{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T16:54:05Z","timestamp":1779900845721,"version":"3.53.1"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319130385","type":"print"},{"value":"9783319130392","type":"electronic"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":[[2014]]},"DOI":"10.1007\/978-3-319-13039-2_25","type":"book-chapter","created":{"date-parts":[[2014,10,24]],"date-time":"2014-10-24T19:36:19Z","timestamp":1414179379000},"page":"428-442","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["A Quantum Algorithm for Computing Isogenies between Supersingular Elliptic Curves"],"prefix":"10.1007","author":[{"given":"Jean-Fran\u00e7ois","family":"Biasse","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Jao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anirudh","family":"Sankar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2014,10,25]]},"reference":[{"issue":"3\u20134","key":"25_CR1","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. the user language. J. Symbolic Comput. 24(3\u20134), 235\u2013265 (1997)","journal-title":"J. Symbolic Comput."},{"key":"25_CR2","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1002\/(SICI)1521-3978(199806)46:4\/5<493::AID-PROP493>3.0.CO;2-P","volume":"46","author":"M Boyer","year":"1998","unstructured":"Boyer, M., Brassard, G.: P. H\u00f8yer, and A. Tapp. Tight bounds on quantum searching. Fortschritte Der Physik 46, 493\u2013505 (1998)","journal-title":"Fortschritte Der Physik"},{"issue":"3","key":"25_CR3","first-page":"269","volume":"1","author":"R Br\u00f6ker","year":"2009","unstructured":"Br\u00f6ker, R.: Constructing supersingular elliptic curves. J. Comb. Number Theory 1(3), 269\u2013273 (2009)","journal-title":"J. Comb. Number Theory"},{"key":"25_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1007\/978-3-540-85538-5_7","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2008","author":"R Br\u00f6ker","year":"2008","unstructured":"Br\u00f6ker, R., Charles, D., Lauter, K.: Evaluating Large Degree Isogenies and Applications to Pairing Based Cryptography. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 100\u2013112. Springer, Heidelberg (2008)"},{"key":"25_CR5","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s00145-007-9002-x","volume":"22","author":"D Charles","year":"2009","unstructured":"Charles, D., Lauter, K., Goren, E.: Cryptographic hash functions from expander graphs. Jornal of Cryptology 22, 93\u2013113 (2009)","journal-title":"Jornal of Cryptology"},{"issue":"1","key":"25_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/jmc-2012-0016","volume":"8","author":"A Childs","year":"2013","unstructured":"Childs, A., Jao, D., Soukharev, V.: Constructing elliptic curve isogenies in quantum subexponential time. Journal of Mathematical Cryptology 8(1), 1\u201329 (2013)","journal-title":"Journal of Mathematical Cryptology"},{"key":"25_CR7","unstructured":"Couveignes, J.-M.: Hard homgeneous spaces. http:\/\/eprint.iacr.org\/2006\/291"},{"key":"25_CR8","unstructured":"Cox, D. A.: Primes of the form $$x^2+n y^2$$. John Wiley & Sons (1989)"},{"key":"25_CR9","unstructured":"Delfs, C., Galbraith, S.: Computing isogenies between supersingular elliptic curves over $$\\mathbb{F}_p$$. The Proceedings of the 11th Algorithmic Nnumber Theory Symposium (ANTS XI) (to appear)"},{"key":"25_CR10","doi-asserted-by":"crossref","unstructured":"De Feo, L., Jao, D., Pl\u00fbt, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. Journal of Mathematical Cryptology (to appear, 2014). http:\/\/eprint.iacr.org\/2011\/506","DOI":"10.1515\/jmc-2012-0015"},{"key":"25_CR11","doi-asserted-by":"crossref","unstructured":"Galbraith, S.: Constructing isogenies between elliptic curves over finite fields. LMS Journal of Computation and Mathematics 2, 118\u2013138 (1999)","DOI":"10.1112\/S1461157000000097"},{"issue":"2","key":"25_CR12","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s00200-013-0185-0","volume":"24","author":"S Galbraith","year":"2013","unstructured":"Galbraith, S., Stolbunov, A.: Improved algorithm for the isogeny problem for ordinary elliptic curves. Applicable Algebra in Engineering, Communication and Computing 24(2), 107\u2013131 (2013)","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"key":"25_CR13","doi-asserted-by":"crossref","unstructured":"Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC 1996, pp. 212\u2013219. ACM, New York (1996)","DOI":"10.1145\/237814.237866"},{"key":"25_CR14","doi-asserted-by":"crossref","unstructured":"Littlewood, J.: