{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T21:29:14Z","timestamp":1775338154605,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642400834","type":"print"},{"value":"9783642400841","type":"electronic"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-40084-1_7","type":"book-chapter","created":{"date-parts":[[2013,8,14]],"date-time":"2013-08-14T05:56:37Z","timestamp":1376459797000},"page":"109-128","source":"Crossref","is-referenced-by-count":44,"title":["On the Function Field Sieve and the Impact of Higher Splitting Probabilities"],"prefix":"10.1007","author":[{"given":"Faruk","family":"G\u00f6lo\u011flu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Granger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gary","family":"McGuire","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jens","family":"Zumbr\u00e4gel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"1-2","key":"7_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1006\/inco.1998.2761","volume":"151","author":"L.M. Adleman","year":"1999","unstructured":"Adleman, L.M., Huang, M.D.A.: Function field sieve method for discrete logarithms over finite fields. Inform. and Comput.\u00a0151(1-2), 5\u201316 (1999)","journal-title":"Inform. and Comput."},{"key":"7_CR2","unstructured":"Bailey, D.V., Paar, C., Sarkozy, G., Hofri, M.: Computation in optimal extension fields. In: Conference on The Mathematics of Public Key Cryptography, The Fields Institute for Research in the Mathematical Sciences, pp. 12\u201317 (2000)"},{"issue":"3","key":"7_CR3","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/j.ffa.2003.08.004","volume":"10","author":"A.W. Bluher","year":"2004","unstructured":"Bluher, A.W.: On xq\u2009+\u20091\u2009+\u2009ax\u2009+\u2009b. Finite Fields and Their Applications\u00a010(3), 285\u2013305 (2004)","journal-title":"Finite Fields and Their Applications"},{"issue":"2","key":"7_CR4","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1090\/S0894-0347-1989-0965008-X","volume":"2","author":"F.R.K. Chung","year":"1989","unstructured":"Chung, F.R.K.: Diameters and eigenvalues. J. Amer. Math. Soc.\u00a02(2), 187\u2013196 (1989)","journal-title":"J. Amer. Math. Soc."},{"issue":"4","key":"7_CR5","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1109\/TIT.1984.1056941","volume":"30","author":"D. Coppersmith","year":"1984","unstructured":"Coppersmith, D.: Fast evaluation of logarithms in fields of characteristic two. IEEE Trans. Inform. Theory\u00a030(4), 587\u2013593 (1984)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"7_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/978-3-642-13190-5_14","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"J.-C. Faug\u00e8re","year":"2010","unstructured":"Faug\u00e8re, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic cryptanalysis of mcEliece variants with compact keys. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol.\u00a06110, pp. 279\u2013298. Springer, Heidelberg (2010)"},{"key":"7_CR7","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":"1","key":"7_CR8","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":"7_CR9","unstructured":"G\u00f6lo\u011flu, F., Granger, R., McGuire, G., Zumbr\u00e4gel, J.: Discrete Logarithms in GF(21971). NMBRTHRY list (February 19, 2013)"},{"key":"7_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1007\/11535218_5","volume-title":"Advances in Cryptology \u2013 CRYPTO 2005","author":"R. Granger","year":"2005","unstructured":"Granger, R., Vercauteren, F.: On the discrete logarithm problem on algebraic tori. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol.\u00a03621, pp. 66\u201385. Springer, Heidelberg (2005)"},{"key":"7_CR11","unstructured":"Granlund, T.: The GMP\u00a0development team: GNU MP: The GNU Multiple Precision Arithmetic Library, 5.0.5 edn (2012), \n                      \n                        http:\/\/gmplib.org\/"},{"issue":"1","key":"7_CR12","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s12095-009-0018-y","volume":"2","author":"T. Helleseth","year":"2010","unstructured":"Helleseth, T., Kholosha, A.: \n                      \n                        \n                      \n                      $x^{{2^l}+1}+x+a$\n                     and related affine polynomials over GF(2\n                      k\n                    ). Cryptogr. Commun.\u00a02(1), 85\u2013109 (2010)","journal-title":"Cryptogr. Commun."},{"key":"7_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/978-3-642-38348-9_11","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"A. Joux","year":"2013","unstructured":"Joux, A.: Faster index calculus for the medium prime case application to 1175-bit and 1425-bit finite fields. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol.