{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T22:45:34Z","timestamp":1648507534900},"publisher-location":"Berlin, Heidelberg","reference-count":29,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540646938","type":"print"},{"value":"9783540691051","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998]]},"DOI":"10.1007\/bfb0054023","type":"book-chapter","created":{"date-parts":[[2006,6,7]],"date-time":"2006-06-07T07:42:35Z","timestamp":1149666155000},"page":"164-181","source":"Crossref","is-referenced-by-count":13,"title":["Secure hyperelliptic cryptosystems and their performance"],"prefix":"10.1007","author":[{"given":"Yasuyuki","family":"Sakai","sequence":"first","affiliation":[]},{"given":"Kouichi","family":"Sakurai","sequence":"additional","affiliation":[]},{"given":"Hirokazu","family":"Ishizuka","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,5,24]]},"reference":[{"key":"14_CR1","doi-asserted-by":"crossref","unstructured":"L.M. Adleman, J. DeMarrais and M. Huang, \u201dA Subexponential Algorithm for Discrete Logarithm over the Rational Subgroup of the Jacobians of Large Genus Hyperelliptic Curves over Finite Fields\u201d, Proc. of ANTS1, LNCS, vol. 877, Springer-Verlag, (1994), 28\u201340","DOI":"10.1007\/3-540-58691-1_39"},{"issue":"No.5","key":"14_CR2","doi-asserted-by":"publisher","first-page":"804","DOI":"10.1109\/49.223883","volume":"11","author":"G.B. Agnew","year":"1993","unstructured":"G.B. Agnew, R.C. Mullin and S.A. Vanstone, \u201dAn Implementation of Elliptic Curve Cryptosystems Over % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr-epeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa% aaleaacaaIYaWaaWbaaWqabeaacaaIXaGaaGynaiaaiwdaaaaaleqa% aaaa!3A10! $$F_{2^{155} }$$ \u201d, IEEE J. Selected Areas in Communications11, No.5 (1993), 804\u2013813","journal-title":"IEEE J. Selected Areas in Communications"},{"key":"14_CR3","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1007\/3-540-46416-6_27","volume":"547","author":"T. Beth","year":"1991","unstructured":"T. Beth and F. Scaefer, \u201dNon supersingular elliptic curves for public key cryptosystems\u201d, Advances in Cryptology \u2014 EUROCRYPT '91, Lecture Notes in Computer Science, 547, pp.316\u2013327 (1991).","journal-title":"Advances in Cryptology \u2014 EUROCRYPT '91, Lecture Notes in Computer Science"},{"issue":"No.177","key":"14_CR4","doi-asserted-by":"publisher","first-page":"95","DOI":"10.2307\/2007876","volume":"48","author":"D.G. Cantor","year":"1987","unstructured":"D.G. Cantor, \u201dComputing in the Jacobian of a Hyperelliptic Curve\u201d, Math. Comp, 48, No.177 (1987), 95\u2013101","journal-title":"Math. Comp"},{"key":"14_CR5","doi-asserted-by":"crossref","unstructured":"J. Chao, K. Tanaka, and S. Tsujii, \u201dDesign of elliptic curves with control-lable lower boundary of extension degree for reduction attacks\u201d, Advances in Cryptology \u2014 Crypto'94, Springer-Verlag, (1994), 50\u201355.","DOI":"10.1007\/3-540-48658-5_6"},{"key":"14_CR6","unstructured":"G. Frey, \u201d Aspects of DL-systems based on hyperelliptic curves\u201d, Keynote Lecture in Waterloo-Workshop on Elliptic Curve Discrete Logarithm Problem, 4th of Nov. (1997)."},{"issue":"No.206","key":"14_CR7","doi-asserted-by":"publisher","first-page":"865","DOI":"10.2307\/2153546","volume":"62","author":"G. Frey","year":"1994","unstructured":"G. Frey and H.G. R\u00fcck, \u201dA Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves\u201d, Math. Comp, 62, No.206 (1994), 865\u2013874","journal-title":"Math. Comp"},{"key":"14_CR8","first-page":"31","volume":"44","author":"T. Itoh","year":"1986","unstructured":"T. Itoh, O. Teechai and S. Tsujii, \u201dA fast algorithm for computing multiplicative inverse in GF(2t) using normal bases\u201d (in Japanese), J. Society for Electronic Communications (Japan), 44, (1986), 31\u201336.","journal-title":"J. Society for Electronic Communications (Japan)"},{"key":"14_CR9","volume-title":"The Art of Computer Programing, Vol.2, Seminumerical Algo-rithm","author":"D.E. Knuth","year":"1981","unstructured":"D.E. Knuth, \u201dThe Art of Computer Programing, Vol.2, Seminumerical Algo-rithm\u201d, Addison-Wesley, Reading MA, 2nd edition (1981)","edition":"2nd edition"},{"key":"14_CR10","doi-asserted-by":"publisher","first-page":"203","DOI":"10.2307\/2007884","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz, \u201dElliptic curve cryptosystems\u201d, Mathematics of Computation, 48 (1987), 203\u2013209.","journal-title":"Mathematics of Computation"},{"key":"14_CR11","doi-asserted-by":"crossref","unstructured":"N. Koblitz, \u201dA Family of Jacobians Suitable for Discrete Log Cryptosystems\u201d, Advances in Cryptology \u2014 Crypto'88, Springer-Verlag, (1990), 94\u201399","DOI":"10.1007\/0-387-34799-2_8"},{"key":"14_CR12","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF02252872","volume":"1","author":"N. Koblitz","year":"1989","unstructured":"N. Koblitz, \u201dHyperelliptic Cryptosystems\u201d, J.Cryptology, 1 (1989), 