{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T22:34:35Z","timestamp":1775774075436,"version":"3.50.1"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030648336","type":"print"},{"value":"9783030648343","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"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":[[2020]]},"DOI":"10.1007\/978-3-030-64834-3_17","type":"book-chapter","created":{"date-parts":[[2020,12,4]],"date-time":"2020-12-04T17:40:49Z","timestamp":1607103649000},"page":"493-519","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Radical Isogenies"],"prefix":"10.1007","author":[{"given":"Wouter","family":"Castryck","sequence":"first","affiliation":[]},{"given":"Thomas","family":"Decru","sequence":"additional","affiliation":[]},{"given":"Frederik","family":"Vercauteren","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,12,5]]},"reference":[{"key":"17_CR1","doi-asserted-by":"crossref","unstructured":"Bernstein, D., De Feo, L., Leroux, A., Smith, B.: Faster computation of isogenies of large prime degree. In: ANTS-XIV. Mathematical Sciences Publishers (2020)","DOI":"10.2140\/obs.2020.4.39"},{"key":"17_CR2","unstructured":"Bernstein, D. J., Lange, T.: Montgomery curves and the Montgomery ladder. In: IACR Cryptology ePrint Archive, p. 293 (2017) https:\/\/ia.cr\/2017\/293"},{"key":"17_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/978-3-030-17656-3_15","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"DJ Bernstein","year":"2019","unstructured":"Bernstein, D.J., Lange, T., Martindale, C., Panny, L.: Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 409\u2013441. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17656-3_15"},{"key":"17_CR4","doi-asserted-by":"crossref","unstructured":"Blake, I.F., Seroussi, G., Smart, N.P. (eds.): Advances in elliptic curve cryptography. London Mathematical Society Lecture Note Series, vol. 317. Cambridge University Press, Cambridge (2005)","DOI":"10.1017\/CBO9780511546570"},{"issue":"3\u20134","key":"17_CR5","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. Journal of Symbolic Computation 24(3\u20134), 235\u2013265 (1997)","journal-title":"Journal of Symbolic Computation"},{"key":"17_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-030-44223-1_7","volume-title":"Post-Quantum Cryptography","author":"W Castryck","year":"2020","unstructured":"Castryck, W., Decru, T.: CSIDH on the surface. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 111\u2013129. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-44223-1_7"},{"key":"17_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/978-3-030-03332-3_15","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2018","author":"W Castryck","year":"2018","unstructured":"Castryck, W., Lange, T., Martindale, C., Panny, L., Renes, J.: CSIDH: an efficient post-quantum commutative group action. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11274, pp. 395\u2013427. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03332-3_15"},{"issue":"1","key":"17_CR8","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s00145-007-9002-x","volume":"22","author":"DX Charles","year":"2007","unstructured":"Charles, D.X., Lauter, K.E., Goren, E.Z.: Cryptographic hash functions from expander graphs. Journal of Cryptology 22(1), 93\u2013113 (2007). https:\/\/doi.org\/10.1007\/s00145-007-9002-x","journal-title":"Journal of Cryptology"},{"key":"17_CR9","unstructured":"Chi-Dom\u00ednguez, J.-J., Rodr\u00edguez-Henr\u00edquez, F.: Optimal strategies for CSIDH. Adv. Math. Commun. (2019)"},{"key":"17_CR10","unstructured":"Conrad, K.: Simple radical extensions. Expository paper. https:\/\/kconrad.math.uconn.edu\/blurbs\/galoistheory\/simpleradical.pdf"},{"key":"17_CR11","unstructured":"Couveignes, J.M.: Hard homogeneous spaces. IACR Cryptology ePrint Archive, p. 291 (2006) https:\/\/ia.cr\/2006\/291"},{"key":"17_CR12","unstructured":"Dang, T., Moody, D.: Twisted Hessian isogenies. IACR Cryptology ePrint Archive, 2019, p. 1003 (2019) https:\/\/ia.cr\/2019\/1003"},{"key":"17_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/978-3-030-03332-3_14","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2018","author":"L De Feo","year":"2018","unstructured":"De Feo, L., Kieffer, J., Smith, B.: Towards practical key exchange from ordinary isogeny graphs. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11274, pp. 365\u2013394. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03332-3_14"},{"key":"17_CR14","unstructured":"Lontouo, P.B.F., Fouotsa, E.: Analogue of V\u00e9lu\u2019s formulas for computing isogenies over Hessian model of elliptic curves. IACR Cryptology ePrint Archive, 2019, p. 1480 (2019) https:\/\/ia.cr\/2019\/1480"},{"key":"17_CR15","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/s00013-003-4773-2","volume":"82","author":"F Hess","year":"2004","unstructured":"Hess, F.: A note on the Tate pairing of curves over finite fields. Archiv der Mathematik 82, 28\u201332 (2004)","journal-title":"Archiv der Mathematik"},{"key":"17_CR16","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). https:\/\/doi.org\/10.1007\/978-3-642-25405-5_2"},{"key":"17_CR17","doi-asserted-by":"publisher","unstructured":"Lang, S.: Algebra, volume 211 of Graduate Texts in Mathematics. Springer-Verlag, New York, third ed. (2002) https:\/\/doi.org\/10.1007\/978-1-4613-0041-0","DOI":"10.1007\/978-1-4613-0041-0"},{"key":"17_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/978-3-030-05378-9_8","volume-title":"Progress in Cryptology \u2013 INDOCRYPT 2018","author":"M Meyer","year":"2018","unstructured":"Meyer, M., Reith, S.: A faster way to the CSIDH. In: Chakraborty, D., Iwata, T. (eds.) INDOCRYPT 2018. LNCS, vol. 11356, pp. 137\u2013152. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-05378-9_8"},{"key":"17_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1007\/978-3-030-40186-3_22","volume-title":"Topics in Cryptology \u2013 CT-RSA 2020","author":"T Moriya","year":"2020","unstructured":"Moriya, T., Onuki, H., Takagi, T.: How to construct CSIDH on edwards curves. In: Jarecki, S. (ed.) CT-RSA 2020. LNCS, vol. 12006, pp. 512\u2013537. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-40186-3_22"},{"key":"17_CR20","unstructured":"Nakagawa, K., Onuki, H., Takayasu, A., Takagi, T.: $$l_1$$-norm ball for CSIDH: optimal strategy for choosing the secret key space. IACR Cryptology ePrint Archive, 2020, p. 181 (2020) https:\/\/ia.cr\/2020\/181"},{"key":"17_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/978-3-319-79063-3_11","volume-title":"Post-Quantum Cryptography","author":"J Renes","year":"2018","unstructured":"Renes, J.: Computing isogenies between montgomery curves using the action of (0, 0). In: Lange, T., Steinwandt, R. (eds.) PQCrypto 2018. LNCS, vol. 10786, pp. 229\u2013247. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-79063-3_11"},{"key":"17_CR22","unstructured":"Rostovtsev, A., Stolbunov, A.: Public-key cryptosystem based on isogenies. IACR Cryptology ePrint Archive, 2006, p. 145 (2006) https:\/\/ia.cr\/2006\/145.pdf"},{"key":"17_CR23","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. GTM, vol. 106. Springer, New York (2009). https:\/\/doi.org\/10.1007\/978-0-387-09494-6"},{"key":"17_CR24","unstructured":"The Stacks project authors. The stacks project (2020) https:\/\/stacks.math.columbia.edu"},{"key":"17_CR25","unstructured":"Streng., M.: Generators of the group of modular units for $$\\Gamma _1(N)$$ over the rationals. Cornell University arXiv:1503.08127v2 (2019)"},{"issue":"278","key":"17_CR26","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1090\/S0025-5718-2011-02538-X","volume":"81","author":"A Sutherland","year":"2012","unstructured":"Sutherland, A.: Constructing elliptic curves over finite fields with prescribed torsion. Mathematics of Computation 81(278), 1131\u20131147 (2012)","journal-title":"Mathematics of Computation"},{"key":"17_CR27","unstructured":"Tsfasman, M.A., Vl\u01cedu\u0163, S.G.: Algebraic-geometric codes, volume 58 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, Translated from the Russian by the authors (1991)"},{"issue":"273","key":"17_CR28","first-page":"238","volume":"I","author":"J V\u00e9lu","year":"1971","unstructured":"V\u00e9lu, J.: Isog\u00e9nies entre courbes elliptiques. Comptes-Rendus de l\u2019Acad\u00e9mie des Sciences, S\u00e9rie I(273), 238\u2013241 (1971)","journal-title":"Comptes-Rendus de l\u2019Acad\u00e9mie des Sciences, S\u00e9rie"},{"key":"17_CR29","doi-asserted-by":"publisher","first-page":"521","DOI":"10.24033\/asens.1183","volume":"2","author":"WC Waterhouse","year":"1969","unstructured":"Waterhouse, W.C.: Abelian varieties over finite fields. Annales scientifiques de l\u2019\u00c9cole Normale Sup\u00e9rieure 2, 521\u2013560 (1969)","journal-title":"Annales scientifiques de l\u2019\u00c9cole Normale Sup\u00e9rieure"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2020"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-64834-3_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T01:04:35Z","timestamp":1701651875000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-64834-3_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030648336","9783030648343"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-64834-3_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"5 December 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ASIACRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on the Theory and Application of Cryptology and Information Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Daejeon","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Korea (Republic of)","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 December 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 December 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"asiacrypt2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/asiacrypt.iacr.org\/2020\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"websubrev","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"316","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"85","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"27% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"19","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference will take place virtually due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}