco.1996.0125"},{"key":"#cr-split#-3_CR1.2","unstructured":"Computational algebra and number theory, London (1993)"},{"issue":"1","key":"3_CR2","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. Compos. Math.\u00a0147(1), 75\u2013104 (2011)","journal-title":"Compos. Math."},{"key":"3_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/978-3-642-15582-6_17","volume-title":"Mathematical Software \u2013 ICMS 2010","author":"J.-C. Faug\u00e8re","year":"2010","unstructured":"Faug\u00e8re, J.-C.: FGb: A Library for Computing Gr\u00f6bner Bases. In: Fukuda, K., van der Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol.\u00a06327, pp. 84\u201387. Springer, Heidelberg (2010)"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.-C., Gaudry, P., Huot, L., Renault, G.: Using symmetries in the index calculus for elliptic curves discrete logarithm. J. Cryptology, 1\u201341 (2013), doi:10.1007\/s00145-013-9158-5.","DOI":"10.1007\/s00145-013-9158-5"},{"issue":"4","key":"3_CR5","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1006\/jsco.1993.1051","volume":"16","author":"J.-C. Faug\u00e8re","year":"1993","unstructured":"Faug\u00e8re, J.-C., Gianni, P., Lazard, D., Mora, T.: Efficient computation of zero-dimensional Gr\u00f6bner bases by change of ordering. J. Symbolic Comput.\u00a016(4), 329\u2013344 (1993)","journal-title":"J. Symbolic Comput."},{"issue":"12","key":"3_CR6","doi-asserted-by":"publisher","first-page":"1690","DOI":"10.1016\/j.jsc.2008.08.005","volume":"44","author":"P. Gaudry","year":"2008","unstructured":"Gaudry, P.: Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem. J. Symbolic Comput.\u00a044(12), 1690\u20131702 (2008)","journal-title":"J. Symbolic Comput."},{"issue":"1","key":"3_CR7","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s00145-001-0011-x","volume":"15","author":"P. Gaudry","year":"2002","unstructured":"Gaudry, P., Hess, F., Smart, N.P.: Constructive and destructive facets of Weil descent on elliptic curves. J. Cryptology\u00a015(1), 19\u201346 (2002)","journal-title":"J. Cryptology"},{"key":"3_CR8","unstructured":"Granger, R., Joux, A., Vitse, V.: New timings for oracle-assisted SDHP on the IPSEC Oakley \u2019Well Known Group\u2019 3 curve. Announcement on the NBRTHRY Mailing List (July 2010), \n                    \n                      http:\/\/listserv.nodak.edu\/archives\/nmbrthry.html"},{"key":"3_CR9","unstructured":"IETF. The Oakley key determination protocol. IETF RFC 2412 (1998)"},{"key":"3_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/978-3-642-29011-4_3","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"A. Joux","year":"2012","unstructured":"Joux, A., Vitse, V.: Cover and Decomposition Index Calculus on Elliptic Curves made practical: Application to a seemingly secure curve over \n                    \n                      \n                    \n                    $\\mathbb{F}_{p^6}$\n                  . In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol.\u00a07237, pp. 9\u201326. Springer, Heidelberg (2012)"},{"issue":"1","key":"3_CR11","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s00145-011-9116-z","volume":"26","author":"A. Joux","year":"2013","unstructured":"Joux, A., Vitse, V.: Elliptic curve discrete logarithm problem over small degree extension fields. J. Cryptology\u00a026(1), 119\u2013143 (2013)","journal-title":"J. Cryptology"},{"issue":"4","key":"3_CR12","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1515\/JMC.2008.014","volume":"2","author":"N. Koblitz","year":"2008","unstructured":"Koblitz, N., Menezes, A.: Another look at non-standard discrete log and Diffie-Hellman problems. J. Math. Cryptol.\u00a02(4), 311\u2013326 (2008)","journal-title":"J. Math. Cryptol."},{"key":"3_CR13","unstructured":"Semaev, I.A.: Summation polynomials and the discrete logarithm problem on elliptic curves. Cryptology ePrint Archive, Report 2004\/031 (2004)"},{"issue":"4","key":"3_CR14","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/BF01405086","volume":"15","author":"J.-P. Serre","year":"1972","unstructured":"Serre, J.-P.: Propri\u00e9t\u00e9s galoisiennes des points d\u2019ordre fini des courbes elliptiques. Invent. Math.\u00a015(4), 259\u2013331 (1972)","journal-title":"Invent. Math."},{"issue":"3","key":"3_CR15","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/S0747-7171(08)80018-1","volume":"9","author":"R. Zippel","year":"1990","unstructured":"Zippel, R.: Interpolating polynomials from their values. Journal of Symbolic Computation\u00a09(3), 375\u2013403 (1990)","journal-title":"Journal of Symbolic Computation"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2014"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-55220-5_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T14:31:44Z","timestamp":1558881104000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-55220-5_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783642552199","9783642552205"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-55220-5_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}