{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T11:06:08Z","timestamp":1744974368476,"version":"3.40.3"},"publisher-location":"Cham","reference-count":17,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031690693"},{"type":"electronic","value":"9783031690709"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-69070-9_11","type":"book-chapter","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T11:23:00Z","timestamp":1724325780000},"page":"178-192","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Computing a\u00a0Basis of\u00a0the\u00a0Set of\u00a0Isogenies Between Two Supersingular Elliptic Curves"],"prefix":"10.1007","author":[{"given":"Akira","family":"Katayama","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masaya","family":"Yasuda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,21]]},"reference":[{"key":"11_CR1","series-title":"Association for Women in Mathematics Series","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-030-19478-9_2","volume-title":"Research Directions in Number Theory","author":"E Bank","year":"2019","unstructured":"Bank, E., Camacho-Navarro, C., Eisentr\u00e4ger, K., Morrison, T., Park, J.: Cycles in the supersingular $$\\ell $$-isogeny graph and corresponding endomorphisms. In: Balakrishnan, J.S., Folsom, A., Lal\u00edn, M., Manes, M. (eds.) Research Directions in Number Theory. AWMS, vol. 19, pp. 41\u201366. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-19478-9_2"},{"key":"11_CR2","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s10623-014-0010-1","volume":"78","author":"C Delfs","year":"2016","unstructured":"Delfs, C., Galbraith, S.D.: Computing isogenies between supersingular elliptic curves over $$\\mathbb{F} _p$$. Des. Codes Crypt. 78, 425\u2013440 (2016)","journal-title":"Des. Codes Crypt."},{"key":"11_CR3","unstructured":"Developers, T.S.: SageMath, the Sage Mathematics Software System (Version 10.1) (2020). http:\/\/www.sagemath.org"},{"key":"11_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/978-3-319-78372-7_11","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2018","author":"K Eisentr\u00e4ger","year":"2018","unstructured":"Eisentr\u00e4ger, K., Hallgren, S., Lauter, K., Morrison, T., Petit, C.: Supersingular isogeny graphs and endomorphism rings: reductions and solutions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 329\u2013368. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-78372-7_11"},{"issue":"1","key":"11_CR5","doi-asserted-by":"publisher","first-page":"215","DOI":"10.2140\/obs.2020.4.215","volume":"4","author":"K Eisentr\u00e4ger","year":"2020","unstructured":"Eisentr\u00e4ger, K., Hallgren, S., Leonardi, C., Morrison, T., Park, J.: Computing endomorphism rings of supersingular elliptic curves and connections to path-finding in isogeny graphs. Open Book Series 4(1), 215\u2013232 (2020)","journal-title":"Open Book Series"},{"key":"11_CR6","unstructured":"Fuselier, J., Iezzi, A., Kozek, M., Morrison, T., Namoijam, C.: Computing supersingular endomorphism rings using inseparable endomorphisms. arXiv preprint arXiv:2306.03051 (2023)"},{"key":"11_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/978-3-662-53887-6_3","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2016","author":"SD Galbraith","year":"2016","unstructured":"Galbraith, S.D., Petit, C., Shani, B., Ti, Y.B.: On the security of supersingular isogeny cryptosystems. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 63\u201391. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53887-6_3"},{"issue":"1","key":"11_CR8","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1007\/s00145-019-09316-0","volume":"33","author":"SD Galbraith","year":"2020","unstructured":"Galbraith, S.D., Petit, C., Silva, J.: Identification protocols and signature schemes based on supersingular isogeny problems. J. Cryptol. 33(1), 130\u2013175 (2020)","journal-title":"J. Cryptol."},{"key":"11_CR9","unstructured":"Kambe, Y., Katayama, A., Aikawa, Y., Ishihara, Y., Yasuda, M., Yokoyama, K.: Computing endomorphism rings of supersingular elliptic curves by finding cycles in concatenated supersingular isogeny graphs. Commentarii Mathematici Universitatis Sancti Pauli (to appear)"},{"key":"11_CR10","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1007\/s13160-023-00638-y","volume":"41","author":"A Katayama","year":"2023","unstructured":"Katayama, A., Yasuda, M.: Computing the Brauer group of the product of two elliptic curves over a finite field. Jpn. J. Ind. Appl. Math. 41, 919\u2013943 (2023)","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"11_CR11","unstructured":"Kohel, D.: Endomorphism rings of elliptic curves over finite fields. Ph.D. thesis, University of California, Berkeley (1996)"},{"issue":"2","key":"11_CR12","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/0021-8693(80)90151-9","volume":"64","author":"A Pizer","year":"1980","unstructured":"Pizer, A.: An algorithm for computing modular forms on $${\\varGamma _0(n)}$$. J. Algebra 64(2), 340\u2013390 (1980)","journal-title":"J. Algebra"},{"key":"11_CR13","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09494-6","volume-title":"The Arithmetic of Elliptic Curves","author":"JH Silverman","year":"2009","unstructured":"Silverman, J.H.: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106, 2nd edn. Springer, New York (2009)","edition":"2"},{"issue":"2","key":"11_CR14","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1007\/BF01404549","volume":"2","author":"J Tate","year":"1966","unstructured":"Tate, J.: Endomorphisms of abelian varieties over finite fields. Invent. Math. 2(2), 134\u2013144 (1966)","journal-title":"Invent. Math."},{"key":"11_CR15","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-56694-4","volume-title":"Quaternion Algebras","author":"J Voight","year":"2021","unstructured":"Voight, J.: Quaternion Algebras. Graduate Texts in Mathematics, vol. 288. Springer, Cham (2021)"},{"key":"11_CR16","doi-asserted-by":"publisher","DOI":"10.1201\/9781420071474","volume-title":"Elliptic Curves: Number Theory and Cryptography","author":"LC Washington","year":"2008","unstructured":"Washington, L.C.: Elliptic Curves: Number Theory and Cryptography, 2nd edn. CRC Press, Boca Raton (2008)","edition":"2"},{"key":"11_CR17","doi-asserted-by":"crossref","unstructured":"Wesolowski, B.: The supersingular isogeny path and endomorphism ring problems are equivalent. In: FOCS 2021, pp. 1100\u20131111. IEEE (2022)","DOI":"10.1109\/FOCS52979.2021.00109"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-69070-9_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T11:36:40Z","timestamp":1724326600000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-69070-9_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031690693","9783031690709"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-69070-9_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"21 August 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Rennes","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":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 September 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 September 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}