{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T13:03:30Z","timestamp":1725714210930},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642363337"},{"type":"electronic","value":"9783642363344"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-36334-4_15","type":"book-chapter","created":{"date-parts":[[2013,1,30]],"date-time":"2013-01-30T19:55:13Z","timestamp":1359575713000},"page":"218-233","source":"Crossref","is-referenced-by-count":4,"title":["The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets"],"prefix":"10.1007","author":[{"given":"Yukihiro","family":"Uchida","sequence":"first","affiliation":[]},{"given":"Shigenori","family":"Uchiyama","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"15_CR1","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1307\/mmj\/1012409966","volume":"49","author":"J. Arledge","year":"2001","unstructured":"Arledge, J., Grant, D.: An explicit theorem of the square for hyperelliptic Jacobians. Michigan Math. J.\u00a049, 485\u2013492 (2001)","journal-title":"Michigan Math. J."},{"key":"15_CR2","series-title":"Ergebnisse der Mathematik und ihrer Grenzgebiete, 3.\u00a0Folge, Band 21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-51438-8","volume-title":"N\u00e9ron Models","author":"S. Bosch","year":"1990","unstructured":"Bosch, S., L\u00fctkebohmert, W., Raynaud, M.: N\u00e9ron Models. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3.\u00a0Folge, Band 21. Springer, Berlin (1990)"},{"key":"15_CR3","first-page":"1","volume":"10","author":"V.M. Buchstaber","year":"1997","unstructured":"Buchstaber, V.M., Enolskii, V.Z., Leykin, D.V.: Kleinian functions, hyperelliptic Jacobians and applications. Rev. Math. Math. Phys.\u00a010, 1\u2013125 (1997)","journal-title":"Rev. Math. Math. Phys."},{"key":"15_CR4","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1007\/BF02466056","volume":"31","author":"V.M. Buchstaber","year":"1997","unstructured":"Buchstaber, V.M., Enolskii, V.Z., Leykin, D.V.: A recursive family of differential polynomials generated by the Sylvester identity and addition theorems for hyperelliptic Kleinian functions. Funct. Anal. Appl.\u00a031, 240\u2013251 (1997)","journal-title":"Funct. Anal. Appl."},{"key":"15_CR5","series-title":"Mathematical Surveys and Monographs","volume-title":"Fundamental Algebraic Geometry: Grothendieck\u2019s FGA explained","author":"B. Fantechi","year":"2005","unstructured":"Fantechi, B., G\u00f6ttsche, L., Illusie, L., Kleiman, S.L., Nitsure, N., Vistoli, A.: Fundamental Algebraic Geometry: Grothendieck\u2019s FGA explained. Mathematical Surveys and Monographs, vol.\u00a0123. American Mathematical Society, Providence (2005)"},{"key":"15_CR6","first-page":"865","volume":"62","author":"G. Frey","year":"1994","unstructured":"Frey, G., R\u00fcck, H.-G.: A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Math. Comp.\u00a062, 865\u2013874 (1994)","journal-title":"Math. Comp."},{"key":"15_CR7","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1080\/00036810903329977","volume":"89","author":"A.N.W. Hone","year":"2010","unstructured":"Hone, A.N.W.: Analytic solutions and integrability for bilinear recurrences of order six. Appl. Anal.\u00a089, 473\u2013492 (2010)","journal-title":"Appl. Anal."},{"key":"15_CR8","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1017\/S0305004105008765","volume":"139","author":"N. Kanayama","year":"2005","unstructured":"Kanayama, N.: Division polynomials and multiplication formulae of Jacobian varieties of dimension 2. Math. Proc. Cambridge Philos. Soc.\u00a0139, 399\u2013409 (2005)","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"15_CR9","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1017\/S0305004110000113","volume":"149","author":"N. Kanayama","year":"2010","unstructured":"Kanayama, N.: Corrections to \u201cDivision polynomials and multiplication formulae in dimension 2\u201d. Math. Proc. Cambridge Philos. Soc.\u00a0149, 189\u2013192 (2010)","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"15_CR10","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/BF01389795","volume":"7","author":"S. Lichtenbaum","year":"1969","unstructured":"Lichtenbaum, S.: Duality theorems for curves over p-adic fields. Invent. Math.\u00a07, 120\u2013136 (1969)","journal-title":"Invent. Math."},{"unstructured":"Maxima.sourceforge.net: Maxima, a Computer Algebra System. Version 5.25.1 (2011), \n                    \n                      http:\/\/maxima.sourceforge.net\/","key":"15_CR11"},{"unstructured":"Miller, V.S.: Short programs for functions on curves (1986) (unpublished manuscript), \n                    \n                      http:\/\/crypto.stanford.edu\/miller\/","key":"15_CR12"},{"key":"15_CR13","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s00145-004-0315-8","volume":"17","author":"V.S. Miller","year":"2004","unstructured":"Miller, V.S.: The Weil pairing, and its efficient calculation. J. Cryptology\u00a017, 235\u2013261 (2004)","journal-title":"J. Cryptology"},{"key":"15_CR14","series-title":"Progress in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-2843-6","volume-title":"Tata Lectures on Theta I","author":"D. Mumford","year":"1983","unstructured":"Mumford, D.: Tata Lectures on Theta I. Progress in Mathematics, vol.\u00a028. Birkh\u00e4user, Boston (1983)"},{"key":"15_CR15","series-title":"Progress in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4578-6","volume-title":"Tata Lectures on Theta II","author":"D. Mumford","year":"1984","unstructured":"Mumford, D.: Tata Lectures on Theta II. Progress in Mathematics, vol.\u00a043. Birkh\u00e4user, Boston (1984)"},{"key":"15_CR16","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1017\/S0013091503000695","volume":"48","author":"Y. \u00d4nishi","year":"2005","unstructured":"\u00d4nishi, Y.: Determinant expressions for hyperelliptic functions (with an appendix by Shigeki Matsutani). Proc. Edinb. Math. Soc.\u00a048, 705\u2013742 (2005)","journal-title":"Proc. Edinb. Math. Soc."},{"key":"15_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/978-3-540-73489-5_19","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2007","author":"K.E. Stange","year":"2007","unstructured":"Stange, K.E.: The Tate Pairing Via Elliptic Nets. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol.\u00a04575, pp. 329\u2013348. Springer, Heidelberg (2007)"},{"key":"15_CR18","doi-asserted-by":"publisher","first-page":"197","DOI":"10.2140\/ant.2011.5.197","volume":"5","author":"K.E. Stange","year":"2011","unstructured":"Stange, K.E.: Elliptic nets and elliptic curves. Algebra Number Theory\u00a05, 197\u2013229 (2011)","journal-title":"Algebra Number Theory"},{"key":"15_CR19","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s00229-010-0394-9","volume":"134","author":"Y. Uchida","year":"2011","unstructured":"Uchida, Y.: Division polynomials and canonical local heights on hyperelliptic Jacobians. Manuscripta Math.\u00a0134, 273\u2013308 (2011)","journal-title":"Manuscripta Math."},{"unstructured":"PARI\/GP, version 2.3.4, Bordeaux (2008), \n                    \n                      http:\/\/pari.math.u-bordeaux.fr\/","key":"15_CR20"}],"container-title":["Lecture Notes in Computer Science","Pairing-Based Cryptography \u2013 Pairing 2012"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-36334-4_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T20:06:52Z","timestamp":1557518812000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-36334-4_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642363337","9783642363344"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-36334-4_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}