{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T05:16:36Z","timestamp":1741238196340,"version":"3.38.0"},"publisher-location":"Berlin, Heidelberg","reference-count":33,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642210303"},{"type":"electronic","value":"9783642210310"}],"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\/978-3-642-21031-0_32","type":"book-chapter","created":{"date-parts":[[2011,5,6]],"date-time":"2011-05-06T10:04:00Z","timestamp":1304676240000},"page":"432-446","source":"Crossref","is-referenced-by-count":3,"title":["Another Elliptic Curve Model for Faster Pairing Computation"],"prefix":"10.1007","author":[{"given":"Lijun","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Kunpeng","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Hong","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Dingfeng","family":"Ye","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"32_CR1","unstructured":"Arene, C., Lange, T., Naehrig, M., Ritzenthaler, C.: Faster computation of the tate pairing. Cryptology ePrint Archive, Report 2009\/155 (2009), http:\/\/eprint.iacr.org\/"},{"key":"32_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\u2013368. Springer, Heidelberg (2002)"},{"key":"32_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/978-3-540-24654-1_2","volume-title":"Selected Areas in Cryptography","author":"P.S.L.M. Barreto","year":"2004","unstructured":"Barreto, P.S.L.M., Lynn, B., Scott, M.: On the selection of pairing-friendly groups. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol.\u00a03006, pp. 17\u201325. Springer, Heidelberg (2004)"},{"key":"32_CR4","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.E. (eds.) SAC 2005. LNCS, vol.\u00a03897, pp. 319\u2013331. Springer, Heidelberg (2006)"},{"key":"32_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-540-28628-8_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M.K. (ed.) CRYPTO 2004. LNCS, vol.\u00a03152, pp. 41\u201355. Springer, Heidelberg (2004)"},{"issue":"3","key":"32_CR6","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1137\/S0097539701398521","volume":"32","author":"D. Boneh","year":"2003","unstructured":"Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. SIAM J. Comput.\u00a032(3), 586\u2013615 (2003)","journal-title":"SIAM J. Comput."},{"key":"32_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/3-540-39200-9_26","volume-title":"Advances in Cryptology \u2013 EUROCRPYT 2003","author":"D. Boneh","year":"2003","unstructured":"Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol.\u00a02656, pp. 416\u2013432. Springer, Heidelberg (2003)"},{"key":"32_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1007\/11496618_13","volume-title":"Information Security and Cryptology \u2013 ICISC 2004","author":"S. Chatterjee","year":"2005","unstructured":"Chatterjee, S., Sarkar, P., Barua, R.: Efficient computation of tate pairing in projective coordinate over general characteristic fields. In: Park, C., Chee, S. (eds.) ICISC 2004. LNCS, vol.\u00a03506, pp. 168\u2013181. Springer, Heidelberg (2005)"},{"key":"32_CR9","unstructured":"Chen, X., Zhang, F., Kim, K.: A new id-based group signature scheme from bilinear pairings. Cryptology ePrint Archive, Report 2003\/116 (2003), http:\/\/eprint.iacr.org\/"},{"key":"32_CR10","unstructured":"Cheng, Z., Nistazakis, M.: Implementing pairing-based cryptosystems. In: IWWST (2005)"},{"key":"32_CR11","unstructured":"Connell, I.: Elliptic curve handbook (1999), http:\/\/www.math.mcgill.ca\/connell\/"},{"key":"32_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/978-3-642-03298-1_7","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2009","author":"C. Costello","year":"2009","unstructured":"Costello, C., Hisil, H., Boyd, C., Nieto, J.M.G., Wong, K.K.H.: Faster pairings on special weierstrass curves. In: Shacham, H., Waters, B. (eds.) Pairing 2009. LNCS, vol.\u00a05671, pp. 89\u2013101. Springer, Heidelberg (2009)"},{"key":"32_CR13","doi-asserted-by":"crossref","unstructured":"Costello, C., Lange, T., Naehrig, M.: Faster pairing computations on curves with high-degree twists. In: Nguyen, P.Q., Pointcheval, D. (eds.) [26], pp. 224\u2013242","DOI":"10.1007\/978-3-642-13013-7_14"},{"key":"32_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1007\/978-3-540-85538-5_14","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2008","author":"M.P.L. Das","year":"2008","unstructured":"Das, M.P.L., Sarkar, P.: Pairing computation on twisted edwards form elliptic curves. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol.