{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T15:39:10Z","timestamp":1769528350594,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":33,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540734888","type":"print"},{"value":"9783540734895","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-73489-5_19","type":"book-chapter","created":{"date-parts":[[2007,9,11]],"date-time":"2007-09-11T08:58:06Z","timestamp":1189501086000},"page":"329-348","source":"Crossref","is-referenced-by-count":35,"title":["The Tate Pairing Via Elliptic Nets"],"prefix":"10.1007","author":[{"given":"Katherine E.","family":"Stange","sequence":"first","affiliation":[]}],"member":"297","reference":[{"issue":"5","key":"19_CR1","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A.J. Menezes","year":"1993","unstructured":"Menezes, A.J., Okamoto, T., Vanstone, S.A.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Inform. Theory\u00a039(5), 1639\u20131646 (1993)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"206","key":"19_CR2","doi-asserted-by":"publisher","first-page":"865","DOI":"10.2307\/2153546","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. Math. Comp.\u00a062(206), 865\u2013874 (1994)","journal-title":"Math. Comp."},{"key":"19_CR3","unstructured":"Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: Symposium on Cryptography and Information Security, Okinawa, Japan (2000)"},{"key":"19_CR4","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-Hellman. In: Bosma, W. (ed.) Algorithmic Number Theory. LNCS, vol.\u00a01838, pp. 385\u2013393. Springer, Heidelberg (2000)"},{"key":"19_CR5","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\u2013229. Springer, Heidelberg (2001)"},{"key":"19_CR6","first-page":"573","volume-title":"Handbook of elliptic and hyperelliptic curve cryptography","author":"S. Duquesne","year":"2006","unstructured":"Duquesne, S., Lange, T.: Pairing-based cryptography. In: Handbook of elliptic and hyperelliptic curve cryptography. Discrete Math. Appl, pp. 573\u2013590. Chapman & Hall\/CRC, Boca Raton, FL (2006)"},{"key":"19_CR7","series-title":"London Math. Soc. Lecture Note Ser.","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/CBO9780511546570.012","volume-title":"Advances in elliptic curve cryptography","author":"K.G. Paterson","year":"2005","unstructured":"Paterson, K.G.: Cryptography from pairings. In: Advances in elliptic curve cryptography. London Math. Soc. Lecture Note Ser., vol.\u00a0317, pp. 215\u2013251. Cambridge Univ. Press, Cambridge (2005)"},{"key":"19_CR8","unstructured":"Barreto, P.S.L.M.: The pairing-based crypto lounge \n                      \n                        http:\/\/planeta.terra.com.br\/informatica\/paulbarreto\/pblounge.html"},{"key":"19_CR9","unstructured":"Miller, V.: Short programs for functions on curves (1986)"},{"key":"19_CR10","series-title":"Discrete Math. Appl.","first-page":"389","volume-title":"Handbook of elliptic and hyperelliptic curve cryptography","author":"S. Duquesne","year":"2006","unstructured":"Duquesne, S., Frey, G.: Implementation of pairings. In: Handbook of elliptic and hyperelliptic curve cryptography, Boca Raton. Discrete Math. Appl., pp. 389\u2013404. Chapman & Hall\/CRC, Boca Raton, FL (2006)"},{"key":"19_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/3-540-45455-1_26","volume-title":"Algorithmic Number Theory","author":"S.D. Galbraith","year":"2002","unstructured":"Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the Tate pairing. In: Fieker, C., Kohel, D.R. (eds.) Algorithmic Number Theory. LNCS, vol.\u00a02369, pp. 324\u2013337. Springer, Heidelberg (2002)"},{"key":"19_CR12","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 sequences. Amer. J. Math.\u00a070, 31\u201374 (1948)","journal-title":"Amer. J. Math."},{"key":"19_CR13","doi-asserted-by":"crossref","unstructured":"Everest, G., Poorten, A.v.d., Shparlinski, I., Ward, T.: Elliptic Divisibility Sequences. American Mathematical Society, Providence, pp. 163\u2013175 (2003)","DOI":"10.1090\/surv\/104\/10"},{"key":"19_CR14","unstructured":"Shipsey, R.: Elliptic Divibility Sequences. PhD thesis, Goldsmiths, University of London (2001)"},{"key":"19_CR15","unstructured":"Stange, K.E.: Elliptic Nets. PhD thesis, Brown University (in preparation)"},{"key":"19_CR16","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4252-7","volume-title":"The arithmetic of elliptic curves","author":"J.H. Silverman","year":"1992","unstructured":"Silverman, J.H.: The arithmetic of elliptic curves (Corrected reprint of the 1986 original). Graduate Texts in Mathematics, vol.\u00a0106. Springer, New York (1992)"},{"key":"19_CR17","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0851-8","volume-title":"Advanced topics in the arithmetic of elliptic curves","author":"J.H. Silverman","year":"1994","unstructured":"Silverman, J.H.: Advanced topics in the arithmetic of elliptic curves. Graduate Texts in Mathematics, vol.