{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T22:33:52Z","timestamp":1775774032332,"version":"3.50.1"},"publisher-location":"Cham","reference-count":39,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032067531","type":"print"},{"value":"9783032067548","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:00:00Z","timestamp":1759363200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:00:00Z","timestamp":1759363200000},"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":[[2026]]},"DOI":"10.1007\/978-3-032-06754-8_6","type":"book-chapter","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T08:23:33Z","timestamp":1759307013000},"page":"145-173","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Orient Express: Using Frobenius to\u00a0Express Oriented Isogenies"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0191-5216","authenticated-orcid":false,"given":"Wouter","family":"Castryck","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2271-6822","authenticated-orcid":false,"given":"Riccardo","family":"Invernizzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0329-080X","authenticated-orcid":false,"given":"Gioella","family":"Lorenzon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1755-8153","authenticated-orcid":false,"given":"Jonas","family":"Meers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7208-9599","authenticated-orcid":false,"given":"Frederik","family":"Vercauteren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,2]]},"reference":[{"key":"6_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/978-3-030-64834-3_14","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"N Alamati","year":"2020","unstructured":"Alamati, N., Feo, L., Montgomery, H., Patranabis, S.: Cryptographic group actions and applications. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020, Part II. LNCS, vol. 12492, pp. 411\u2013439. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_14"},{"key":"6_CR2","doi-asserted-by":"crossref","unstructured":"Allombert, B., et al.: Faster SCALLOP from non-prime conductor suborders in medium sized quadratic fields. In: Public-Key Cryptography \u2013 PKC 2025. Lecture Notes in Computer Science, vol. 15676, pp. 333\u2013363 (2025)","DOI":"10.1007\/978-3-031-91826-1_11"},{"key":"6_CR3","doi-asserted-by":"crossref","unstructured":"Basso, A., et al.: PRISM: simple and compact identification and signatures from large prime degree isogenies. In: Public-Key Cryptography \u2013 PKC 2025. Lecture Notes in Computer Science, vol. 15676, pp. 300\u2013332 (2025)","DOI":"10.1007\/978-3-031-91826-1_10"},{"key":"6_CR4","series-title":"LNCS","first-page":"339","volume-title":"ASIACRYPT 2024, Part III","author":"A Basso","year":"2024","unstructured":"Basso, A., Dartois, P., Feo, L., Leroux, A., Maino, L., Pope, G., Robert, D., Wesolowski, B.: Sqisign2d-west - the fast, the small, and the safer. In: Chung, K.-M., Sasaki, Yu. (eds.) ASIACRYPT 2024, Part III. LNCS, vol. 15486, pp. 339\u2013370. Springer, Singapore (2024)"},{"key":"6_CR5","doi-asserted-by":"crossref","unstructured":"Basso, A., Maino, L.: POK\u00c9: a compact and efficient PKE from higher-dimensional isogenies. In: Advances in Cryptology \u2013 Eurocrypt 2025 Part II. Lecture Notes in Computer Science, vol. 15602, pp. 94\u2013123. Springer (2025)","DOI":"10.1007\/978-3-031-91124-8_4"},{"key":"6_CR6","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":"6_CR7","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":"6_CR8","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1007\/978-3-031-30589-4_15","volume-title":"EUROCRYPT 2023, Part V","author":"W Castryck","year":"2023","unstructured":"Castryck, W., Decru, T.: An efficient key recovery attack on SIDH. In: Hazay, C., Stam, M. (eds.) EUROCRYPT 2023, Part V. LNCS, vol. 14008, pp. 423\u2013447. Springer, Cham (2023)"},{"key":"6_CR9","doi-asserted-by":"crossref","unstructured":"Castryck, W., Houben, M., Vercauteren, F., Wesolowski, B.: On the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves. Res. Number Theory 4(8), Article 99 (2022). Proceedings of ANTS-XV","DOI":"10.1007\/s40993-022-00399-6"},{"key":"6_CR10","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":"3","key":"6_CR11","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s13389-021-00271-w","volume":"12","author":"J Ch\u00e1vez-Saab","year":"2022","unstructured":"Ch\u00e1vez-Saab, J., Chi-Dom\u00ednguez, J.