On the class number of the corpus $$p(\\sqrt{k})$$. Proc. London Math. Soc. 27, 358\u2013372 (1928)","DOI":"10.1112\/plms\/s2-27.1.358"},{"key":"25_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/978-3-642-25405-5_2","volume-title":"Post-Quantum Cryptography","author":"D Jao","year":"2011","unstructured":"Jao, D., De Feo, L.: Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 19\u201334. Springer, Heidelberg (2011)"},{"issue":"6","key":"25_CR16","doi-asserted-by":"publisher","first-page":"1491","DOI":"10.1016\/j.jnt.2008.11.006","volume":"129","author":"D Jao","year":"2009","unstructured":"Jao, D., Miller, S.D., Venkatesan, R.: Expander graphs based on GRH with an application to elliptic curve cryptography. J. Number Theory 129(6), 1491\u20131504 (2009)","journal-title":"J. Number Theory"},{"key":"25_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/11593447_2","volume-title":"Advances in Cryptology - ASIACRYPT 2005","author":"D Jao","year":"2005","unstructured":"Jao, D., Miller, S.D., Venkatesan, R.: Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log? In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 21\u201340. Springer, Heidelberg (2005)"},{"key":"25_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1007\/978-3-319-11659-4_10","volume-title":"Post-Quantum Cryptography","author":"D Jao","year":"2014","unstructured":"Jao, D., Soukharev, V.: Isogeny-Based Quantum-Resistant Undeniable Signatures. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 160\u2013179. Springer, Heidelberg (2014)"},{"issue":"1","key":"25_CR19","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/S0097539703436345","volume":"35","author":"G Kuperberg","year":"2005","unstructured":"Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35(1), 170\u2013188 (2005)","journal-title":"SIAM J. Comput."},{"key":"25_CR20","unstructured":"MAGMA Computational Algebra System. http:\/\/magma.maths.usyd.edu.au\/"},{"key":"25_CR21","unstructured":"Regev, O.: A subexponential time algorithm for the dihedral hidden subgroup problem with polynomial space. arXiv:quant-ph\/0406151"},{"key":"25_CR22","unstructured":"Rostovtsev, A., Stolbunov, A.: Public-key cryptosystem based on isogenies. IACR Cryptology ePrint Archive 2006, 145 (2006)"},{"key":"25_CR23","doi-asserted-by":"publisher","first-page":"219","DOI":"10.5802\/jtnb.142","volume":"7","author":"R Schoof","year":"1995","unstructured":"Schoof, R.: Counting points on elliptic curves over finite fields. Journal de th\u00e9orie des nombres de Bordeaux 7, 219\u2013254 (1995)","journal-title":"Journal de th\u00e9orie des nombres de Bordeaux"},{"key":"25_CR24","doi-asserted-by":"crossref","unstructured":"Seiichiro, T.: Claw finding algorithms using quantum walk. Theoretical Computer Science 410(50), 5285\u20135297 (2009), Mathematical Foundations of Computer Science (MFCS 2007)","DOI":"10.1016\/j.tcs.2009.08.030"},{"key":"25_CR25","unstructured":"Silverman, J.: The arithmetic of elliptic curves, vol. 106. Graduate texts in Mathematics. Springer (1992)"},{"issue":"2","key":"25_CR26","doi-asserted-by":"publisher","first-page":"215","DOI":"10.3934\/amc.2010.4.215","volume":"4","author":"A Stolbunov","year":"2010","unstructured":"Stolbunov, A.: Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Adv. in Math. of Comm. 4(2), 215\u2013235 (2010)","journal-title":"Adv. in Math. of Comm."},{"key":"25_CR27","unstructured":"Sutherland, A.: smoothrelation. http:\/\/math.mit.edu\/~drew\/smooth_relation_v1.2.tar."},{"key":"25_CR28","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1007\/BF01404549","volume":"2","author":"J Tate","year":"1966","unstructured":"Tate, J.: Endomoprhisms of abelian varieties over finite fields. Inventiones Mathematica 2, 134\u2013144 (1966)","journal-title":"Inventiones Mathematica"},{"key":"25_CR29","unstructured":"V\u00e9lu, J.: Isog\u00e9nies entre courbes elliptiques. C. R. Acad. Sci. Paris S\u00e9r. A-B, 273, A238\u2013A241 (1971)"}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology -- INDOCRYPT 2014"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-13039-2_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T19:04:39Z","timestamp":1676660679000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-13039-2_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319130385","9783319130392"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-13039-2_25","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"25 October 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}