{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,15]],"date-time":"2026-08-15T20:36:06Z","timestamp":1786826166845,"version":"3.56.0"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032018861","type":"print"},{"value":"9783032018878","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[[2025]]},"DOI":"10.1007\/978-3-032-01887-8_7","type":"book-chapter","created":{"date-parts":[[2025,8,16]],"date-time":"2025-08-16T19:17:09Z","timestamp":1755371829000},"page":"190-222","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Complete Security Proof of\u00a0SQIsign"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0674-6460","authenticated-orcid":false,"given":"Marius A.","family":"Aardal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3270-1069","authenticated-orcid":false,"given":"Andrea","family":"Basso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9321-0773","authenticated-orcid":false,"given":"Luca","family":"De Feo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2309-7939","authenticated-orcid":false,"given":"Sikhar","family":"Patranabis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1249-6077","authenticated-orcid":false,"given":"Benjamin","family":"Wesolowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,17]]},"reference":[{"key":"7_CR1","unstructured":"Aardal, M.A., et al.: SQIsign - Version 2.0. Technical report, National Institute of Standards and Technology (2025). https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-2-additional-signatures"},{"key":"7_CR2","doi-asserted-by":"crossref","unstructured":"Aardal, M.A., Basso, A., De\u00a0Feo, L., Patranabis, S., Wesolowski, B.: A complete security proof of SQIsign. Cryptology ePrint Archive, Paper 2025\/379 (2025). https:\/\/eprint.iacr.org\/2025\/379","DOI":"10.1007\/978-3-032-01887-8_7"},{"key":"7_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1007\/3-540-46035-7_28","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2002","author":"M Abdalla","year":"2002","unstructured":"Abdalla, M., An, J.H., Bellare, M., Namprempre, C.: From identification to signatures via the Fiat-Shamir transform: minimizing assumptions for security and forward-security. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 418\u2013433. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-46035-7_28"},{"key":"7_CR4","doi-asserted-by":"publisher","unstructured":"Attema, T., Cramer, R., Kohl, L.: A compressed $$\\varSigma $$-protocol theory for lattices. In: Malkin, T., Peikert, C. (eds.) CRYPTO\u00a02021, Part\u00a0II. LNCS, vol. 12826, pp. 549\u2013579. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-84245-1_19","DOI":"10.1007\/978-3-030-84245-1_19"},{"key":"7_CR5","doi-asserted-by":"publisher","unstructured":"Bach, E.: How to generate factored random numbers. SIAM J. Comput. 17(2), 179\u2013193 (1988). https:\/\/doi.org\/10.1137\/0217012","DOI":"10.1137\/0217012"},{"key":"7_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/978-3-030-03638-6_10","volume-title":"Secure IT Systems","author":"M Backendal","year":"2018","unstructured":"Backendal, M., Bellare, M., Sorrell, J., Sun, J.: The Fiat-Shamir zoo: relating the security of different signature variants. In: Gruschka, N. (ed.) NordSec 2018. LNCS, vol. 11252, pp. 154\u2013170. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03638-6_10"},{"key":"7_CR7","doi-asserted-by":"publisher","unstructured":"Basso, A., et al.: Supersingular curves you can trust. In: Hazay, C., Stam, M. (eds.) EUROCRYPT\u00a02023, Part\u00a0II. LNCS, vol. 14005, pp. 405\u2013437. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30617-4_14","DOI":"10.1007\/978-3-031-30617-4_14"},{"key":"7_CR8","doi-asserted-by":"publisher","unstructured":"Basso, A., et al.: SQIsign2D-west - the fast, the small, and the safer. In: Chung, K.M., Sasaki, Y. (eds.) ASIACRYPT\u00a02024, Part\u00a0III. LNCS, vol. 15486, pp. 339\u2013370. Springer, Singapore (2024). https:\/\/doi.org\/10.1007\/978-981-96-0891-1_11","DOI":"10.1007\/978-981-96-0891-1_11"},{"issue":"1","key":"7_CR9","doi-asserted-by":"publisher","first-page":"39","DOI":"10.2140\/obs.2020.4.39","volume":"4","author":"DJ Bernstein","year":"2020","unstructured":"Bernstein, D.J., De Feo, L., Leroux, A., Smith, B.: Faster computation of isogenies of large prime degree. Open Book Ser. 4(1), 39\u201355 (2020). https:\/\/doi.org\/10.2140\/obs.2020.4.39","journal-title":"Open Book Ser."},{"key":"7_CR10","doi-asserted-by":"publisher","unstructured":"Borin, G., Lai, Y.F., Leroux, A.: Erebor and Durian: full anonymous ring signatures from quaternions and isogenies. IACR Commun. Cryptol. 