-J., Jaques, S., Rodr\u00edguez-Henr\u00edquez, F.: The sqale of csidh: sublinear v\u00e9lu quantum-resistant isogeny action with low exponents. J. Cryptogr. Eng. 12(3), 349\u2013368 (2022)","journal-title":"J. Cryptogr. Eng."},{"key":"6_CR12","series-title":"LNCS","first-page":"190","volume-title":"PKC 2024, Part II","author":"M Chen","year":"2024","unstructured":"Chen, M., Leroux, A., Panny, L.: SCALLOP-HD: group action from 2-dimensional isogenies. In: Tang, Q., Teague, V. (eds.) PKC 2024, Part II. LNCS, vol. 14603, pp. 190\u2013216. Springer, Cham (2024)"},{"key":"6_CR13","first-page":"85","volume":"1","author":"M Chenu","year":"2021","unstructured":"Chenu, M., Smith, B.: Higher-degree supersingular group actions. Math. Cryptol. 1, 85\u2013101 (2021)","journal-title":"Math. Cryptol."},{"key":"6_CR14","doi-asserted-by":"crossref","unstructured":"Col\u00f2, L., Kohel, D.: Orienting supersingular isogeny graphs. Cryptology ePrint Archive, Report 2020\/985 (2020)","DOI":"10.1515\/jmc-2019-0034"},{"key":"6_CR15","doi-asserted-by":"crossref","unstructured":"Corte-Real Santos, M., Eriksen, J.K., Meyer, M., Reijnders, K.: Apr\u00e8ssqi: extra fast verification for sqisign using extension-field signing. In: EUROCRYPT 2024, pp. 63\u201393. Springer (2024)","DOI":"10.1007\/978-3-031-58716-0_3"},{"key":"6_CR16","unstructured":"Couveignes, J.-M.: Hard homogeneous spaces. Cryptology ePrint Archive, Paper 2006\/291 (2006)"},{"key":"6_CR17","unstructured":"Cox, D.A.: Primes of the Form $$x^2+ny^2$$\u202f: Fermat, Class Field Theory, and Complex Multiplication. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley (2013)"},{"key":"6_CR18","doi-asserted-by":"crossref","unstructured":"Dartois, P., et al.: PEGASIS: practical effective class group action using 4-dimensional isogenies. In: Advances in Cryptology \u2013 Crypto 2025. Lecture Notes in Computer Science (2025, to appear)","DOI":"10.1007\/978-3-032-01855-7_3"},{"key":"6_CR19","series-title":"LNCS","first-page":"304","volume-title":"ASIACRYPT 2024, Part III","author":"P Dartois","year":"2024","unstructured":"Dartois, P., Maino, L., Pope, G., Robert, D.: An algorithmic approach to (2, 2)-isogenies in the theta model and applications to isogeny-based cryptography. In: Chung, K.-M., Sasaki, Yu. (eds.) ASIACRYPT 2024, Part III. LNCS, vol. 15486, pp. 304\u2013338. Springer, Singapore (2024)"},{"key":"6_CR20","doi-asserted-by":"crossref","unstructured":"Feo, L.D., et al.: SCALLOP: scaling the CSI-FiSh. In: Boldyreva, A., Kolesnikov, V. (eds.) Public-Key Cryptography \u2013 PKC 2023, Part I. LNCS, vol. 13940, pp. 345\u2013375. Springer, Cham (2023)","DOI":"10.1007\/978-3-031-31368-4_13"},{"key":"6_CR21","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"},{"key":"6_CR22","doi-asserted-by":"crossref","unstructured":"Eriksen, J.K., Panny, L., Sot\u00e1kov\u00e1, J., Veroni, M.: Deuring for the people: supersingular elliptic curves with prescribed endomorphism ring in general characteristic. In: LuCaNT 2023. Contemporary Mathematics, vol. 796, pp. 339\u2013373. American Mathematical Society (2024)","DOI":"10.1090\/conm\/796\/16008"},{"issue":"4","key":"6_CR23","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1090\/S0894-0347-1989-1002631-0","volume":"2","author":"JL Hafner","year":"1989","unstructured":"Hafner, J.L., McCurley, K.S.: A rigorous subexponential algorithm for computation of class groups. J. Am. Math. Soc. 2(4), 837\u2013850 (1989)","journal-title":"J. Am. Math. Soc."},{"key":"6_CR24","unstructured":"Houben, M.: Isogeny-based key exchange from orientations of large discriminant. In: Advances in Cryptology \u2013 Crypto 2025. Lecture Notes in Computer Science (2025, to appear)"},{"key":"6_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/978-3-030-81652-0_13","volume-title":"Selected Areas in Cryptography","author":"S Jaques","year":"2021","unstructured":"Jaques, S., Schrottenloher, A.: Low-gate quantum golden collision\u00a0finding. In: Dunkelman, O., Jacobson, Jr., M.J., O\u2019Flynn, C. (eds.) SAC 2020. LNCS, vol. 12804, pp. 329\u2013359. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-81652-0_13"},{"key":"6_CR26","first-page":"93","volume":"485","author":"E Kani","year":"1997","unstructured":"Kani, E.: The number of curves of genus two with elliptic differentials. Journal f\u00fcr die reine und angewandte Mathematik 485, 93\u2013122 (1997)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"6_CR27","unstructured":"Kopp, G.S., Lagarias, J.C.: Class field theory for orders of number fields (2022)"},{"key":"6_CR28","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1007\/978-3-031-30589-4_16","volume-title":"EUROCRYPT 2023, Part V","author":"L Maino","year":"2023","unstructured":"Maino, L., Martindale, C., Panny, L., Pope, G., Wesolowski, B.: A direct key recovery attack on SIDH. In: Hazay, C., Stam, M. (eds.) EUROCRYPT 2023, Part V. LNCS, vol. 14008, pp. 448\u2013471. Springer, Cham (2023)"},{"key":"6_CR29","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-031-68388-6_4","volume-title":"CRYPTO 2024, Part V","author":"K Nakagawa","year":"2024","unstructured":"Nakagawa, K., Onuki, H.: QFESTA: efficient algorithms and parameters for FESTA using quaternion algebras. In: Reyzin, L., Stebila, D. (eds.) CRYPTO 2024, Part V. LNCS, vol. 14924, pp. 75\u2013106. Springer, Cham (2024)"},{"key":"6_CR30","doi-asserted-by":"crossref","unstructured":"Onuki, H.: On oriented supersingular elliptic curves. Finite Fields Appl. 69, Article No. 101777 (2021)","DOI":"10.1016\/j.ffa.2020.101777"},{"key":"6_CR31","unstructured":"Page, A., Robert, D.: Introducing clapoti(s): evaluating the isogeny class group action in polynomial time. Cryptology ePrint Archive, Paper 2023\/1766 (2023)"},{"key":"6_CR32","unstructured":"Panny, L.: CSI-FiSh really isn\u2019t polynomial-time (2023). Blah post available at https:\/\/yx7.cc\/blah\/2023-04-14.html"},{"key":"6_CR33","unstructured":"Panny, L., Petit, C., Stopar, M.: KLaPoTi: an asymptotically efficient isogeny group action from 2-dimensional isogenies. Cryptology ePrint Archive, Report 2024\/1844 (2024)"},{"key":"6_CR34","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1007\/978-3-031-30589-4_17","volume-title":"EUROCRYPT 2023, Part V","author":"D Robert","year":"2023","unstructured":"Robert, D.: Breaking SIDH in polynomial time. In: Hazay, C., Stam, M. (eds.) EUROCRYPT 2023, Part V. LNCS, vol. 14008, pp. 472\u2013503. Springer, Cham (2023)"},{"key":"6_CR35","unstructured":"Rostovtsev, A., Stolbunov, A.: Public-Key Cryptosystem Based On Isogenies. Cryptology ePrint Archive, Report 2006\/145 (2006)"},{"key":"6_CR36","unstructured":"Sanon, S.P.: Endomorphism rings of ordinary abelian varieties. Ph.D. thesis, TU Kaiserslautern (2022)"},{"issue":"2","key":"6_CR37","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0097-3165(87)90003-3","volume":"46","author":"R Schoof","year":"1987","unstructured":"Schoof, R.: Nonsingular plane cubic curves over finite fields. J. Comb. Theory Ser. A 46(2), 183\u2013211 (1987)","journal-title":"J. Comb. Theory Ser. A"},{"key":"6_CR38","unstructured":"The Sage Developers. SageMath, the Sage Mathematics Software System (Version 10.6.beta7) (2025). https:\/\/www.sagemath.org"},{"issue":"4","key":"6_CR39","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(4), 521\u2013560 (1969)","journal-title":"Annales Scientifiques de l\u2019\u00c9cole Normale Sup\u00e9rieure"}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 LATINCRYPT 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-06754-8_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T08:23:44Z","timestamp":1759307024000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-06754-8_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,2]]},"ISBN":["9783032067531","9783032067548"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-06754-8_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,2]]},"assertion":[{"value":"2 October 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"LATINCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Cryptology and Information Security in Latin America","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Medell\u00edn","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Colombia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 October 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 October 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"latincrypt2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ciencias.medellin.unal.edu.co\/eventos\/latincrypt\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}