{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:41:03Z","timestamp":1777675263851,"version":"3.51.4"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031159817","type":"print"},{"value":"9783031159824","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-15982-4_10","type":"book-chapter","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T04:40:54Z","timestamp":1665463254000},"page":"285-314","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Accelerating the Delfs\u2013Galbraith Algorithm with Fast Subfield Root Detection"],"prefix":"10.1007","author":[{"given":"Maria","family":"Corte-Real Santos","sequence":"first","affiliation":[]},{"given":"Craig","family":"Costello","sequence":"additional","affiliation":[]},{"given":"Jia","family":"Shi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,12]]},"reference":[{"key":"10_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1007\/978-3-030-10970-7_15","volume-title":"Selected Areas in Cryptography","author":"G Adj","year":"2018","unstructured":"Adj, G., Cervantes-V\u00e1zquez, D., Chi-Dom\u00ednguez, J., Menezes, A., Rodr\u00edguez-Henr\u00edquez, F.: On the cost of computing isogenies between supersingular elliptic curves. In: Cid, C., Jacobson, M., Jr. (eds.) SAC 2018. LNCS, vol. 11349, pp. 322\u2013343. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-10970-7_15"},{"issue":"11","key":"10_CR2","doi-asserted-by":"publisher","first-page":"2829","DOI":"10.1109\/TC.2013.145","volume":"63","author":"G Adj","year":"2013","unstructured":"Adj, G., Rodr\u00edguez-Henr\u00edquez, F.: Square root computation over even extension fields. IEEE Trans. Comput. 63(11), 2829\u20132841 (2013)","journal-title":"IEEE Trans. Comput."},{"key":"10_CR3","unstructured":"Arpin, S., et al.: Adventures in supersingularland. Exp. Math. 1\u201328 (2021)"},{"issue":"111","key":"10_CR4","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1090\/S0025-5718-1970-0276200-X","volume":"24","author":"ER Berlekamp","year":"1970","unstructured":"Berlekamp, E.R.: Factoring polynomials over large finite fields. Math. Comput. 24(111), 713\u2013735 (1970)","journal-title":"Math. Comput."},{"key":"10_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/978-3-030-34578-5_9","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2019","author":"W Beullens","year":"2019","unstructured":"Beullens, W., Kleinjung, T., Vercauteren, F.: CSI-FiSh: efficient isogeny based signatures through class group computations. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 227\u2013247. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34578-5_9"},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.jnt.2015.07.002","volume":"161","author":"JH Bruinier","year":"2016","unstructured":"Bruinier, J.H., Ono, K., Sutherland, A.V.: Class polynomials for nonholomorphic modular functions. J. Number Theory 161, 204\u2013229 (2016)","journal-title":"J. Number Theory"},{"key":"10_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-030-77870-5_11","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2021","author":"J Burdges","year":"2021","unstructured":"Burdges, J., De Feo, L.: Delay encryption. In: Canteaut, A., Standaert, F. (eds.) EUROCRYPT 2021, Part I. LNCS, vol. 12696, pp. 302\u2013326. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77870-5_11"},{"key":"10_CR8","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1090\/S0025-5718-1981-0606517-5","volume":"36","author":"DG Cantor","year":"1981","unstructured":"Cantor, D.G., Zassenhaus, H.: A new algorithm for factoring polynomials over finite fields. Math. Comput. 36, 587\u2013592 (1981)","journal-title":"Math. Comput."},{"key":"10_CR9","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":"10_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1007\/978-3-030-64834-3_17","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"W Castryck","year":"2020","unstructured":"Castryck, W., Decru, T., Vercauteren, F.: Radical isogenies. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020, Part II. LNCS, vol. 12492, pp. 493\u2013519. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_17"},{"key":"10_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1007\/978-3-030-64834-3_15","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"C Costello","year":"2020","unstructured":"Costello, C.: B-SIDH: supersingular isogeny Diffie-Hellman using twisted torsion. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 440\u2013463. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_15"},{"key":"10_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1007\/978-3-030-77870-5_10","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2021","author":"C Costello","year":"2021","unstructured":"Costello, C., Meyer, M., Naehrig, M.: Sieving for twin smooth integers with solutions to the Prouhet-Tarry-Escott problem. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 272\u2013301. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77870-5_10"},{"issue":"2","key":"10_CR13","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 Cryptogr. 78(2), 425\u2013440 (2016)","journal-title":"Des. Codes Cryptogr."