{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T13:33:28Z","timestamp":1776778408638,"version":"3.51.2"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319566191","type":"print"},{"value":"9783319566207","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-56620-7_23","type":"book-chapter","created":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T02:29:18Z","timestamp":1490927358000},"page":"659-678","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Twisted $${\\mu }_4$$ -Normal Form for Elliptic Curves"],"prefix":"10.1007","author":[{"given":"David","family":"Kohel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,4,1]]},"reference":[{"issue":"1","key":"23_CR1","doi-asserted-by":"publisher","first-page":"65","DOI":"10.2307\/1969420","volume":"55","author":"NC Ankeny","year":"1952","unstructured":"Ankeny, N.C.: The least quadratic non residue. Ann. Math. Second Ser. 55(1), 65\u201372 (1952)","journal-title":"Ann. Math. Second Ser."},{"key":"23_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/978-3-540-76900-2_3","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2007","author":"DJ Bernstein","year":"2007","unstructured":"Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 29\u201350. Springer, Heidelberg (2007). doi:\n                      10.1007\/978-3-540-76900-2_3"},{"key":"23_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1007\/978-3-540-85053-3_16","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2008","author":"DJ Bernstein","year":"2008","unstructured":"Bernstein, D.J., Lange, T., Rezaeian Farashahi, R.: Binary edwards curves. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 244\u2013265. Springer, Heidelberg (2008). doi:\n                      10.1007\/978-3-540-85053-3_16"},{"key":"23_CR4","unstructured":"Bernstein, D.J., Lange, T.: Explicit formulas database. \n                      http:\/\/www.hyperelliptic.org\/EFD\/"},{"key":"23_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/978-3-540-68164-9_26","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2008","author":"DJ Bernstein","year":"2008","unstructured":"Bernstein, D.J., Birkner, P., Joye, M., Lange, T., Peters, C.: Twisted edwards curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389\u2013405. Springer, Heidelberg (2008). doi:\n                      10.1007\/978-3-540-68164-9_26"},{"key":"23_CR6","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1090\/S0273-0979-07-01153-6","volume":"44","author":"H Edwards","year":"2007","unstructured":"Edwards, H.: A normal form for elliptic curves. Bull. Am. Math. Soc. 44, 393\u2013422 (2007)","journal-title":"Bull. Am. Math. Soc."},{"key":"23_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/978-3-540-89255-7_20","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"H Hisil","year":"2008","unstructured":"Hisil, H., Wong, K.K.-H., Carter, G., Dawson, E.: Twisted edwards curves revisited. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 326\u2013343. Springer, Heidelberg (2008). doi:\n                      10.1007\/978-3-540-89255-7_20"},{"issue":"5","key":"23_CR8","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1016\/j.jnt.2010.12.001","volume":"131","author":"D Kohel","year":"2011","unstructured":"Kohel, D.: Addition law structure of elliptic curves. J. Number Theory 131(5), 894\u2013919 (2011)","journal-title":"J. Number Theory"},{"key":"23_CR9","unstructured":"Kohel, D.: A normal form for elliptic curves in characteristic 2. talk at Arithmetic, Geometry, Cryptography and Coding Theory, Luminy, 15 March 2011. \n                      http:\/\/iml.univ-mrs.fr\/kohel\/pub\/normal_form.pdf"},{"key":"23_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1007\/978-3-642-34931-7_22","volume-title":"Progress in Cryptology - INDOCRYPT 2012","author":"D Kohel","year":"2012","unstructured":"Kohel, D.: Efficient arithmetic on elliptic curves in characteristic 2. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 378\u2013398. Springer, Heidelberg (2012). doi:\n                      10.1007\/978-3-642-34931-7_22"},{"key":"23_CR11","unstructured":"Kohel, D., et al.: Echidna algorithms, v. 5.0 (2016). \n                      http:\/\/echidna.maths.usyd.edu.au\/echidna\/index.html"},{"key":"23_CR12","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/BF01390234","volume":"54","author":"JC Lagarias","year":"1979","unstructured":"Lagarias, J.C., Montgomery, H.L., Odlyzko, A.M.: A bound for the least prime ideal in the Chebotarev density theorem. Invent. Math. 54, 271\u2013296 (1979)","journal-title":"Invent. Math."},{"issue":"3","key":"23_CR13","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1007\/BF01388526","volume":"79","author":"H Lange","year":"1985","unstructured":"Lange, H., Ruppert, W.: Complete systems of addition laws on abelian varieties. Invent. Math. 79(3), 603\u2013610 (1985)","journal-title":"Invent. Math."},{"key":"23_CR14","unstructured":"Magma Computational Algebra System (Version 2.20) (2015). \n                      http:\/\/magma.maths.usyd.edu.au\/magma\/handbook\/"},{"key":"23_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-642-40349-1_18","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2013","author":"T Oliveira","year":"2013","unstructured":"Oliveira, T., L\u00f3pez, J., Aranha, D.F., Rodr\u00edguez-Henr\u00edquez, F.: Lambda coordinates for binary elliptic curves. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 311\u2013330. Springer, Heidelberg (2013). doi:\n                      10.1007\/978-3-642-40349-1_18"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2017"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-56620-7_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T00:09:40Z","timestamp":1586477380000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-56620-7_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319566191","9783319566207"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-56620-7_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]},"assertion":[{"value":"1 April 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EUROCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paris","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 April 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 May 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"36","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt2017.di.ens.fr\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}