{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T23:12:53Z","timestamp":1725491573371},"publisher-location":"Berlin, Heidelberg","reference-count":31,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540734888"},{"type":"electronic","value":"9783540734895"}],"license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-73489-5_9","type":"book-chapter","created":{"date-parts":[[2007,9,11]],"date-time":"2007-09-11T04:58:06Z","timestamp":1189486686000},"page":"152-176","source":"Crossref","is-referenced-by-count":14,"title":["Constructing Pairing-Friendly Genus 2 Curves with Ordinary Jacobians"],"prefix":"10.1007","author":[{"given":"David","family":"Freeman","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"9_CR1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s001459900040","volume":"11","author":"R. Balasubramanian","year":"1998","unstructured":"Balasubramanian, R., Koblitz, N.: The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm. Journal of Cryptology\u00a011, 141\u2013145 (1998)","journal-title":"Journal of Cryptology"},{"key":"9_CR2","unstructured":"Bernstein, D.: Elliptic vs. hyperelliptic, part 1. Talk at ECC 2006, Toronto, Canada (20 September 2006), Slides available at \n                      \n                        http:\/\/cr.yp.to\/talks\/2006.09.20\/slides.pdf"},{"key":"9_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/978-3-540-30576-7_18","volume-title":"Theory of Cryptography","author":"D. Boneh","year":"2005","unstructured":"Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 325\u2013341. Springer, Heidelberg (2005)"},{"key":"9_CR4","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s10623-004-3808-4","volume":"37","author":"F. Brezing","year":"2005","unstructured":"Brezing, F., Weng, A.: Elliptic curves suitable for pairing based cryptography. Designs, Codes and Cryptography\u00a037, 133\u2013141 (2005)","journal-title":"Designs, Codes and Cryptography"},{"key":"9_CR5","unstructured":"Cocks, C., Pinch, R.G.E.: Identity-based cryptosystems based on the Weil pairing (Unpublished manuscript 2001)"},{"key":"9_CR6","unstructured":"Eisentr\u00e4ger, K., Lauter, K.: A CRT algorithm for constructing genus 2 curves over finite fields. In: AGCT-11, 2007 (to appear), preprint available at \n                      \n                        http:\/\/arxiv.org\/abs\/math.NT\/0405305"},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"Freeman, D., Lauter, K.: Computing endomorphism rings of Jacobians of genus 2 curves over finite fields. In: Symposium on Algebraic Geometry and its Applications, Tahiti 2007 (to appear), preprint available at \n                      \n                        http:\/\/eprint.iacr.org","DOI":"10.1142\/9789812793430_0002"},{"key":"9_CR8","unstructured":"Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. Cryptology eprint 2006 \/371, available at \n                      \n                        http:\/\/eprint.iacr.org"},{"key":"9_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1007\/11792086_33","volume-title":"Algorithmic Number Theory","author":"G. Frey","year":"2006","unstructured":"Frey, G., Lange, T.: Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves. In: Hess, F., Pauli, S., Pohst, M. (eds.) Algorithmic Number Theory. LNCS, vol.\u00a04076, pp. 466\u2013479. Springer, Heidelberg (2006)"},{"key":"9_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/3-540-45682-1_29","volume-title":"Advances in Cryptology - ASIACRYPT 2001","author":"S. Galbraith","year":"2001","unstructured":"Galbraith, S.: Supersingular curves in cryptography. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol.\u00a02248, pp. 495\u2013513. Springer, Heidelberg (2001)"},{"key":"9_CR11","unstructured":"Galbraith, S., McKee, J., Valen\u00e7a, P.: Ordinary abelian varieties having small embedding degree. In: Finite Fields and Their Applications (to appear), preprint available at \n                      \n                        http:\/\/eprint.iacr.org"},{"key":"9_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/11935230_8","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2006","author":"P. Gaudry","year":"2006","unstructured":"Gaudry, P., Houtmann, T., Kohel, D., Ritzenthaler, C., Weng, A.: The 2-adic CM method for genus 2 curves with application to cryptography. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol.\u00a04284, pp. 114\u2013129. Springer, Heidelberg (2006)"},{"key":"9_CR13","unstructured":"Goren, E., Lauter, K.: Class invariants for quartic CM fields. In: Annales Inst. Fourier (to appear), preprint available at \n                      \n                        http:\/\/arxiv.org\/abs\/math\/0404378"},{"key":"9_CR14","unstructured":"Hitt, L.: Families of genus 2 curves with small embedding degree. Cryptology eprint 2007\/001, available at \n                      \n                        http:\/\/eprint.iacr.org"},{"key":"9_CR15","doi-asserted-by":"crossref","unstructured":"Hitt, L.: On the minimal embedding field. In: Pairing 2007, LNCS, vol. 4575, pp. 294\u2013301(to appear), preprint available at \n                      \n                        http:\/\/eprint.iacr.org","DOI":"10.1007\/978-3-540-73489-5_16"},{"key":"9_CR16","doi-asserted-by":"publisher","first-page":"2361","DOI":"10.2307\/2154828","volume":"347","author":"E. Howe","year":"1995","unstructured":"Howe, E.: Principally polarized ordinary abelian varieties over finite fields. Trans. Amer. Math. Soc.