{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T17:13:34Z","timestamp":1778087614083,"version":"3.51.4"},"publisher-location":"Cham","reference-count":49,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032253262","type":"print"},{"value":"9783032253279","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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\/978-3-032-25327-9_22","type":"book-chapter","created":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:41:34Z","timestamp":1778085694000},"page":"636-665","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["$$\\textsf{qt}$$-$$\\textsf{Pegasis}$$: Simpler and\u00a0Faster Effective Class Group Actions"],"prefix":"10.1007","author":[{"given":"Pierrick","family":"Dartois","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan Komada","family":"Eriksen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Invernizzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frederik","family":"Vercauteren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,7]]},"reference":[{"key":"22_CR1","unstructured":"Aardal, M.A., et al.: SQIsign. Technical Report available at https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-2-additional-signatures. National Institute of Standards and Technology (2024)"},{"key":"22_CR2","doi-asserted-by":"crossref","unstructured":"Aardal, M.A., Basso, A., De Feo, L., Patranabis, S., Wesolowski, B.: A Complete Security Proof of SQIsign. Cryptology ePrint Archive, Report 2025\/379 (2025)","DOI":"10.1007\/978-3-032-01887-8_7"},{"key":"22_CR3","doi-asserted-by":"crossref","unstructured":"Allombert, B.,et al.: Faster SCALLOP from Non-prime Conductor Suborders in Medium Sized Quadratic Fields. In: PKC 2025, Part III. Ed. by T. Jager and J. Pan. Vol. 15676. LNCS. Springer, Cham, pp. 333\u2013363 (2025)","DOI":"10.1007\/978-3-031-91826-1_11"},{"key":"22_CR4","doi-asserted-by":"crossref","unstructured":"Basso, A.,et al.: PRISM: simple and compact identification and signatures from large prime degree isogenies. In: PKC 2025, Part III. Ed. by T. Jager and J. Pan. Vol. 15676. LNCS. Springer, Cham, pp. 300\u2013332 (2025)","DOI":"10.1007\/978-3-031-91826-1_10"},{"key":"22_CR5","doi-asserted-by":"crossref","unstructured":"Basso, A.,et al.: SQIsign2D-West - The Fast, the Small, and the Safer. In: ASIACRYPT 2024, Part III. Ed. by Chung, K.-M., Sasaki, Y., Vol. 15486. LNCS. Springer, Singapore, pp. 339\u2013370 (2024)","DOI":"10.1007\/978-981-96-0891-1_11"},{"key":"22_CR6","unstructured":"Belding, J.V.: Number theoretic algorithms for elliptic curves. PhD thesis. PhD thesis, University of Maryland College Park (2008)"},{"key":"22_CR7","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., De Feo, L., Leroux, A., Smith, B.: Faster computation of isogenies of large prime degree. In: Open Book Series, Proceedings of the Fourteenth Algorithmic Number Theory Symposium \u2013 ANTS XIV 4.1, pp. 39\u201355 (2020)","DOI":"10.2140\/obs.2020.4.39"},{"key":"22_CR8","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":"22_CR9","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":"22_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-06307-1","volume-title":"Complex Abelian Varieties","author":"C Birkenhake","year":"2004","unstructured":"Birkenhake, C., Lange, H.: Complex Abelian Varieties. Springer, Berlin Heidelberg, Berlin, Heidelberg (2004)"},{"key":"22_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1007\/978-3-030-45724-2_17","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"X Bonnetain","year":"2020","unstructured":"Bonnetain, X., Schrottenloher, A.: Quantum security analysis of CSIDH. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 493\u2013522. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45724-2_17"},{"key":"22_CR12","doi-asserted-by":"crossref","unstructured":"Borin, G., et al.: Qlapoti: simple and efficient translation of quaternion ideals to isogenies. In: Cryptology ePrint Archive (2025)","DOI":"10.1007\/978-981-95-5113-2_6"},{"key":"22_CR13","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":"22_CR14","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"},{"key":"22_CR15","doi-asserted-by":"crossref","unstructured":"Chen, M., Leroux, A., Panny, L.: SCALLOP-HD: Group Action from 2-Dimensional Isogenies. In: PKC 2024, Part II. Ed. by Q. Tang and V. Teague. Vol. 14603. LNCS. Springer, Cham, Apr, pp. 190\u2013216 (2024)","DOI":"10.1007\/978-3-031-57725-3_7"},{"key":"22_CR16","unstructured":"L. Col\u00f2. Oriented supersingular elliptic curves and class group actions (2022). https:\/\/www.leonardocolo.com\/documents\/thesis\/PhD_Thesis.pdf"},{"key":"22_CR17","doi-asserted-by":"crossref","unstructured":"Col\u00f2, L., Kohel, D.: Orienting supersingular isogeny graphs. J. Math. Cryptol. 