{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:47:28Z","timestamp":1776844048095,"version":"3.51.2"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,2,10]],"date-time":"2010-02-10T00:00:00Z","timestamp":1265760000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Cryptol"],"published-print":{"date-parts":[[2011,1]]},"DOI":"10.1007\/s00145-010-9057-y","type":"journal-article","created":{"date-parts":[[2010,2,9]],"date-time":"2010-02-09T14:19:21Z","timestamp":1265725161000},"page":"24-41","update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["An L(1\/3) Discrete Logarithm Algorithm for Low Degree Curves"],"prefix":"10.1007","volume":"24","author":[{"given":"Andreas","family":"Enge","sequence":"first","affiliation":[]},{"given":"Pierrick","family":"Gaudry","sequence":"additional","affiliation":[]},{"given":"Emmanuel","family":"Thom\u00e9","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,2,10]]},"reference":[{"issue":"1","key":"9057_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1006\/inco.1998.2761","volume":"151","author":"L.M. Adleman","year":"1999","unstructured":"L.M. Adleman, M.-D. Huang, Function field sieve methods for discrete logarithms over finite fields. Inf. Comput.\n                           151(1), 5\u201316 (1999)","journal-title":"Inf. Comput."},{"key":"9057_CR2","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/3-540-58691-1_39","volume-title":"ANTS-I","author":"L.M. Adleman","year":"1994","unstructured":"L.M. Adleman, J. DeMarrais, M.-D. Huang, A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields, in ANTS-I, ed. by L. Adleman, M.-D. Huang. Lecture Notes in Comput. Sci., vol. 877 (Springer, Berlin, 1994), pp. 28\u201340"},{"key":"9057_CR3","series-title":"Studies in Advanced Mathematics","first-page":"221","volume-title":"Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A.O.L. Atkin","author":"R.L. Bender","year":"1998","unstructured":"R.L. Bender, C. Pomerance, Rigorous discrete logarithm computations in finite fields via smooth polynomials, in Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A.O.L. Atkin, ed. by D.A. Buell, J.T. Teitelbaum. Studies in Advanced Mathematics, vol. 7 (American Mathematical Society, Providence, 1998), pp. 221\u2013232"},{"key":"9057_CR4","series-title":"Lecture Notes in Math.","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/BFb0091539","volume-title":"The development of the number field sieve","author":"J.P. Buhler","year":"1993","unstructured":"J.P. Buhler, A.K. Lenstra, J.M. Pollard, Factoring integers with the number field sieve, in The development of the number field sieve, ed. by A.K. Lenstra, H.W. Lenstra Jr. Lecture Notes in Math., vol. 1554 (Springer, Berlin, 1993), pp. 50\u201394"},{"key":"9057_CR5","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1007\/978-3-540-79456-1_20","volume-title":"ANTS-VIII","author":"W. Castryck","year":"2008","unstructured":"W. Castryck, H. Hubrechts, F. Vercauteren, Computing zeta functions in families of C\n                           \n                    ab\n                   curves using deformation, in ANTS-VIII, ed. by A. van\u00a0der Poorten, A. Stein. Lecture Notes in Comput. Sci., vol. 5011 (Springer, Berlin, 2008), pp. 296\u2013311"},{"issue":"4","key":"9057_CR6","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1109\/TIT.1984.1056941","volume":"IT\u201330","author":"D. Coppersmith","year":"1984","unstructured":"D. Coppersmith, Fast evaluation of logarithms in fields of characteristic two. IEEE Trans. Inf. Theory\n                           IT\u201330(4), 587\u2013594 (1984)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9057_CR7","first-page":"17","volume-title":"Public-key Cryptography and Computational Number Theory","author":"J.-M. Couveignes","year":"2001","unstructured":"J.-M. Couveignes, Algebraic groups and discrete logarithm, in Public-key Cryptography and Computational Number Theory (de Gruyter, Berlin, 2001), pp. 17\u201327"},{"key":"9057_CR8","unstructured":"C. Diem, An index calculus algorithm for non-singular plane curves of high genus (2006). Talk at ECC 2006 Workshop, slides available at \n                    https:\/\/linproxy.fan.workers.dev:443\/http\/www.cacr.math.uwaterloo.ca\/conferences\/2006\/ecc2006\/diem.pdf\n                    \n                  ."},{"key":"9057_CR9","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/11792086_38","volume-title":"ANTS-VII","author":"C. Diem","year":"2006","unstructured":"C. Diem, An index calculus algorithm for plane curves of small degree, in ANTS-VII, ed. by F. He\u00df, S. Pauli, M. Pohst. Lecture Notes in Comput. Sci., vol. 4076 (Springer, Berlin, 2006), pp. 543\u2013557"},{"key":"9057_CR10","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1007\/s00145-007-9014-6","volume":"21","author":"C. Diem","year":"2008","unstructured":"C. Diem, E. Thom\u00e9, Index calculus in class groups of non-hyperelliptic curves of genus three. J. Cryptol.\n                           21, 593\u2013611 (2008)","journal-title":"J. Cryptol."},{"key":"9057_CR11","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1090\/S0025-5718-01-01363-1","volume":"71","author":"A. Enge","year":"2002","unstructured":"A. Enge, Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time. Math. Comput.\n                           71, 729\u2013742 (2002)","journal-title":"Math. Comput."