{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T23:12:34Z","timestamp":1778022754260,"version":"3.51.4"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032253323","type":"print"},{"value":"9783032253330","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\/978-3-032-25333-0_3","type":"book-chapter","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:41:39Z","timestamp":1778020899000},"page":"63-90","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Magic Pot: Cryptanalysis of\u00a0Full AIM2 in\u00a0the\u00a0Standard and\u00a0Related-\/reused-Key Settings Using New Elimination Framework"],"prefix":"10.1007","author":[{"given":"Alex","family":"Biryukov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo","family":"Garc\u00eda Fern\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aleksei","family":"Udovenko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,6]]},"reference":[{"key":"3_CR1","unstructured":"Aguilar-Melchor, C., et al: HQC. Technical Report, National Institute of Standards and Technology (2022). Available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/round-4-submissions"},{"key":"3_CR2","doi-asserted-by":"publisher","unstructured":"Bariant, A., et al.: The algebraic FreeLunch: Efficient Gr\u00f6bner basis attacks against arithmetization-oriented primitives. In: Reyzin, L., Stebila, D. (eds.) CRYPTO\u00a02024, Part\u00a0IV. LNCS, vol. 14923, pp. 139\u2013173. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-68385-5_5","DOI":"10.1007\/978-3-031-68385-5_5"},{"key":"3_CR3","doi-asserted-by":"publisher","unstructured":"Bariant, A., Bouvier, C., Leurent, G., Perrin, L.: Algebraic attacks against some arithmetization-oriented primitives. IACR Trans. Symm. Cryptol. 2022(3), 73\u2013101 (2022). https:\/\/doi.org\/10.46586\/tosc.v2022.i3.73-101","DOI":"10.46586\/tosc.v2022.i3.73-101"},{"key":"3_CR4","unstructured":"Bernstein, D.J., et al.: Report on evaluation of KPQC round-2 candidates. Cryptology ePrint Archive, Report 2024\/2077 (2024). https:\/\/eprint.iacr.org\/2024\/2077"},{"key":"3_CR5","doi-asserted-by":"publisher","unstructured":"Berthomieu, J., Neiger, V., Safey El\u00a0Din, M.: Faster change of order algorithm for gr\u00f6bner bases under shape and stability assumptions. In: ISSAC 2022, pp. 409\u2013418. ACM, New York, NY, USA (2022). https:\/\/doi.org\/10.1145\/3476446.3535484","DOI":"10.1145\/3476446.3535484"},{"key":"3_CR6","doi-asserted-by":"publisher","unstructured":"Biryukov, A., Garc\u00eda\u00a0Fern\u00e1ndez, P., Udovenko, A.: Magic pot: cryptanalysis of full AIM2 in the standard and related-\/reused-key settings using new elimination framework - supporting code (2026). https:\/\/doi.org\/10.5281\/zenodo.18727305","DOI":"10.5281\/zenodo.18727305"},{"key":"3_CR7","doi-asserted-by":"publisher","unstructured":"Cheon, J.H., et al.: HAETAE: Shorter lattice-based fiat-Shamir signatures. IACR TCHES 2024(3), 25\u201375 (2024). https:\/\/doi.org\/10.46586\/tches.v2024.i3.25-75","DOI":"10.46586\/tches.v2024.i3.25-75"},{"key":"3_CR8","doi-asserted-by":"publisher","unstructured":"Cheon, J.H., Choe, H., Hong, D., Yi, M.: SMAUG: pushing lattice-based key encapsulation mechanisms to the limits. In: Carlet, C., Mandal, K., Rijmen, V. (eds.) SAC 2023. LNCS, vol. 14201, pp. 127\u2013146. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-53368-6_7","DOI":"10.1007\/978-3-031-53368-6_7"},{"key":"3_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1007\/3-540-45539-6_27","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2000","author":"N Courtois","year":"2000","unstructured":"Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392\u2013407. