{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T12:10:39Z","timestamp":1725624639757},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642251405"},{"type":"electronic","value":"9783642251412"}],"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\/978-3-642-25141-2_5","type":"book-chapter","created":{"date-parts":[[2011,10,22]],"date-time":"2011-10-22T13:30:01Z","timestamp":1319290201000},"page":"65-78","source":"Crossref","is-referenced-by-count":5,"title":["Cryptographic Pairings Based on Elliptic Nets"],"prefix":"10.1007","author":[{"given":"Naoki","family":"Ogura","sequence":"first","affiliation":[]},{"given":"Naoki","family":"Kanayama","sequence":"additional","affiliation":[]},{"given":"Shigenori","family":"Uchiyama","sequence":"additional","affiliation":[]},{"given":"Eiji","family":"Okamoto","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"3","key":"5_CR1","doi-asserted-by":"publisher","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.D., \u00d3h\u00c9igeartaigh, C., Scott, M.: Efficient pairing computation on supersingular abelian varieties. Designs, Codes and Cryptography\u00a042(3), 239\u2013271 (2007)","journal-title":"Designs, Codes and Cryptography"},{"key":"5_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/3-540-45708-9_23","volume-title":"Advances in Cryptology - CRYPTO 2002","author":"P.S.L.M. Barreto","year":"2002","unstructured":"Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol.\u00a02442, pp. 354\u2013369. Springer, Heidelberg (2002)"},{"key":"5_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"D. Boneh","year":"2001","unstructured":"Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 213\u2013369. Springer, Heidelberg (2001)"},{"key":"5_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/3-540-36413-7_19","volume-title":"Security in Communication Networks","author":"P.S.L.M. Barreto","year":"2003","unstructured":"Barreto, P.S.L.M., Lynn, B., Scott, M.: Constructing elliptic curves with prescribed embedding degrees. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol.\u00a02576, pp. 257\u2013267. Springer, Heidelberg (2003)"},{"key":"5_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/11693383_22","volume-title":"Selected Areas in Cryptography","author":"P.S.L.M. Barreto","year":"2006","unstructured":"Barreto, P.S.L.M., Naehrig, M.: Pairing-friendly elliptic curves of prime order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol.\u00a03897, pp. 319\u2013331. Springer, Heidelberg (2006)"},{"key":"5_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-540-40061-5_7","volume-title":"Advances in Cryptology - ASIACRYPT 2003","author":"I. Duursma","year":"2003","unstructured":"Duursma, I., Lee, H.-S.: Tate Pairing Implementation for Hyperelliptic Curves y\n                  2\u2009=\u2009x\n                  \n                    p\n                  \u2009\u2212\u2009x\u2009+\u2009d. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol.\u00a02894, pp. 111\u2013123. Springer, Heidelberg (2003)"},{"key":"5_CR7","volume-title":"Advances in Elliptic Curve Cryptography, Ch. IX","author":"S.D. Galbraith","year":"2005","unstructured":"Galbraith, S.D.: Pairings. In: Blake, I., Seroussi, G., Smart, N. (eds.) Advances in Elliptic Curve Cryptography, Ch. IX, Cambridge University Press, Cambridge (2005)"},{"issue":"10","key":"5_CR8","doi-asserted-by":"publisher","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 Transaction on Information Theory\u00a052(10), 4595\u20134602 (2006)","journal-title":"IEEE Transaction on Information Theory"},{"key":"5_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/10722028_23","volume-title":"Algorithmic Number Theory","author":"A. Joux","year":"2000","unstructured":"Joux, A.: A one round protocol for tripartite Diffie\u2013Hellman. In: Bosma, W. (ed.) ANTS 2000 Part IV. LNCS, vol.\u00a01838, pp. 385\u2013393. Springer, Heidelberg (2000)"},{"issue":"4","key":"5_CR10","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1109\/TIT.2009.2013048","volume":"55","author":"E. Lee","year":"2009","unstructured":"Lee, E., Lee, H.S., Park, C.M.: Efficient and generalized pairing computation on abelian varieties. IEEE Transactions on Information Theory\u00a055(4), 1793\u20131803 (2009)","journal-title":"IEEE Transactions on Information Theory"},{"key":"5_CR11","unstructured":"Miller, V.S.: Short programs for functions on curves (1986), \n                    \n                      http:\/\/crypto.stanford.edu\/miller\/miller.pdf"},{"issue":"4","key":"5_CR12","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. Journal of Cryptology\u00a017(4), 235\u2013261 (2004)","journal-title":"Journal of Cryptology"},{"key":"5_CR13","unstructured":"Murphy, A., Fitzpatrick, N.: Elliptic Curves for Pairing Applications. Cryptology ePrint Archive, Report 2005\/302 (2005), \n                    \n                      http:\/\/eprint.iacr.org\/2005\/302.pdf"},{"key":"5_CR14","unstructured":"Ogura, N., Uchiyama, S., Kanayama, N., Okamoto, E.: A note on the pairing computation using normalized Miller functions, to appear in IEICE Transaction on Fundamentals of Electronics, Communications and Computer Sciences"},{"key":"5_CR15","unstructured":"Sakai, R., Ohgshi, K., Kasahara, M.: Cryptosystems based on pairings. In: Symposium on Cryptography and Information Security 2000, SCIS (2000)"},{"key":"5_CR16","first-page":"483","volume":"44","author":"R. Schoof","year":"1985","unstructured":"Schoof, R.: Elliptic curves over finite fields and computation of square roots mod p. Math. Comp.\u00a044, 483\u2013494 (1985)","journal-title":"Math. Comp."},{"key":"5_CR17","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","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. Graduate Texts in Mathematics, vol.\u00a0106. Springer, Heidelberg (1986)"},{"key":"5_CR18","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":"5_CR19","unstructured":"Taylor, G.: Stange\u2019s algorithm for elliptic nets, \n                    \n                      http:\/\/maths.straylight.co.uk\/archives\/102"},{"issue":"7","key":"5_CR20","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s10207-008-0054-1","volume":"6","author":"C.-A. Zhao","year":"2008","unstructured":"Zhao, C.-A., Zhang, F., Huang, J.: A note on the Ate pairing. International Journal of Information Security\u00a06(7), 379\u2013382 (2008)","journal-title":"International Journal of Information Security"},{"issue":"1","key":"5_CR21","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1109\/TIT.2009.2034881","volume":"56","author":"F. Vercauteren","year":"2010","unstructured":"Vercauteren, F.: Optimal pairings. IEEE Transactions on Information Theory\u00a056(1), 455\u2013461 (2010)","journal-title":"IEEE Transactions on Information Theory"},{"key":"5_CR22","doi-asserted-by":"publisher","first-page":"31","DOI":"10.2307\/2371930","volume":"70","author":"M. Ward","year":"1948","unstructured":"Ward, M.: Memoir on elliptic divisibility sequence. American Journal of Mathematics\u00a070, 31\u201374 (1948)","journal-title":"American Journal of Mathematics"},{"key":"5_CR23","unstructured":"MAGMA group, Magma, \n                    \n                      http:\/\/magma.maths.usyd.edu.au\/magma\/"}],"container-title":["Lecture Notes in Computer Science","Advances in Information and Computer Security"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-25141-2_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,1,19]],"date-time":"2019-01-19T21:45:20Z","timestamp":1547934320000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-25141-2_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642251405","9783642251412"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-25141-2_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}