14.1, pp. 414\u2013437 (2020)","DOI":"10.1515\/jmc-2019-0034"},{"key":"22_CR18","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, Part I. Ed. by Joye, M., Leander, G., Vol. 14651. LNCS. Springer, Cham, pp. 63\u201393 (2024)","DOI":"10.1007\/978-3-031-58716-0_3"},{"key":"22_CR19","unstructured":"Couveignes, J.-M.: Hard Homogeneous Spaces. Cryptology ePrint Archive, Report 2006\/291 (2006)"},{"key":"22_CR20","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1016\/j.jalgebra.2025.06.033","volume":"683","author":"P Dartois","year":"2025","unstructured":"Dartois, P.: Fast computation of 2-isogenies in dimension 4 and cryptographic applications. J. Algebra 683, 449\u2013514 (2025)","journal-title":"J. Algebra"},{"key":"22_CR21","unstructured":"Dartois, P.: Fast computation of higher dimensional isogenies for cryptographic applications. PhD thesis. Universit\u00e9 de Bordeaux, France (2025)"},{"key":"22_CR22","unstructured":"Dartois, P.: Towards constant time implementation of 2-isogenies in dimension 4. In preparation (2025)"},{"key":"22_CR23","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. Ed. by Tauman Kalai, Y., Kamara, S.F., Cham: Springer Nature Switzerland, pp. 67\u201399 (2025)","DOI":"10.1007\/978-3-032-01855-7_3"},{"key":"22_CR24","doi-asserted-by":"crossref","unstructured":"Dartois, P.,et al.: PEGASIS: practical effective class group action using 4-dimensional isogenies. Cryptology ePrint Archive, Report 2025\/401 (2025)","DOI":"10.1007\/978-3-032-01855-7_3"},{"key":"22_CR25","unstructured":"Dartois, P., Eriksen, J.K., Invernizzi, R., Vercauteren, F.: qt-Pegasis: simpler and faster effective class group actions. Cryptology ePrint Archive, Report 2025\/1859 (2025)"},{"key":"22_CR26","doi-asserted-by":"crossref","unstructured":"De Feo, L., et al.: SCALLOP: Scaling the CSI-FiSh. In: PKC 2023, Part I. Ed. by Boldyreva, A., Kolesnikov, V.: Vol. 13940. LNCS. Springer, Cham, pp. 345\u2013375 (2023)","DOI":"10.1007\/978-3-031-31368-4_13"},{"key":"22_CR27","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":"22_CR28","doi-asserted-by":"crossref","unstructured":"De Feo, L., Leroux, A., Longa, P., Wesolowski, B.: New Algorithms for the Deuring Correspondence - Towards Practical and Secure SQISign Signatures. In: EUROCRYPT 2023, Part V. Ed. by Hazay, C., Stam, M., Vol. 14008. LNCS. Springer, Cham, pp. 659\u2013690 (2023)","DOI":"10.1007\/978-3-031-30589-4_23"},{"key":"22_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/978-3-030-45388-6_7","volume-title":"Public-Key Cryptography \u2013 PKC 2020","author":"L De Feo","year":"2020","unstructured":"De Feo, L., Meyer, M.: Threshold schemes from isogeny assumptions. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 187\u2013212. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45388-6_7"},{"key":"22_CR30","doi-asserted-by":"crossref","unstructured":"Duparc, M.: Superglue: Fast formulae for (2, 2) gluing isogenies. Cryptology ePrint Archive, Paper 2025\/736 (2025)","DOI":"10.1007\/978-981-95-5113-2_12"},{"key":"22_CR31","doi-asserted-by":"crossref","unstructured":"Elkies, N.D.: Elliptic and modular curves over finite fields and related computational issues. In: Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of Atkin, A.O.L., ed. by Buell, D.A., Teitelbaum, J.T., Vol. 7. AMS\/IP Studies in Advanced Mathematics. American Mathematical Society, International Press, pp. 21\u201376 (1998)","DOI":"10.1090\/amsip\/007\/03"},{"key":"22_CR32","unstructured":"Feo, L.D.: Mathematics of Isogeny Based Cryptography (2017)"},{"key":"22_CR33","doi-asserted-by":"crossref","unstructured":"Kohel, D., Lauter, K., Petit, C., Tignol, J.