{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:05:13Z","timestamp":1761743113877},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2008,6,18]],"date-time":"2008-06-18T00:00:00Z","timestamp":1213747200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sci. China Ser. F-Inf. Sci."],"published-print":{"date-parts":[[2008,8]]},"DOI":"10.1007\/s11432-008-0070-9","type":"journal-article","created":{"date-parts":[[2008,6,18]],"date-time":"2008-06-18T16:36:01Z","timestamp":1213806961000},"page":"1096-1105","source":"Crossref","is-referenced-by-count":7,"title":["Efficient Tate pairing computation using double-base chains"],"prefix":"10.1007","volume":"51","author":[{"given":"ChangAn","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FangGuo","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JiWu","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,6,18]]},"reference":[{"key":"70_CR1","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A. Menezes","year":"1993","unstructured":"Menezes A, Okamoto T, Vanstone S. Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans Inf Theory, 1993, 39: 1639\u20131646","journal-title":"IEEE Trans Inf Theory"},{"key":"70_CR2","first-page":"865","volume":"52","author":"G. Frey","year":"1994","unstructured":"Frey G, R\u00fcck H. A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Math Comp, 1994, 52: 865\u2013874","journal-title":"Math Comp"},{"key":"70_CR3","series-title":"LNCS","first-page":"385","volume-title":"A one round protocol for tripartite Diffie-Hellman","author":"A. Joux","year":"2000","unstructured":"Joux A. A one round protocol for tripartite Diffie-Hellman. In: Goos G, Hartmanis J, Leeuwen V J, eds. Algorithm Number Theory Symposium-ANTS IV. Berlin\/Heidelberg: Springer-Verlag, 2000, LNCS 1838: 385\u2013394"},{"key":"70_CR4","unstructured":"Sakai R, Ohgishi K, Kasahara M. Cryptosystems based on pairing. In: Symposium on Cryptography and Information Security-SCIS\u20192000, Okinawa, Japan, Jan. 2000. 26\u201328"},{"key":"70_CR5","series-title":"LNCS","first-page":"213","volume-title":"Proceeding of Advances in Cryptology-Crypto\u20192001","author":"D. Boneh","year":"2001","unstructured":"Boneh D, Franklin M. Identity-based encryption from the Weil pairing. In: Proceeding of Advances in Cryptology-Crypto\u20192001. Berlin\/Heidelberg: Springer-Verlag, 2001. LNCS 2139: 213\u2013229"},{"key":"70_CR6","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/11426639_7","volume-title":"Proceeding of Advances in Cryptology-Eurocrypt\u2019 2005","author":"B. Waters","year":"2005","unstructured":"Waters B. Efficient identity-based encryption without random oracles. In: Proceeding of Advances in Cryptology-Eurocrypt\u2019 2005. Berlin\/Heidelberg: Springer-Verlag, 2005, LNCS 3494: 114\u2013127"},{"key":"70_CR7","series-title":"LNCS","first-page":"443","volume-title":"Proceeding of Advances in Cryptology-Crypto\u20192004","author":"D. Boneh","year":"2004","unstructured":"Boneh D, Boyen X. Secure identity based encryption without random oracles. In: Proceeding of Advances in Cryptology-Crypto\u20192004. Berlin\/Heidelberg: Springer-Verlag, 2004. LNCS 3152: 443\u2013459"},{"key":"70_CR8","series-title":"LNCS","first-page":"514","volume-title":"Advances in Cryptology-Asiacrypt\u20192001","author":"D. Boneh","year":"2001","unstructured":"Boneh D, Lynn B, Shacham H. Short signatures from the Weil pairing. In: Advances in Cryptology-Asiacrypt\u20192001. Berlin\/Heidelberg: Springer-Verlag, 2001, LNCS 2248: 514\u2013532"},{"key":"70_CR9","series-title":"LNCS","first-page":"277","volume-title":"Proceeding of PKC\u20192004","author":"F. Zhang","year":"2004","unstructured":"Zhang F, Safavi-Naini R, Susilo W. An efficient signature scheme from bilinear pairings and its applications. In: Proceeding of