\u00a0347, 2361\u20132401 (1995)","journal-title":"Trans. Amer. Math. Soc."},{"key":"9_CR17","unstructured":"Katz, N.: Serre-Tate local moduli. In: Surfaces alg\u00e9briques (S\u00e9m. de g\u00e9om. alg\u00e9br. d\u2019Orsay 1976-78), Springer Lect. Notes in Math., expos\u00e9 V-bis, vol. 868, pp. 138\u2013202 (1981)"},{"key":"9_CR18","unstructured":"Lange, T.: Elliptic vs. hyperelliptic, part 2, talk at ECC 2006, Toronto, Canada (20 September, 2006) Slides available at \n                      \n                        http:\/\/hyperelliptic.org\/tanja\/vortraege\/ECC06.ps"},{"key":"9_CR19","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1215\/ijm\/1258131069","volume":"48","author":"F. Luca","year":"2004","unstructured":"Luca, F., Mireles, D., Shparlinski, I.: MOV attack in various subgroups on elliptic curves. Illinois J. Math.\u00a048, 1041\u20131052 (2004)","journal-title":"Illinois J. Math."},{"key":"9_CR20","doi-asserted-by":"publisher","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 Transactions on Information Theory\u00a039, 1639\u20131646 (1993)","journal-title":"IEEE Transactions on Information Theory"},{"key":"9_CR21","doi-asserted-by":"crossref","unstructured":"Mestre, J.-F.: Construction de courbes de genre 2 \u00e0 partir de leurs modules. In: Effective methods in algebraic geometry, Birkh\u00e4user Progr. Math. vol. 94, pp. 313\u2013334 (1991)","DOI":"10.1007\/978-1-4612-0441-1_21"},{"key":"9_CR22","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/978-1-4613-8655-1_5","volume-title":"Arithmetic Geometry","author":"J.S. Milne","year":"1986","unstructured":"Milne, J.S.: Abelian varieties. In: Cornell, G., Silverman, J. (eds.) Arithmetic Geometry, pp. 103\u2013150. Springer, Heidelberg (1986)"},{"key":"9_CR23","first-page":"1234","volume":"E84-A","author":"A. Miyaji","year":"2001","unstructured":"Miyaji, A., Nakabayashi, M., Takano, S.: New explicit conditions of elliptic curve traces for FR-reduction. IEICE Transactions on Fundamentals\u00a0E84-A, 1234\u20131243 (2001)","journal-title":"IEICE Transactions on Fundamentals"},{"key":"9_CR24","first-page":"377","volume":"20","author":"F. Oort","year":"1973","unstructured":"Oort, F., Ueno, K.: Principally polarized abelian varieties of dimension two or three are Jacobian varieties. J. Fac. Sci. Univ. Tokyo Sect. IA Math.\u00a020, 377\u2013381 (1973)","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math."},{"key":"9_CR25","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/CBO9780511546570.012","volume-title":"Advances in Elliptic Curve Cryptography","author":"K. Paterson","year":"2005","unstructured":"Paterson, K.: Cryptography from pairings. In: Blake, I.F., Seroussi, G., Smart, N.P. (eds.) Advances in Elliptic Curve Cryptography, pp. 215\u2013251. Cambridge University Press, Cambridge (2005)"},{"key":"9_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1007\/3-540-45708-9_22","volume-title":"Advances in Cryptology - CRYPTO 2002","author":"K. Rubin","year":"2002","unstructured":"Rubin, K., Silverberg, A.: Supersingular abelian varieties in cryptology. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol.\u00a02442, pp. 336\u2013353. Springer, Heidelberg (2002)"},{"key":"9_CR27","unstructured":"Spallek, A.-M.: Kurven vom Geschlecht 2 und ihre Anwendung in Public-Key-Kryptosystemen. Ph.D. thesis, Institut f\u00fcr Experimentelle Mathematik, Universit\u00e4t GH Essen (1994)"},{"key":"9_CR28","doi-asserted-by":"crossref","unstructured":"Tate, J.: Classes d\u2019isog\u00e9nie des vari\u00e9t\u00e9s ab\u00e9liennes sur un corps fini (d\u2019apr\u00e8s T. Honda), S\u00e9minaire Bourbaki 1968\/69, Springer Lect. Notes in Math. expos\u00e9 352, vol. 179, pp. 95\u2013110 (1971)","DOI":"10.1007\/BFb0058807"},{"key":"9_CR29","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1090\/S0025-5718-99-01020-0","volume":"68","author":"P. Wamelen van","year":"1999","unstructured":"van Wamelen, P.: Examples of genus two CM curves defined over the rationals. Math.\u00a0Comp.\u00a068, 307\u2013320 (1999)","journal-title":"Math.\u00a0Comp."},{"key":"9_CR30","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1090\/pspum\/020\/0314847","volume":"20","author":"W.C. Waterhouse","year":"1971","unstructured":"Waterhouse, W.C., Milne, J.S.: Abelian varieties over finite fields. Proc. Symp. Pure Math.\u00a020, 53\u201364 (1971)","journal-title":"Proc. Symp. Pure Math."},{"key":"9_CR31","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1090\/S0025-5718-02-01422-9","volume":"72","author":"A. Weng","year":"2003","unstructured":"Weng, A.: Constructing hyperelliptic curves of genus 2 suitable for cryptography. Math.\u00a0Comp.\u00a072, 435\u2013458 (2003)","journal-title":"Math.\u00a0Comp."}],"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_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,21]],"date-time":"2019-05-21T21:36:34Z","timestamp":1558474594000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-73489-5_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540734888","9783540734895"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-73489-5_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2007]]}}}