\u00a0151. Springer, New York (1994)"},{"key":"19_CR18","unstructured":"Swart, C.: Elliptic curves and related sequences. PhD thesis, Royal Holloway and Bedford New College, University of London (2003)"},{"issue":"2","key":"19_CR19","first-page":"19","volume":"8","author":"A.J. Poorten","year":"2005","unstructured":"van der Poorten, A.J.: Elliptic curves and continued fractions. J. Integer Seq. Article 05.2.5, (electronic) 8(2), 19 (2005)","journal-title":"J. Integer Seq. Article 05.2.5, (electronic)"},{"key":"19_CR20","unstructured":"Propp, J.: Robbins forum \n                      \n                        http:\/\/www.math.wisc.edu\/~propp\/about-robbins"},{"key":"19_CR21","series-title":"Discrete Math. Appl.","first-page":"115","volume-title":"Handbook of elliptic and hyperelliptic curve cryptography","author":"S. Duquesne","year":"2006","unstructured":"Duquesne, S., Frey, G.: Background on pairings. In: Handbook of elliptic and hyperelliptic curve cryptography. Discrete Math. Appl., pp. 115\u2013124. Chapman & Hall\/CRC, Boca Raton, FL (2006)"},{"key":"19_CR22","series-title":"London Math. Soc. Lecture Note Ser.","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1017\/CBO9780511546570.011","volume-title":"Advances in elliptic curve cryptography","author":"S. Galbraith","year":"2005","unstructured":"Galbraith, S.: Pairings. In: Advances in elliptic curve cryptography. London Math. Soc. Lecture Note Ser., vol.\u00a0317, pp. 183\u2013213. Cambridge Univ. Press, Cambridge (2005)"},{"key":"19_CR23","series-title":"Discrete Math. Appl.","first-page":"45","volume-title":"Handbook of elliptic and hyperelliptic curve cryptography","author":"G. Frey","year":"2006","unstructured":"Frey, G., Lange, T.: Background on curves and Jacobians. In: Handbook of elliptic and hyperelliptic curve cryptography. Discrete Math. Appl., pp. 45\u201385. Chapman & Hall\/CRC, Boca Raton, FL (2006)"},{"key":"19_CR24","series-title":"Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-52244-4","volume-title":"Elliptic functions","author":"K. Chandrasekharan","year":"1985","unstructured":"Chandrasekharan, K.: Elliptic functions. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol.\u00a0281. Springer, Heidelberg (1985)"},{"key":"19_CR25","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Elliptic curves in cryptography","author":"I.F. Blake","year":"2000","unstructured":"Blake, I.F., Seroussi, G., Smart, N.P.: Elliptic curves in cryptography (Reprint of the 1999 original). London Mathematical Society Lecture Note Series, vol.\u00a0265. Cambridge University Press, Cambridge (2000)"},{"key":"19_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-44499-8_1","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2000","author":"D. Hankerson","year":"2000","unstructured":"Hankerson, D., Hernandez, J.L., Menezes, A.: Software implementation of elliptic curve cryptography over binary fields. In: Paar, C., Ko\u00e7, \u00c7.K. (eds.) CHES 2000. LNCS, vol.\u00a01965, pp. 1\u201324. Springer, Heidelberg (2000)"},{"key":"19_CR27","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)"},{"issue":"2","key":"19_CR28","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10623-005-3299-y","volume":"39","author":"M. Ciet","year":"2006","unstructured":"Ciet, M., Joye, M., Lauter, K., Montgomery, P.L.: Trading inversions for multiplications in elliptic curve cryptography. Des. Codes Cryptogr.\u00a039(2), 189\u2013206 (2006)","journal-title":"Des. Codes Cryptogr."},{"key":"19_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/11586821_2","volume-title":"Cryptography and Coding","author":"N. Koblitz","year":"2005","unstructured":"Koblitz, N., Menezes, A.: Pairing-based cryptography at high security levels. In: Smart, N.P. (ed.) Cryptography and Coding. LNCS, vol.\u00a03796, pp. 13\u201336. Springer, Heidelberg (2005)"},{"key":"19_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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":"19_CR31","unstructured":"The PARI Group: Pari\/gp development headquarters \n                      \n                        http:\/\/pari.math.u-bordeaux.fr\/"},{"key":"19_CR32","unstructured":"Stange, K.E.: Pari\/gp scripts for tate pairing via elliptic nets. \n                      \n                        http:\/\/www.math.brown.edu\/~stange\/tatepairing\/"},{"key":"19_CR33","unstructured":"Lynn, B.: Pairing-based cryptography library \n                      \n                        http:\/\/crypto.stanford.edu\/pbc\/"}],"container-title":["Lecture Notes in Computer Science","Pairing-Based Cryptography \u2013 Pairing 2007"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-73489-5_19.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T10:14:18Z","timestamp":1619518458000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-73489-5_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540734888","9783540734895"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-73489-5_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[]}}