{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T01:40:08Z","timestamp":1737078008678,"version":"3.33.0"},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540007166"},{"type":"electronic","value":"9783540365525"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/3-540-36552-4_20","type":"book-chapter","created":{"date-parts":[[2007,6,6]],"date-time":"2007-06-06T23:22:37Z","timestamp":1181172157000},"page":"283-297","source":"Crossref","is-referenced-by-count":17,"title":["Efficient Computations of the Tate Pairing for the Large MOV Degrees"],"prefix":"10.1007","author":[{"given":"Tetsuya","family":"Izu","sequence":"first","affiliation":[]},{"given":"Tsuyoshi","family":"Takagi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2003,3,14]]},"reference":[{"key":"20_CR1","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"Identity-based encryption from the Weil pairing","author":"D. Boneh","year":"2001","unstructured":"D. Boneh, and M. Franklin, \u201cIdentity-based encryption from the Weil pairing\u201d, CRYPTO 2001, LNCS 2139, pp.213\u2013229, Springer-Verlag, 2001. 284"},{"key":"20_CR2","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/3-540-45708-9_23","volume-title":"CRYPTO 2002","author":"P. Barreto","year":"2002","unstructured":"P. Barreto, H. Kim, B. Lynn, and M. Scott, \u201cEfficient Algorithmsfor Pairing-Based Cryptosystems\u201d, CRYPTO 2002, LNCS 2442, pp.354\u2013368, Springer-Verlag, 2002. 284, 292, 293, 294"},{"key":"20_CR3","doi-asserted-by":"crossref","unstructured":"D. Coppersmith, \u201cEvaluating Logarithms in GF(2 n)\u201d, STOC 1984, pp.201\u2013207, 1983. 284","DOI":"10.1145\/800057.808682"},{"key":"20_CR4","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/3-540-49649-1_6","volume-title":"Asiacrypt\u201998","author":"H. Cohen","year":"1998","unstructured":"H. Cohen, A. Miyaji and T. Ono, \u201cEfficient elliptic curve exponentiation using mixed coordinates\u201d, Asiacrypt\u201998, LNCS 1514, pp.51\u201365, Springer-Verlag, 1998. 285"},{"key":"20_CR5","unstructured":"R. Dunport, A. Enge, and F. Morain, \u201cBuilding curveswit h arbitrary small MOV degree over finite prime fields\u201d, Cryptology ePrint Archive, Report 2002\/094, 2002. 284"},{"key":"20_CR6","doi-asserted-by":"publisher","first-page":"1717","DOI":"10.1109\/18.771254","volume":"45","author":"G. Frey","year":"1999","unstructured":"G. Frey, M. M\u00fcller, and H. R\u00fcck, \u201cThe Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems\u201d, IEEE Trans. on Information Theory, vol.45, pp.1717\u20131718, 1999. 283","journal-title":"IEEE Trans. on Information Theory"},{"key":"20_CR7","series-title":"Lect Notes Comput Sci","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/3-540-45682-1_29","volume-title":"Asiacrypt 2001","author":"S.D. Galbraith","year":"2001","unstructured":"S.D. Galbraith, \u201cSupersingular Curves in Cryptography\u201d, Asiacrypt 2001, LNCS 2248, pp.495\u2013513, Springer-Verlag, 2001. 284"},{"key":"20_CR8","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1007\/3-540-45455-1_26","volume-title":"ANTS V","author":"S.D. Galbraith","year":"2002","unstructured":"S.D. Galbraith, K. Harrison, and D. Soldera, \u201cImplementing the Tate pairing\u201d, ANTS V, LNCS 2369, pp.324\u2013337, Springer-Verlag, 2002. 284, 287, 291, 292, 294"},{"key":"20_CR9","unstructured":"F. Hess, \u201cExponent Group Signature Schemes and Efficient Identity Based Signature Schemes Based on Pairings\u201d, Cryptology ePrint Archive, Report 2002\/012, 2002. 284"},{"key":"20_CR10","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/3-540-48059-5_7","volume-title":"CHES\u201999","author":"K. Itoh","year":"1999","unstructured":"K. Itoh, M. Takenaka, N. Torii, S. Temma, and Y. Kurihara, \u201cFast Implementation of Public-Key Cryptography on DSP TMS320C6201\u201d, CHES\u201999, LNCS 1717, pp.61\u201372, 1999. 291"},{"key":"20_CR11","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/10722028_23","volume-title":"ANTS IV","author":"A. Joux","year":"2000","unstructured":"A. Joux, \u201cA One Round Protocol for Tripartite Diffie-Hellman\u201d, ANTS IV, LNCS 1838, pp.385\u2013393, Springer-Verlag, 2000. 