-P.: On the quaternion isogeny path problem (2014)","DOI":"10.1112\/S1461157014000151"},{"key":"22_CR34","doi-asserted-by":"crossref","unstructured":"Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35.1, 170\u2013188 (2005)","DOI":"10.1137\/S0097539703436345"},{"key":"22_CR35","doi-asserted-by":"crossref","unstructured":"Lang, S.: Elliptic Functions. Springer-Verlag, p. 324 (1987)","DOI":"10.1007\/978-1-4612-4752-4"},{"key":"22_CR36","doi-asserted-by":"crossref","unstructured":"Leroux, A., Rom\u00e9as, M.: Updatable encryption from group actions. In: Post-Quantum Cryptography - 15th International Workshop, PQCrypto 2024, Part II. Ed. by Saarinen, M.-J., Smith-Tone, D., Springer, Cham, pp. 20\u201353 (2024)","DOI":"10.1007\/978-3-031-62746-0_2"},{"key":"22_CR37","doi-asserted-by":"crossref","unstructured":"Milne, J.S.: Abelian Varieties. In: Arithmetic Geometry. New York, NY: Springer New York, pp. 103\u2013150 (1986)","DOI":"10.1007\/978-1-4613-8655-1_5"},{"key":"22_CR38","doi-asserted-by":"crossref","unstructured":"Moriya, T., Onuki, H., Takagi, T.: SiGamal: a supersingular isogenybased PKE and its application to a PRF. In: ASIACRYPT 2020, Part II. Ed. by Moriai, S., Wang, H., Vol. 12492. LNCS. Springer, Cham, pp. 551\u2013580 (2020)","DOI":"10.1007\/978-3-030-64834-3_19"},{"key":"22_CR39","doi-asserted-by":"crossref","unstructured":"Mumford, D.: On the equations defining abelian varieties 1. In: Inventiones mathematicae 1.4, pp. 287\u2013354 (1966)","DOI":"10.1007\/BF01389737"},{"key":"22_CR40","unstructured":"Mumford, D.: Abelian varieties. Second Edition. Tata Institute of fundamental research studies in mathematics. London: Oxford University Press, pp. x+279 (1974)"},{"key":"22_CR41","doi-asserted-by":"crossref","unstructured":"Onuki, H.: On oriented supersingular elliptic curves. In: Finite Fields and Their Applications 69, p. 101777 (2021)","DOI":"10.1016\/j.ffa.2020.101777"},{"key":"22_CR42","unstructured":"Page, A., Robert, D.: Introducing Clapoti(s): evaluating the isogeny class group action in polynomial time. Cryptology ePrint Archive, Report 2023\/1766 (2023)"},{"key":"22_CR43","doi-asserted-by":"crossref","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)","DOI":"10.62056\/ahp2wakrz"},{"key":"22_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/978-3-030-45724-2_16","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"C Peikert","year":"2020","unstructured":"Peikert, C.: He Gives C-Sieves on the CSIDH. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 463\u2013492. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45724-2_16"},{"key":"22_CR45","unstructured":"Robert, D.: Theta functions and cryptographic applications. PhD thesis. Universit\u00e9 Henri-Poincarr\u00e9, Nancy 1, France (2010)"},{"key":"22_CR46","unstructured":"Robert, D.: A note on optimising 2 n-isogenies in higher dimension. http:\/\/www.normalesup.org\/~robert\/pro\/publications\/notes\/2023-06-optimising_isogenies.pdf (2023)"},{"key":"22_CR47","unstructured":"Rostovtsev, A., Stolbunov, A.: Public-Key Cryptosystem Based On Isogenies. Cryptology ePrint Archive, Report 2006\/145 (2006)"},{"key":"22_CR48","unstructured":"J. V\u00e9lu. Isog\u00e9nies entre courbes elliptiques. In: Comptes-rendus de l\u2019Acad\u00e9mie des Sciences 273, pp. 238\u2013241 (1971). Available at https:\/\/gallica.bnf. fr"},{"key":"22_CR49","doi-asserted-by":"crossref","unstructured":"Waterhouse, W.C.: Abelian varieties over finite fields. Eng. In: Annales Scientifiques de l\u2019\u00c9cole Normale Sup\u00e9rieure 2.4, pp. 521\u2013560 (1969)","DOI":"10.24033\/asens.1183"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2026"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-25327-9_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:41:55Z","timestamp":1778085715000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-25327-9_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032253262","9783032253279"],"references-count":49,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-25327-9_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"7 May 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EUROCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Rome","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 May 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 May 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"45","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt.iacr.org\/2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}