{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T01:05:10Z","timestamp":1725584710476},"publisher-location":"Berlin, Heidelberg","reference-count":10,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642209000"},{"type":"electronic","value":"9783642209017"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"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":[[2011]]},"DOI":"10.1007\/978-3-642-20901-7_13","type":"book-chapter","created":{"date-parts":[[2011,6,4]],"date-time":"2011-06-04T10:11:30Z","timestamp":1307182290000},"page":"213-222","source":"Crossref","is-referenced-by-count":1,"title":["Local Duality and the Discrete Logarithm Problem"],"prefix":"10.1007","author":[{"given":"Ming-Deh","family":"Huang","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"13_CR1","volume-title":"Algebraic Number Theory","author":"J.W.S. Cassels","year":"1967","unstructured":"Cassels, J.W.S., Fr\u00f6hlich, A.: Algebraic Number Theory. Academic Press, London (1967)"},{"issue":"5","key":"13_CR2","doi-asserted-by":"publisher","first-page":"1717","DOI":"10.1109\/18.771254","volume":"45","author":"G. Frey","year":"1999","unstructured":"Frey, G., M\u00fcller, M., R\u00fcck, H.-G.: The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. IEEE Trans. Inform. Theory\u00a045(5), 1717\u20131719 (1999)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"206","key":"13_CR3","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. Mathematics of Computation\u00a062(206), 865\u2013874 (1994)","journal-title":"Mathematics of Computation"},{"key":"13_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/3-540-45455-1_3","volume-title":"Algorithmic Number Theory","author":"A. Joux","year":"2002","unstructured":"Joux, A.: The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol.\u00a02369, pp. 20\u201332. Springer, Heidelberg (2002)"},{"key":"13_CR5","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."},{"key":"13_CR6","volume-title":"Arithmetic Duality Theorems. Perspectives in Mathematics","author":"J.S. Milne","year":"1986","unstructured":"Milne, J.S.: Arithmetic Duality Theorems. Perspectives in Mathematics, vol.\u00a01. Academic Press, London (1986)"},{"key":"13_CR7","unstructured":"Nguyen, K.: Explicit Arithmetic of Brauer Groups \u2013 Ray Class Fields and Index Calculus, Thesis, Univesit\u00e4t Essen (2001)"},{"key":"13_CR8","doi-asserted-by":"crossref","unstructured":"Serre, J.-P.: Local Fields. Graduate Texts in Mathematics, vol.\u00a067, Springer, Heidelberg (1979)","DOI":"10.1007\/978-1-4757-5673-9"},{"key":"13_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/3-540-61581-4_66","volume-title":"Algorithmic Number Theory","author":"O. Schirokauer","year":"1996","unstructured":"Schirokauer, O., Weber, D., Denny, T.: Discrete logarithms: The effectiveness of the index calculus method. In: Cohen, H. (ed.) ANTS 1996. LNCS, vol.\u00a01122, pp. 337\u2013361. Springer, Heidelberg (1996)"},{"key":"13_CR10","first-page":"13","volume":"156","author":"J. Tate","year":"1957","unstructured":"Tate, J.: WC-groups over p-adic fields. Sem. Bourbaki\u00a0156, 13 (1957)","journal-title":"Sem. Bourbaki"}],"container-title":["Lecture Notes in Computer Science","Coding and Cryptology"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-20901-7_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T08:07:14Z","timestamp":1560240434000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-20901-7_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642209000","9783642209017"],"references-count":10,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-20901-7_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}