1(4) (2025). https:\/\/doi.org\/10.62056\/ava3zivrzn","DOI":"10.62056\/ava3zivrzn"},{"key":"7_CR11","unstructured":"Chavez-Saab, J., et al.: SQIsign. Technical report, National Institute of Standards and Technology (2023). https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-1-additional-signatures"},{"key":"7_CR12","doi-asserted-by":"publisher","unstructured":"Cremers, C., D\u00fczl\u00fc, S., Fiedler, R., Fischlin, M., Janson, C.: BUFFing signature schemes beyond unforgeability and the case of post-quantum signatures. In: 2021 IEEE Symposium on Security and Privacy, pp. 1696\u20131714. IEEE Computer Society Press (2021). https:\/\/doi.org\/10.1109\/SP40001.2021.00093","DOI":"10.1109\/SP40001.2021.00093"},{"key":"7_CR13","doi-asserted-by":"publisher","unstructured":"Dartois, P., Leroux, A., Robert, D., Wesolowski, B.: SQIsignHD: new dimensions in cryptography. In: Joye, M., Leander, G. (eds.) EUROCRYPT\u00a02024, Part\u00a0I. LNCS, vol. 14651, pp. 3\u201332. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-58716-0_1","DOI":"10.1007\/978-3-031-58716-0_1"},{"key":"7_CR14","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":"7_CR15","doi-asserted-by":"publisher","unstructured":"De Feo, L., Leroux, A., Longa, P., Wesolowski, B.: New algorithms for the deuring correspondence - towards practical and secure SQISign signatures. In: Hazay, C., Stam, M. (eds.) EUROCRYPT\u00a02023, Part\u00a0V. LNCS, vol. 14008, pp. 659\u2013690. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30589-4_23","DOI":"10.1007\/978-3-031-30589-4_23"},{"key":"7_CR16","doi-asserted-by":"publisher","unstructured":"Duparc, M., Fouotsa, T.B.: SQIPrime: a dimension 2 variant of SQISignHD with non-smooth challenge isogenies. In: Chung, K.M., Sasaki, Y. (eds.) ASIACRYPT\u00a02024, Part\u00a0III. LNCS, vol. 15486, pp. 396\u2013429. Springer, Singapore (2024). https:\/\/doi.org\/10.1007\/978-981-96-0891-1_13","DOI":"10.1007\/978-981-96-0891-1_13"},{"key":"7_CR17","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":"7_CR18","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 Ser. 4(1), 215\u2013232 (2020). https:\/\/doi.org\/10.2140\/obs.2020.4.215","journal-title":"Open Book Ser."},{"issue":"485","key":"7_CR19","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1515\/crll.1997.485.93","volume":"1997","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 1997(485), 93\u2013122 (1997)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"7_CR20","unstructured":"Leroux, A.: Quaternion algebras and isogeny-based cryptography. (Alg\u00e8bres de quaternions et cryptographie \u00e0 base d\u2019isog\u00e9nies). Ph.D. thesis, Polytechnic Institute of Paris, France (2022)"},{"key":"7_CR21","doi-asserted-by":"publisher","unstructured":"Nakagawa, K., et al.: SQIsign2D-east: a new signature scheme using 2-dimensional isogenies. In: Chung, K.M., Sasaki, Y. (eds.) ASIACRYPT\u00a02024, Part\u00a0III. LNCS, vol. 15486, pp. 272\u2013303. Springer, Singapore (2024). https:\/\/doi.org\/10.1007\/978-981-96-0891-1_9","DOI":"10.1007\/978-981-96-0891-1_9"},{"key":"7_CR22","doi-asserted-by":"publisher","unstructured":"Page, A., Wesolowski, B.: The supersingular endomorphism ring and one endomorphism problems are equivalent. In: Joye, M., Leander, G. (eds.) EUROCRYPT\u00a02024, Part\u00a0VI. LNCS, vol. 14656, pp. 388\u2013417. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-58751-1_14","DOI":"10.1007\/978-3-031-58751-1_14"},{"key":"7_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/3-540-68339-9_33","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201996","author":"D Pointcheval","year":"1996","unstructured":"Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387\u2013398. Springer, Heidelberg (1996). https:\/\/doi.org\/10.1007\/3-540-68339-9_33"},{"key":"7_CR24","unstructured":"Robert, D.: Evaluating isogenies in polylogarithmic time. Cryptology ePrint Archive, Report 2022\/1068 (2022). https:\/\/eprint.iacr.org\/2022\/1068"},{"key":"7_CR25","doi-asserted-by":"publisher","unstructured":"Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124\u2013134 (1994). https:\/\/doi.org\/10.1109\/SFCS.1994.365700","DOI":"10.1109\/SFCS.1994.365700"},{"key":"7_CR26","doi-asserted-by":"crossref","unstructured":"Silverman, J.H.: The Arithmetic of Elliptic curves, Graduate Texts in Mathematics, vol.\u00a0106. Springer (1986)","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"7_CR27","doi-asserted-by":"publisher","unstructured":"Wesolowski, B.: The supersingular isogeny path and endomorphism ring problems are equivalent. In: 62nd FOCS, pp. 1100\u20131111. IEEE Computer Society Press (2022). https:\/\/doi.org\/10.1109\/FOCS52979.2021.00109","DOI":"10.1109\/FOCS52979.2021.00109"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-01887-8_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T12:32:52Z","timestamp":1786105972000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-01887-8_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783032018861","9783032018878"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-01887-8_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"17 August 2025","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":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 August 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 August 2025","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":"crypto2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}