\u00a05209, pp. 192\u2013210. Springer, Heidelberg (2008)"},{"key":"32_CR15","doi-asserted-by":"crossref","unstructured":"Farashahi, R.R., Joye, M.: Efficient arithmetic on hessian curves. In: Nguyen, P.Q., Pointcheval, D. (eds.) [26], pp. 243\u2013260","DOI":"10.1007\/978-3-642-13013-7_15"},{"issue":"2","key":"32_CR16","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1007\/s00145-009-9048-z","volume":"23","author":"D. Freeman","year":"2010","unstructured":"Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. J. Cryptology\u00a023(2), 224\u2013280 (2010)","journal-title":"J. Cryptology"},{"key":"32_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1007\/3-540-36178-2_34","volume-title":"Advances in Cryptology - ASIACRYPT 2002","author":"C. Gentry","year":"2002","unstructured":"Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol.\u00a02501, pp. 548\u2013566. Springer, Heidelberg (2002)"},{"key":"32_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1007\/11792086_34","volume-title":"Algorithmic Number Theory","author":"R. Granger","year":"2006","unstructured":"Granger, R., Page, D., Smart, N.P.: High security pairing-based cryptography revisited. In: Hess, F., Pauli, S., Pohst, M.E. (eds.) ANTS 2006. LNCS, vol.\u00a04076, pp. 480\u2013494. Springer, Heidelberg (2006)"},{"key":"32_CR19","doi-asserted-by":"crossref","unstructured":"Gu, H., Gu, D., Xie, W.: Efficient pairing computation on elliptic curves in hessian form. In: ICISC (2010)","DOI":"10.1007\/978-3-642-24209-0_11"},{"key":"32_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1007\/978-3-540-89754-5_31","volume-title":"Progress in Cryptology - INDOCRYPT 2008","author":"S. Ionica","year":"2008","unstructured":"Ionica, S., Joux, A.: Another approach to pairing computation in edwards coordinates. In: Chowdhury, D.R., Rijmen, V., Das, A. (eds.) INDOCRYPT 2008. LNCS, vol.\u00a05365, pp. 400\u2013413. Springer, Heidelberg (2008)"},{"issue":"4","key":"32_CR21","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s00145-004-0312-y","volume":"17","author":"A. Joux","year":"2004","unstructured":"Joux, A.: A one round protocol for tripartite diffie-hellman. J. Cryptology\u00a017(4), 263\u2013276 (2004)","journal-title":"J. Cryptology"},{"key":"32_CR22","doi-asserted-by":"crossref","unstructured":"Joye, M., Quisquater, J.J.: Hessian elliptic curves and side-channel attacks. In: Ko\u00e7, \u00c7.K., et al. [23], pp. 402\u2013410","DOI":"10.1007\/3-540-44709-1_33"},{"key":"32_CR23","unstructured":"Joye, M., Tibouchi, M., Vergnaud, D.: Huff\u2019s Model for Elliptic Curves. Cryptology ePrint Archive, Report (2010), http:\/\/eprint.iacr.org\/2010\/383"},{"key":"32_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-540-77272-9_18","volume-title":"Cryptography and Coding","author":"S. Matsuda","year":"2007","unstructured":"Matsuda, S., Kanayama, N., Hess, F., Okamoto, E.: Optimised versions of the ate and twisted ate pairings. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol.\u00a04887, pp. 302\u2013312. Springer, Heidelberg (2007)"},{"issue":"4","key":"32_CR25","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(4), 235\u2013261 (2004)","journal-title":"J. Cryptology"},{"key":"32_CR26","series-title":"Lecture Notes in Computer Science","volume-title":"Public Key Cryptography \u2013 PKC 2010","year":"2010","unstructured":"Nguyen, P.Q., Pointcheval, D. (eds.): PKC 2010. LNCS, vol.\u00a06056. Springer, Heidelberg (2010)"},{"key":"32_CR27","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/BF02395746","volume":"85","author":"E.S. Selmer","year":"1951","unstructured":"Selmer, E.S.: The diophantine equation ax 3\u2009+\u2009by 3\u2009+\u2009cz 3\u2009=\u20090.. Acta Mathematica\u00a085, 203\u2013362 (1951)","journal-title":"Acta Mathematica"},{"key":"32_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9884-4","volume-title":"A Course in Arithmetic","author":"J.P. Serre","year":"1973","unstructured":"Serre, J.P.: A Course in Arithmetic. Springer, New York (1973)"},{"key":"32_CR29","doi-asserted-by":"crossref","unstructured":"Smart, N.P.: The hessian form of an elliptic curve. In: Ko\u00e7, \u00c7.K., et al [23], pp. 118\u2013125","DOI":"10.1007\/3-540-44709-1_11"},{"key":"32_CR30","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":"32_CR31","unstructured":"Vercauteren, F.: Optimal pairings. Cryptology ePrint Archive, Report 2008\/096 (2008), http:\/\/eprint.iacr.org\/"},{"key":"32_CR32","unstructured":"Wang, H., Wang, K., Zhang, L., Li, B.: Pairing computation on elliptic curves of jacobi quartic form. Cryptology ePrint Archive, Report 2010\/475 (2010), http:\/\/eprint.iacr.org\/"},{"key":"32_CR33","unstructured":"Zhao, C.A., Zhang, F., Huang, J.: A note on the ate pairing. Cryptology ePrint Archive, Report 2007\/247 (2007), http:\/\/eprint.iacr.org\/"}],"container-title":["Lecture Notes in Computer Science","Information Security Practice and Experience"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-21031-0_32","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T11:57:24Z","timestamp":1741175844000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-21031-0_32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642210303","9783642210310"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-21031-0_32","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}