284"},{"key":"20_CR12","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/3-540-45455-1_3","volume-title":"ANTS V","author":"A. Joux","year":"2002","unstructured":"A. Joux, \u201cThe Weil and Tate Pairings asBu ilding Blocksfor Public Key Cryptosystems (survey)\u201d, ANTS V, LNCS 2369, pp.20\u201332, Springer-Verlag, 2002. 284, 294"},{"key":"20_CR13","doi-asserted-by":"publisher","first-page":"203","DOI":"10.2307\/2007884","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz, \u201cElliptic curve cryptosystems\u201d,Math. of Comp., vol.48, pp.203\u2013209, 1987. 283","journal-title":"Math. of Comp."},{"key":"20_CR14","doi-asserted-by":"crossref","unstructured":"A. Menezes, \u201cElliptic Curve Public Key Cryptosystems\u201d, Kluwer Academic Publishers, 1993. 288, 293","DOI":"10.1007\/978-1-4615-3198-2"},{"key":"20_CR15","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/3-540-39799-X_31","volume-title":"CRYPTO\u201985","author":"V. Miller","year":"1986","unstructured":"V. Miller, \u201cUse of elliptic curves in cryptography\u201d, CRYPTO\u201985, LNCS 218. p.417\u2013426, Springer-Verlag, 1986. 283"},{"key":"20_CR16","unstructured":"A. Miyaji, M. Nakabayashi, and S. Takano, \u201cNew explicit conditions of elliptic curve tracesfor FR-reduction\u201d, IEICE Trans. Fundamentals, E84-A(5), May, 2001. 284"},{"key":"20_CR17","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A. Menezes","year":"1993","unstructured":"A. Menezes, T. Okamoto, and S. Vanstone, \u201cReducing Elliptic Curve Logarithmst o Logarithms in a Finite Field\u201d, IEEE Trans. on Information Theory, vol.39, pp.1639\u20131646, 1993. 283, 287","journal-title":"IEEE Trans. on Information Theory"},{"key":"20_CR18","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1007\/3-540-44586-2_8","volume-title":"PKC 2001","author":"T. Okamoto","year":"2001","unstructured":"T. Okamoto, P. Pointcheval, \u201cThe Gap Problems: a new class of problems for the security of cryptographic primitives\u201d, PKC 2001, LNCS 1992, pp.104\u2013118, Springer-Verlag, 2001. 284"},{"key":"20_CR19","unstructured":"K. G. Paterson, \u201cID-based Signatures from Pairings on Elliptic Curves\u201d, Cryptology ePrint Archive, Report 2002\/004, 2002. 284"},{"key":"20_CR20","doi-asserted-by":"crossref","unstructured":"D. Page, and N. Smart, \u201cHardware Implementation of Finite Fieldsof Characteristic Three\u201d, to appear in the proceedings of CHES 2002. 284","DOI":"10.1007\/3-540-36400-5_38"},{"key":"20_CR21","unstructured":"N.P. Smart, \u201cAn Identity Based Authentificated Key Agreement Protocol Based on the Weil Pairing\u201d, Cryptology ePrint Archive, Report 2001\/111, 2001. 284"},{"key":"20_CR22","unstructured":"R. Sakai, K. Ohgishi, and M. Kasahara, \u201cCryptosystems Based on Pairing\u201d, 2000 Symposium on Cryptography and Information Security (SCIS 2000), Okinawa, Japan, Jan. 26-28, 2000. 284"},{"key":"20_CR23","unstructured":"N.P. Smart, and J. Westwood, \u201cPoint Multiplication on Ordinary Elliptic Curveso ver Fieldsof Characteristic Three\u201d, Cryptology ePrint Archive, Report 2002\/114, 2002. 284"},{"key":"20_CR24","series-title":"Lect Notes Comput Sci","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/3-540-45682-1_31","volume-title":"ASIACRYPT 2001","author":"E.R. Verheul","year":"2001","unstructured":"E.R. Verheul, \u201cSelf-Blindable Credential Certificatesfrom the Weil pairing\u201d, ASIACRYPT 2001, LNCS 2248, pp.533\u2013551, Springer-Verlag, 2001. 284"}],"container-title":["Lecture Notes in Computer Science","Information Security and Cryptology \u2014 ICISC 2002"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-36552-4_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T01:10:23Z","timestamp":1737076223000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-36552-4_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540007166","9783540365525"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/3-540-36552-4_20","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2003]]}}}