},{"key":"9057_CR12","series-title":"Contemporary Mathematics","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1090\/conm\/461\/08988","volume-title":"Finite Fields and Applications","author":"A. Enge","year":"2008","unstructured":"A. Enge, Discrete logarithms in curves over finite fields, in Finite Fields and Applications, ed. by G.L. Mullen, D. Panario, I.E. Shparlinski. Contemporary Mathematics, vol. 461 (American Mathematical Society, Providence, 2008), pp. 119\u2013139"},{"key":"9057_CR13","doi-asserted-by":"publisher","first-page":"83","DOI":"10.4064\/aa102-1-6","volume":"102","author":"A. Enge","year":"2002","unstructured":"A. Enge, P. Gaudry, A general framework for subexponential discrete logarithm algorithms. Acta Arith.\n                           102, 83\u2013103 (2002)","journal-title":"Acta Arith."},{"key":"9057_CR14","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/978-3-540-72540-4_22","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2007","author":"A. Enge","year":"2007","unstructured":"A. Enge, P. Gaudry, An L(1\/3+\u03b5) algorithm for the discrete logarithm problem for low degree curves, in Advances in Cryptology\u2014EUROCRYPT 2007, ed. by M. Naor. Lecture Notes in Comput. Sci., vol.\u00a04515 (Springer, Berlin, 2007), pp. 379\u2013393"},{"key":"9057_CR15","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1090\/S0025-5718-01-01352-7","volume":"71","author":"A. Enge","year":"2002","unstructured":"A. Enge, A. Stein, Smooth ideals in hyperelliptic function fields. Math. Comput.\n                           71, 1219\u20131230 (2002)","journal-title":"Math. Comput."},{"key":"9057_CR16","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1090\/S0025-5718-06-01900-4","volume":"76","author":"P. Gaudry","year":"2007","unstructured":"P. Gaudry, E. Thom\u00e9, N. Th\u00e9riault, C. Diem, A double large prime variation for small genus hyperelliptic index calculus. Math. Comput.\n                           76, 475\u2013492 (2007)","journal-title":"Math. Comput."},{"issue":"1","key":"9057_CR17","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1137\/0406010","volume":"6","author":"D.M. Gordon","year":"1993","unstructured":"D.M. Gordon, Discrete logarithms in GF(p) using the number field sieve. SIAM J. Discrete Math.\n                           6(1), 124\u2013138 (1993)","journal-title":"SIAM J. Discrete Math."},{"key":"9057_CR18","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1006\/jsco.2001.0513","volume":"33","author":"F. He\u00df","year":"2002","unstructured":"F. He\u00df, Computing Riemann\u2013Roch spaces in algebraic function fields and related topics. J. Symb. Comput.\n                           33, 425\u2013445 (2002)","journal-title":"J. Symb. Comput."},{"key":"9057_CR19","unstructured":"F. He\u00df, Computing relations in divisor class groups of algebraic curves over finite fields. Preprint (2004)"},{"key":"9057_CR20","series-title":"Mathematical Sciences Research Institute Publications","first-page":"579","volume-title":"Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography","author":"A.G.B. Lauder","year":"2008","unstructured":"A.G.B. Lauder, D. Wan, Counting points on varieties over finite fields of small characteristic, in Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography, ed. by J.P. Buhler, P. Stevenhagen. Mathematical Sciences Research Institute Publications, vol. 44 (Cambridge University Press, Cambridge, 2008), pp. 579\u2013612"},{"key":"9057_CR21","unstructured":"E. Manstavi\u010dius, Semigroup elements free of large prime factors, in New Trends in Probability and Statistic, ed. by F. Schweiger, E. Manstavi\u010dius (1992), pp.\u00a0135\u2013153"},{"key":"9057_CR22","unstructured":"M. Minzlaff, Computing zeta functions of superelliptic curves in larger characteristic, in Proc. 1st International Conference on Symbolic Computation and Cryptography (SCC08) (2008)"},{"key":"9057_CR23","first-page":"1398","volume":"J81-A","author":"S. Miura","year":"1998","unstructured":"S. Miura, Linear codes on affine algebraic curves. IEICE Transactions\n                           J81-A, 1398\u20131421 (1998). In Japanese. English summary by Ryutaroh Matsumoto available at \n                    https:\/\/linproxy.fan.workers.dev:443\/http\/www.rmatsumoto.org\/cab.pdf","journal-title":"IEICE Transactions"},{"issue":"226","key":"9057_CR24","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1090\/S0025-5718-99-01040-6","volume":"68","author":"V. M\u00fcller","year":"1999","unstructured":"V. M\u00fcller, A. Stein, C. Thiel, Computing discrete logarithms in real quadratic congruence function fields of large genus. Math. Comput.\n                           68(226), 807\u2013822 (1999)","journal-title":"Math. Comput."}],"container-title":["Journal of Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s00145-010-9057-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/article\/10.1007\/s00145-010-9057-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s00145-010-9057-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s00145-010-9057-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T08:45:32Z","timestamp":1586335532000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/10.1007\/s00145-010-9057-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,10]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["9057"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1007\/s00145-010-9057-y","relation":{},"ISSN":["0933-2790","1432-1378"],"issn-type":[{"value":"0933-2790","type":"print"},{"value":"1432-1378","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,10]]},"assertion":[{"value":"14 May 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 December 2009","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2010","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}