\u00a07881, pp. 177\u2013193. Springer, Heidelberg (2013)"},{"key":"7_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1007\/3-540-45455-1_34","volume-title":"Algorithmic Number Theory","author":"A. Joux","year":"2002","unstructured":"Joux, A., Lercier, R.: The function field sieve is quite special. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol.\u00a02369, pp. 431\u2013445. Springer, Heidelberg (2002)"},{"issue":"242","key":"7_CR15","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1090\/S0025-5718-02-01482-5","volume":"72","author":"A. Joux","year":"2003","unstructured":"Joux, A., Lercier, R.: Improvements to the general number field sieve for discrete logarithms in prime fields: a comparison with the gaussian integer method. Math. Comput.\u00a072(242), 953\u2013967 (2003)","journal-title":"Math. Comput."},{"key":"7_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1007\/11761679_16","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"A. Joux","year":"2006","unstructured":"Joux, A., Lercier, R.: The function field sieve in the medium prime case. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 254\u2013270. Springer, Heidelberg (2006)"},{"key":"7_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/978-3-642-10868-6_21","volume-title":"Cryptography and Coding","author":"A. Joux","year":"2009","unstructured":"Joux, A., Lercier, R., Naccache, D., Thom\u00e9, E.: Oracle-assisted static diffie-hellman is easier than discrete logarithms. In: Parker, M.G. (ed.) Cryptography and Coding 2009. LNCS, vol.\u00a05921, pp. 351\u2013367. Springer, Heidelberg (2009)"},{"key":"7_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/3-540-38424-3_8","volume-title":"Advances in Cryptology - CRYPTO \u201990","author":"B.A. LaMacchia","year":"1991","unstructured":"LaMacchia, B.A., Odlyzko, A.M.: Solving large sparse linear systems over finite fields. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol.\u00a0537, pp. 109\u2013133. Springer, Heidelberg (1991)"},{"key":"7_CR19","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0091534","volume-title":"The development of the number field sieve","author":"A.K. Lenstra","year":"1993","unstructured":"Lenstra, A.K., Lenstra Jr., H.W.: The development of the number field sieve. Lecture Notes in Mathematics, vol.\u00a01554. Springer, Heidelberg (1993)"},{"issue":"193","key":"7_CR20","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1090\/S0025-5718-1991-1052099-2","volume":"56","author":"H.W. Lenstra Jr.","year":"1991","unstructured":"Lenstra Jr., H.W.: Finding isomorphisms between finite fields. Math. Comp.\u00a056(193), 329\u2013347 (1991)","journal-title":"Math. Comp."},{"key":"7_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1007\/978-3-642-05445-7_24","volume-title":"Selected Areas in Cryptography","author":"R. Misoczki","year":"2009","unstructured":"Misoczki, R., Barreto, P.S.L.M.: Compact McEliece keys from Goppa codes. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol.\u00a05867, pp. 376\u2013392. Springer, Heidelberg (2009)"},{"issue":"143","key":"7_CR22","first-page":"918","volume":"32","author":"J.M. Pollard","year":"1978","unstructured":"Pollard, J.M.: Monte carlo methods for index computation (mod p). Math. Comp.\u00a032(143), 918\u2013924 (1978)","journal-title":"Math. Comp."},{"key":"7_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/978-3-540-45146-4_21","volume-title":"Advances in Cryptology - CRYPTO 2003","author":"K. Rubin","year":"2003","unstructured":"Rubin, K., Silverberg, A.: Torus-based cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol.\u00a02729, pp. 349\u2013365. Springer, Heidelberg (2003)"},{"key":"7_CR24","unstructured":"Shoup, V.: NTL: A library for doing number theory, 5.5.2 edn. (2009), \n                      \n                        http:\/\/www.shoup.net\/ntl\/"},{"key":"7_CR25","unstructured":"Wagstaff, S., et al.: The Cunningham Project, \n                      \n                        http:\/\/homes.cerias.purdue.edu\/~ssw\/cun\/index.html"},{"issue":"219","key":"7_CR26","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1090\/S0025-5718-97-00835-1","volume":"66","author":"D. Wan","year":"1997","unstructured":"Wan, D.: Generators and irreducible polynomials over finite fields. Math. Comp.\u00a066(219), 1195\u20131212 (1997)","journal-title":"Math. Comp."}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2013"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-40084-1_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T11:28:16Z","timestamp":1558006096000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-40084-1_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642400834","9783642400841"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-40084-1_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}