PKC\u20192004. Berlin\/Heidelberg: Springer-Verlag, 2004. LNCS 2947: 277\u2013290"},{"key":"70_CR10","series-title":"LNCS","first-page":"56","volume-title":"Proceeding of Advances in Cryptology-Eurocrypt\u20192004","author":"D. Boneh","year":"2004","unstructured":"Boneh D, Boyen X. Short signatures without random oracles. In: Proceeding of Advances in Cryptology-Eurocrypt\u20192004. Berlin\/Heidelberg: Springer-Verlag, 2004, LNCS 3027: 56\u201373"},{"key":"70_CR11","series-title":"LNCS","first-page":"41","volume-title":"Proceeding of Advances in Cryptology-Crypto\u20192004","author":"D. Boneh","year":"2004","unstructured":"Boneh D, Boyen X, Shacham H. Short group signatures. In: Proceeding of Advances in Cryptology-Crypto\u20192004. Berlin\/ Heidelberg: Springer-Verlag, 2004. LNCS 3152: 41\u201355"},{"key":"70_CR12","unstructured":"Miller V S. Short programs for functions on curves, unpublished manuscript, 1986"},{"key":"70_CR13","series-title":"LNCS","first-page":"354","volume-title":"Proceeding of Advances in Cryptology-Crypto\u20192002","author":"P. S. L. M. Barreto","year":"2002","unstructured":"Barreto P S L M, Kim H Y, Lynn B, et al. Efficient algorithms for pairing-based cryptosystems. In: Proceeding of Advances in Cryptology-Crypto\u20192002. Berlin\/Heidelberg: Springer-Verlag, 2002, LNCS 2442: 354\u2013368"},{"key":"70_CR14","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1007\/3-540-45455-1_26","volume-title":"Proceeding of Algorithm Number Theory Symposium-ANTS V","author":"S. D. Galbraith","year":"2002","unstructured":"Galbraith S D, Harrison K, Soldera D. Implementing the Tate pairing. In: Proceeding of Algorithm Number Theory Symposium-ANTS V. Berlin\/Heidelberg: Springer-Verlag, 2002, LNCS 2369: 324\u2013337"},{"key":"70_CR15","series-title":"LNCS","first-page":"111","volume-title":"Proceeding of Advances in Cryptology-Asiacrypt\u20192003","author":"I. Duursma","year":"2003","unstructured":"Duursma I, Lee H-S. Tate pairing implementation for hyperelliptic curves y 2 = x p \u2212 x + d. In: Proceeding of Advances in Cryptology-Asiacrypt\u20192003. Berlin\/Heidelberg: Springer-Verlag, 2003, LNCS 2894: 111\u2013123"},{"key":"70_CR16","series-title":"LNCS","first-page":"343","volume-title":"Proceeding of CT-RSA\u20192003","author":"K. Eisentr\u00e4er","year":"2003","unstructured":"Eisentr\u00e4er K, Lauter K, Montgomery P L. Fast elliptic curve arithmetic and improvedWeil pairing evaluation. In: Proceeding of CT-RSA\u20192003. Berlin\/Heidelberg: Springer-Verlag, 2003, LNCS 2612: 343\u2013354"},{"key":"70_CR17","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/s11390-005-0264-1","volume":"20","author":"L. Hu","year":"2005","unstructured":"Hu L, Dong J, Pei D. An implementation of cryptosystems based on Tate pairing. J Comp Sci Tech, 2005, 20: 264\u2013269","journal-title":"J Comp Sci Tech"},{"key":"70_CR18","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jalgor.2005.01.009","volume":"58","author":"I. Blake","year":"2006","unstructured":"Blake I, Murty K, Xu G. Refinements of Miller\u2019s algorithm for computing Weil\/Tate pairing. J Algor, 2006, 58: 134\u2013149","journal-title":"J Algor"},{"key":"70_CR19","series-title":"LNCS","first-page":"283","volume-title":"proceeding of ICISC\u201902","author":"T. Izu","year":"2003","unstructured":"Izu T, Takagi T. Efficient computations of the Tate pairing for the large MOV degrees. In: proceeding of ICISC\u201902. Berlin\/Heidelberg: Springer-Verlag, 2003. LNCS 2587: 283\u2013297"},{"key":"70_CR20","first-page":"595","volume":"7","author":"A. Karatsuba","year":"1963","unstructured":"Karatsuba A, Ofman Y. Multiplication on Many-Digittal Numbers by Automatic Computers. Sov Trans Phys-Doklady, 1963, 7: 595\u2013596","journal-title":"Sov Trans