{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T21:12:25Z","timestamp":1725484345089},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540438618"},{"type":"electronic","value":"9783540454502"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002]]},"DOI":"10.1007\/3-540-45450-0_17","type":"book-chapter","created":{"date-parts":[[2007,5,19]],"date-time":"2007-05-19T16:53:10Z","timestamp":1179593590000},"page":"203-213","source":"Crossref","is-referenced-by-count":0,"title":["Compact Representation of Domain Parameters of Hyperelliptic Curve Cryptosystems"],"prefix":"10.1007","author":[{"given":"Fangguo","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Shengli","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Kwangjo","family":"Kim","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2002,6,21]]},"reference":[{"key":"17_CR1","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/3-540-58691-1_39","volume-title":"ANTS-1, Algorithmic Number Theory","author":"L. Adleman","year":"1994","unstructured":"L. Adleman, J. De Marrais, 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-1, Algorithmic Number Theory, Editors L.M. Adlemand and M-D. Huang, Springer-Verlag, LNCS 877, pp. 28\u201340, 1994."},{"key":"17_CR2","series-title":"Lect Notes Comput Sci","first-page":"1","volume-title":"ANTS-2","author":"L. Adleman","year":"1996","unstructured":"L. Adleman, M.-D Huang, Counting rational points on curves and abelian varieties over finite fields, In ANTS-2:, LNCS 1122, Springer-Verlag, pp. 1\u201316, 1996."},{"key":"17_CR3","doi-asserted-by":"publisher","first-page":"95","DOI":"10.2307\/2007876","volume":"48","author":"D.G. Cantor","year":"1987","unstructured":"D.G. Cantor, Computing in the Jacobian of a hyperelliptic curve, Mathematics of Computation, Volume 48, pp. 95\u2013101, 1987.","journal-title":"Mathematics of Computation"},{"key":"17_CR4","doi-asserted-by":"publisher","first-page":"865","DOI":"10.2307\/2153546","volume":"62","author":"G. Frey","year":"1994","unstructured":"G. Frey and H. R\u00fcck, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Mathematics of Computation, 62, pp. 865\u2013874, 1994.","journal-title":"Mathematics of Computation"},{"key":"17_CR5","unstructured":"S.D. Galbraith, Supersingular curves in cryptography. Available at http:\/\/www.cs.bris.ac.uk\/stenve"},{"key":"17_CR6","doi-asserted-by":"crossref","unstructured":"S.D. Galbraith, Weil descent of Jacobians. Presented at WCC 2001. Available at http:\/\/www.cs.bris.ac.uk\/stenve .","DOI":"10.1016\/S1571-0653(04)00198-2"},{"key":"17_CR7","series-title":"Lect Notes Comput Sci","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/3-540-45539-6_2","volume-title":"Eurocrypt 2000","author":"P. Gaudry","year":"2000","unstructured":"P. Gaudry, An algorithm for solving the discrete log problem on hyperelliptic curves, In B. Preneel(ed.), Eurocrypt 2000, LNCS 1807, Springer-Verlag, pp. 19\u201334, 2000."},{"key":"17_CR8","doi-asserted-by":"crossref","unstructured":"P. Gaudry and R. Harley, Counting Points on Hyperelliptic Curves over finite fields. Available at http:\/\/www.cs.bris.ac.uk\/Tools\/Reports\/Abstract\/2000-gaudry.htm","DOI":"10.1007\/10722028_18"},{"key":"17_CR9","unstructured":"D.E. Knuth, and E. Donald E., Seminumerical Algorithms, Addison-Wesley, 1981."},{"key":"17_CR10","doi-asserted-by":"publisher","first-page":"203","DOI":"10.2307\/2007884","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz, Elliptic Curve Crypto systems, Mathematics of Computation, 48, pp. 203\u2013209, 1987.","journal-title":"Mathematics of Computation"},{"key":"17_CR11","doi-asserted-by":"crossref","unstructured":"N. Koblitz, Hyperelliptic cryptography, J.of Crypto., No. 1, pp. 139\u2013150, 1989.","DOI":"10.1007\/BF02252872"},{"key":"17_CR12","doi-asserted-by":"publisher","first-page":"729","DOI":"10.2307\/2154650","volume":"342","author":"P. Lockhart","year":"1994","unstructured":"P. Lockhart, On the discriminant of a hyperelliptic curve, Trans. Amer. Math. Soc. 342 No. 2, pp. 729\u2013752, 1994.","journal-title":"Trans. Amer. Math. Soc."