139\u2013150","journal-title":"J.Cryptology"},{"key":"14_CR13","unstructured":"N. Koblitz, \u201dA Very Easy Way to Generate Curves over Prime Fields for Hyperelliptic Cryptosystems\u201d, Crypto'97 Rump Talk (1997)"},{"key":"14_CR14","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/3-540-39799-X_31","volume":"218","author":"V. Miller","year":"1986","unstructured":"V. Miller, \u201dUses of elliptic curves in cryptography\u201d, Lecture Notes in Computer Science, 218 (1986), 417\u2013426. (Advances in Cryptology \u2014 CRYPTO '85.)","journal-title":"Lecture Notes in Computer Science"},{"key":"14_CR15","first-page":"9","volume":"97\u201330","author":"K. Matsuo","year":"1997","unstructured":"K. Matsuo, J. Chao and S.Tsujii, \u201dDesign of Cryptosystems Based on Abelian Varieties over Extension Fields\u201d, IEICE ISEC, 97\u201330 (1997), 9\u201318","journal-title":"IEICE ISEC"},{"key":"14_CR16","doi-asserted-by":"crossref","unstructured":"A. Miyaji, \u201dElliptic curve over Fp suitable for cryptosystems\u201d, Advances in Cryptology \u2014 Asiacrypt'92, Springer-Verlag, (1993), 479\u2013491.","DOI":"10.1007\/3-540-57220-1_86"},{"key":"14_CR17","first-page":"50","volume":"E76-A","author":"A. Miyaji","year":"1993","unstructured":"A. Miyaji, \u201dElliptic curve cryptosystems immune to any reduction into the discrete logarithm problem\u201d, IEICE Trans., Fundamentals, E76-A (1993), pp. 50\u201354.","journal-title":"IEICE Trans., Fundamentals"},{"key":"14_CR18","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A.J. Menezes","year":"1993","unstructured":"A.J. Menezes, T. Okamoto and S.A. Vanstone, \u201dReducing elliptic curve logarithm to logarithm in a finite field\u201d, IEEE Trans. on IT, 39, (1993), 1639\u20131646","journal-title":"IEEE Trans. on IT"},{"key":"14_CR19","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/0166-218X(88)90090-X","volume":"22","author":"R.C. Mullin","year":"1988\/89","unstructured":"R.C. Mullin, I.M. Onyszchuk, S.A. Vanstone and R.M. Wilson,\u201dOptimal Normal Bases in GF(pn)\u201d, Discrete Applied Mathematics, 22, (1988\/89), 149\u2013161","journal-title":"Discrete Applied Mathematics"},{"key":"14_CR20","doi-asserted-by":"crossref","unstructured":"A. Odlyzko, \u201dDiscrete logarithm and their cryptographic significance\u201d, Advances in Cryptology \u2014 Eurocrypto'84, Springer-Verlag, (1985), 224\u2013314","DOI":"10.1007\/3-540-39757-4_20"},{"issue":"No.206","key":"14_CR21","doi-asserted-by":"publisher","first-page":"745","DOI":"10.2307\/2008445","volume":"55","author":"J. Pila","year":"1990","unstructured":"J. Pila, \u201dFrobenius maps of abelian varieties and finding roots of unity in finite fields\u201d, Math. Comp, 55, No.206 (1990), 745\u2013763.","journal-title":"Math. Comp"},{"key":"14_CR22","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/TIT.1978.1055817","volume":"24","author":"S.C. Pohlig","year":"1978","unstructured":"S.C. Pohlig and M.E. Hellman, \u201dAn improved algorithm for computing logarithms over GF(p) and its cryptographic significance\u201d, IEEE Trans. on IT, 24, (1978), 106\u2013110","journal-title":"IEEE Trans. on IT"},{"key":"14_CR23","unstructured":"R. Lidl and H. Niederreiter, \u201dFinite Fields\u201d, Encyclopedia of Mathematics and Its Application, (1987)"},{"key":"14_CR24","unstructured":"http:\/\/www.rsa.com"},{"key":"14_CR25","unstructured":"H.G. R\u00fcck, \u201dOn the discrete logarithms in the divisor class group of curves\u201d, To appear in Math. Comp. (1997)"},{"key":"14_CR26","unstructured":"T. Satoh and K. Araki, \u201dFermat Quotients and the Polynomial Time Discrete Log Algorithm for Anomalous Elliptic Curves\u201d, preprint, (1997)"},{"key":"14_CR27","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1090\/S0025-5718-98-00887-4","volume":"76","author":"I.A. Semaev","year":"1998","unstructured":"I.A. Semaev, \u201dEvaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p\u201d, Math. Comp., Vol.76 (1998),pp.353\u2013356.","journal-title":"Math. Comp."},{"key":"14_CR28","doi-asserted-by":"publisher","first-page":"483","DOI":"10.2307\/2007968","volume":"44","author":"R. Schoof","year":"1985","unstructured":"R. Schoof, \u201dElliptic curves over finite fields and the computation of square root mod p\u201d, Math. Comp, 44, (1985), 483\u2013494.","journal-title":"Math. Comp"},{"key":"14_CR29","unstructured":"N.P. Smart, \u201dThe Discrete Logarithm Problem on Elliptic Curves of Trace One\u201d, preprint, (1997)"}],"container-title":["Public Key Cryptography","Lecture Notes in Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0054023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,19]],"date-time":"2019-04-19T06:46:38Z","timestamp":1555656398000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0054023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"ISBN":["9783540646938","9783540691051"],"references-count":29,"URL":"http:\/\/dx.doi.org\/10.1007\/bfb0054023","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"published":{"date-parts":[[1998]]}}}