},{"issue":"3","key":"10_CR14","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1515\/jmc-2012-0015","volume":"8","author":"L De Feo","year":"2014","unstructured":"De Feo, L., Jao, D., Pl\u00fbt, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. J. Math. Cryptol. 8(3), 209\u2013247 (2014)","journal-title":"J. Math. Cryptol."},{"key":"10_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1007\/978-3-030-64837-4_3","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"L De Feo","year":"2020","unstructured":"De Feo, L., Kohel, D., Leroux, A., Petit, C., Wesolowski, B.: SQISign: compact post-quantum signatures from quaternions and isogenies. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12491, pp. 64\u201393. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64837-4_3"},{"issue":"1","key":"10_CR16","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":"10_CR17","unstructured":"Hamburg, M.: Fast and compact elliptic-curve cryptography. Cryptol. ePrint Arch. Report 2012\/309 (2012). https:\/\/ia.cr\/2012\/309"},{"key":"10_CR18","volume-title":"Topics in Matrix Analysis","author":"RA Horn","year":"1994","unstructured":"Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1994)"},{"key":"10_CR19","unstructured":"Jao, D., et al.: SIKE: supersingular isogeny key encapsulation. Manuscript available at sike.org\/ (2017)"},{"key":"10_CR20","unstructured":"Leonardi, C.: Security analysis of isogeny-based cryptosystems. Ph.D. thesis, University of Waterloo, Ontario, Canada (2020)"},{"key":"10_CR21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172769","volume-title":"Introduction to Finite Fields and their Applications","author":"R Lidl","year":"1994","unstructured":"Lidl, R., Niederreiter, H.: Introduction to Finite Fields and their Applications. Cambridge University Press, Cambridge (1994)"},{"key":"10_CR22","doi-asserted-by":"publisher","DOI":"10.1201\/9780429466335","volume-title":"Handbook of Applied Cryptography","author":"AJ Menezes","year":"2018","unstructured":"Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (2018)"},{"key":"10_CR23","unstructured":"Mestre, J.-F.: La m\u00e9thode des graphes. Examples et applications. In: Proceedings of the International Conference on Class Numbers and Fundamental Units of Algebraic Number Fields (Katata), pp. 217\u2013242. Citeseer (1986)"},{"issue":"1","key":"10_CR24","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1090\/S0273-0979-1990-15918-X","volume":"23","author":"AK Pizer","year":"1990","unstructured":"Pizer, A.K.: Ramanujan graphs and Hecke operators. Bull. Am. Math. Soc. 23(1), 127\u2013137 (1990)","journal-title":"Bull. Am. Math. Soc."},{"key":"10_CR25","unstructured":"Scott, M.: A note on the calculation of some functions in finite fields: tricks of the trade. IACR Cryptol. ePrint Arch. 1497 (2020)"},{"key":"10_CR26","volume-title":"A Computational Introduction to Number Theory and Algebra","author":"V Shoup","year":"2009","unstructured":"Shoup, V.: A Computational Introduction to Number Theory and Algebra. Cambridge University Press, Cambridge (2009)"},{"key":"10_CR27","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, vol. 106. Springer, New York (2009). https:\/\/doi.org\/10.1007\/978-0-387-09494-6"},{"key":"10_CR28","unstructured":"Sutherland, A.V.: Modular polynomials. https:\/\/math.mit.edu\/~drew\/ClassicalModPolys.html. Accessed 30 Sept 2021"},{"issue":"1","key":"10_CR29","doi-asserted-by":"publisher","first-page":"531","DOI":"10.2140\/obs.2013.1.531","volume":"1","author":"AV Sutherland","year":"2013","unstructured":"Sutherland, A.V.: On the evaluation of modular polynomials. Open Book Ser. 1(1), 531\u2013555 (2013)","journal-title":"Open Book Ser."},{"key":"10_CR30","unstructured":"The Sage Developers. SageMath, the Sage Mathematics Software System (Version 9.2) (2021). https:\/\/www.sagemath.org"},{"issue":"A238\u2013A241","key":"10_CR31","first-page":"5","volume":"273","author":"J V\u00e9lu","year":"1971","unstructured":"V\u00e9lu, J.: Isog\u00e9nies entre courbes elliptiques. CR Acad. Sci. Paris S\u00e9r. AB 273(A238\u2013A241), 5 (1971)","journal-title":"CR Acad. Sci. Paris S\u00e9r. AB"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2022"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-15982-4_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:04:04Z","timestamp":1760133844000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-15982-4_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031159817","9783031159824"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-15982-4_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"12 October 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CRYPTO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Cryptology Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santa Barbara, CA","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 August 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 August 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"42","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2022\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}