},{"key":"17_CR13","volume-title":"Algebraic Aspects of Cryptography","author":"A. Menezes","year":"1998","unstructured":"A. Menezes, Y. Wu, R. Zuccherato, An Elementary Introduction to Hyperelliptic Curves. In: Koblitz, N., Algebraic Aspects of Cryptography, Springer-Verlag Berlin Heidelberg 1998. Available at http:\/\/www.cacr.math.uwaterloo.ca\/techreports\/ 1997\/techreports97.html"},{"key":"17_CR14","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/3-540-39799-X_31","volume-title":"Advances in Cryptology-CRYPTO\u201985","author":"V.S. Miller","year":"1986","unstructured":"V.S. Miller, Use of Elliptic Curve in Cryptography, In Advances in Cryptology-CRYPTO\u201985 (Santa Barbara,Calif.,1985), LNCS. 218, Spring-Verlag, pp. 417\u2013426, 1986."},{"key":"17_CR15","doi-asserted-by":"publisher","first-page":"745","DOI":"10.2307\/2008445","volume":"55","author":"J. Pila","year":"1996","unstructured":"J. Pila, Frobenius maps of abelian varieties and finding roots of unity in finite fields. Math.Comp., 55, pp. 745\u2013763, 1996.","journal-title":"Math.Comp."},{"key":"17_CR16","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1090\/S0025-5718-99-01043-1","volume":"68","author":"H.G. R\u00fcck","year":"1999","unstructured":"H.G. R\u00fcck, On the discrete logarithms in the divisor class group of curves, Math.Comp., 68, pp. 805\u2013806, 1999.","journal-title":"Math.Comp."},{"key":"17_CR17","unstructured":"T. Satoh, Canonical Lifting of Elliptic Curves and p-Adic Point Counting-Theoretical Background, Workshop on Elliptic Curve Cryptography-ECC\u201900, 2000. Available at http:\/\/www.exp-math.uni-essen.de\/ galbra\/eccslides\/eccslides.html"},{"key":"17_CR18","first-page":"81","volume":"47","author":"T. Satoh","year":"1998","unstructured":"T. Satoh, and K. Araki, Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, Commentari Math. Univ. St. Pauli 47 (1998), 81\u201392.","journal-title":"Commentari Math. Univ. St. Pauli"},{"key":"17_CR19","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1090\/S0025-5718-98-00887-4","volume":"67","author":"I.A. Semaev","year":"1998","unstructured":"I.A. Semaev, Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p, Mathematics of Computation 67 (1998), 353\u2013356.","journal-title":"Mathematics of Computation"},{"key":"17_CR20","unstructured":"J. Scholten, and Huijun Zhu, Hyperelliptic Supersingular Curves over Fields of Characteristic 2. Available at http:\/\/www.math.berkeley.edu\/ zhu\/preprints.html"},{"key":"17_CR21","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s001459900052","volume":"12","author":"N.P. Smart","year":"1999","unstructured":"N.P. Smart, The discrete logarithms problem on elliptic curves of trace one, Journal of Cryptology 12 (1999), 193\u2013196.","journal-title":"Journal of Cryptology"},{"key":"17_CR22","unstructured":"N.P. Smart, Compressed ECC Parameters. Available at http:\/\/www.secg.org\/collateral\/compressed_ecc.pdf"},{"key":"17_CR23","volume-title":"Technical Reports","author":"J.A. Solinas","year":"1999","unstructured":"J.A. Solinas, Generalized Mersenne number, Technical Reports, CACR, Waterloo, 1999. Available at: http:\/\/www.cacr.math.uwaterloo.ca\/techreports\/1999\/tech_reports99.html"}],"container-title":["Lecture Notes in Computer Science","Information Security and Privacy"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45450-0_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T01:39:15Z","timestamp":1556415555000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45450-0_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002]]},"ISBN":["9783540438618","9783540454502"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/3-540-45450-0_17","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2002]]}}}