Phys-Doklady"},{"issue":"1","key":"70_CR21","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1093\/ietfec\/e89-a.1.134","volume":"E89-A","author":"T. Kobayashi","year":"2006","unstructured":"Kobayashi T, Aoki K, Imai H. Efficient algorithms for Tate pairing. IEICE Trans Fundam, 2006, E89-A(1): 134\u2013143","journal-title":"IEICE Trans Fundam"},{"issue":"3","key":"70_CR22","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s10623-006-9033-6","volume":"42","author":"P. S. L. M. Barreto","year":"2007","unstructured":"Barreto P S L M, Galbraith S, \u00d3h\u00c9igeartaigh C. et al. Efficient pairing computation on supersingular abelian varieties. Des Cod Crypto, 2007, 42(3): 239\u2013271","journal-title":"Des Cod Crypto"},{"key":"70_CR23","doi-asserted-by":"crossref","first-page":"4595","DOI":"10.1109\/TIT.2006.881709","volume":"52","author":"F. Hess","year":"2006","unstructured":"Hess F, Smart N P, Vercauteren F. The Eta pairing revisited. IEEE Trans Inf Theory, 2006, 52: 4595\u20134602","journal-title":"IEEE Trans Inf Theory"},{"key":"70_CR24","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s00200-005-0187-7","volume":"16","author":"J. A. Muir","year":"2006","unstructured":"Muir J A, Stinson D R. On the low hamming weight discrete logarithm problem for nonadjacent representations. Appl Alg Eng, Commun Comput, 2006, 16: 461\u2013472","journal-title":"Appl Alg Eng, Commun Comput"},{"key":"70_CR25","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The Arithmetic of Elliptic Curves","author":"J. H. Silverman","year":"1986","unstructured":"Silverman J H. The Arithmetic of Elliptic Curves. New York: Springer-Verlag, 1986. 31\u201334"},{"key":"70_CR26","series-title":"LNCS","first-page":"59","volume-title":"Proceeding of Advances in Cryptology-Asiacrypt\u20192005","author":"V. S. Dimitrov","year":"2005","unstructured":"Dimitrov V S, Imbert L, Mishra P K. Efficient and secure elliptic curve point multiplication using double-base chains. In: Proceeding of Advances in Cryptology-Asiacrypt\u20192005. Berlin\/Heidelberg: Springer-Verlag, 2005, LNCS 3788: 59\u201378"},{"key":"70_CR27","volume-title":"Pairings-Advances in Elliptic Curve Cryptography","author":"S. D. Galbraith","year":"2005","unstructured":"Galbraith S D. Pairings-Advances in Elliptic Curve Cryptography. Cambridge: Cambridge University Press, 2005"},{"issue":"2","key":"70_CR28","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10623-005-3299-y","volume":"39","author":"M. Ciet","year":"2006","unstructured":"Ciet M, Joye M, Lauter K, et al. Trading inversions for multiplications in elliptic curve cryptography. Des Cod Crypto, 2006, 39(2): 189\u2013206","journal-title":"Des Cod Crypto"},{"issue":"1","key":"70_CR29","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1093\/ietfec\/e89-a.1.334","volume":"E89-A","author":"D. Adachi","year":"2006","unstructured":"Adachi D, Hirata T. Refined computations for points of the form 2k P based on Montgomery Trick. IEICE Trans Fund, 2006, E89-A(1): 334\u2013339","journal-title":"IEICE Trans Fund"}],"container-title":["Science in China Series F: Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-008-0070-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11432-008-0070-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-008-0070-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T15:35:55Z","timestamp":1559403355000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11432-008-0070-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6,18]]},"references-count":29,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2008,8]]}},"alternative-id":["70"],"URL":"https:\/\/doi.org\/10.1007\/s11432-008-0070-9","relation":{},"ISSN":["1009-2757","1862-2836"],"issn-type":[{"value":"1009-2757","type":"print"},{"value":"1862-2836","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6,18]]}}}