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/3-540-45539-6_27"},{"key":"3_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/3-540-36178-2_17","volume-title":"Advances in Cryptology \u2014 ASIACRYPT 2002","author":"NT Courtois","year":"2002","unstructured":"Courtois, N.T., Pieprzyk, J.: Cryptanalysis of block ciphers with overdefined systems of equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267\u2013287. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-36178-2_17"},{"key":"3_CR11","doi-asserted-by":"publisher","unstructured":"Dobraunig, C., Kales, D., Rechberger, C., Schofnegger, M., Zaverucha, G.: Shorter signatures based on tailor-made minimalist symmetric-key crypto. In: Yin, H., Stavrou, A., Cremers, C., Shi, E. (eds.) ACM CCS 2022, pp. 843\u2013857. ACM Press (2022). https:\/\/doi.org\/10.1145\/3548606.3559353","DOI":"10.1145\/3548606.3559353"},{"issue":"12","key":"3_CR12","doi-asserted-by":"publisher","first-page":"6265","DOI":"10.1109\/TIT.2010.2079016","volume":"56","author":"S Gao","year":"2010","unstructured":"Gao, S., Mateer, T.: Additive fast Fourier transforms over finite fields. IEEE Trans. Inf. Theory 56(12), 6265\u20136272 (2010). https:\/\/doi.org\/10.1109\/TIT.2010.2079016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3_CR13","unstructured":"Gathen, J.v.z., Gerhard, J.: Modern computer algebra. Cambridge University Press, Cambridge, third edition. Edn. (2013)"},{"key":"3_CR14","doi-asserted-by":"publisher","unstructured":"Giorgi, P., Jeannerod, C.P., Villard, G.: On the complexity of polynomial matrix computations. In: ISSAC 2003, pp. 135\u2013142. ACM, New York, NY, USA (2003). https:\/\/doi.org\/10.1145\/860854.860889","DOI":"10.1145\/860854.860889"},{"key":"3_CR15","doi-asserted-by":"publisher","unstructured":"van\u00a0der Hoeven, J.: Optimizing the half-GCD algorithm. Applicable Algebra in Engineering, Communication and Computing (2025). https:\/\/doi.org\/10.1007\/s00200-025-00690-w","DOI":"10.1007\/s00200-025-00690-w"},{"key":"3_CR16","unstructured":"H\u00fclsing, A., et al.: SPHINCS+. Technical Report, National Institute of Standards and Technology (2022). Available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022"},{"key":"3_CR17","doi-asserted-by":"publisher","unstructured":"Jeannerod, C.P., Neiger, V., Villard, G.: Fast computation of approximant bases in canonical form. J. Sym. Comput. 98, 192\u2013224 (2020). https:\/\/doi.org\/10.1016\/j.jsc.2019.07.011. Special issue on Symbolic and Algebraic Computation: ISSAC 2017","DOI":"10.1016\/j.jsc.2019.07.011"},{"key":"3_CR18","unstructured":"Kim, J., Park, J.H.: NTRU+: Compact construction of NTRU using simple encoding method. Cryptology ePrint Archive, Report 2022\/1664 (2022). https:\/\/eprint.iacr.org\/2022\/1664"},{"key":"3_CR19","unstructured":"Kim, S., Ha, J., Son, M., Lee, B.: Efficacy and mitigation of the cryptanalysis on AIM. Cryptology ePrint Archive, Report 2023\/1474 (2023). https:\/\/eprint.iacr.org\/2023\/1474"},{"key":"3_CR20","doi-asserted-by":"publisher","unstructured":"Kim, S., et al.: AIM: Symmetric primitive for shorter signatures with stronger security. In: Meng, W., Jensen, C.D., Cremers, C., Kirda, E. (eds.) ACM CCS 2023, pp. 401\u2013415. ACM Press (2023). https:\/\/doi.org\/10.1145\/3576915.3616579","DOI":"10.1145\/3576915.3616579"},{"key":"3_CR21","unstructured":"Kim, S., et al.: The AIMer signature scheme. Version 2.1. Samsung, S. D. S. (2024). https:\/\/aimer-signature.org\/docs\/AIMer-specification-v2.1.pdf"},{"key":"3_CR22","doi-asserted-by":"publisher","unstructured":"Labahn, G., Neiger, V., Zhou, W.: Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix. J. Complex. 42, 44\u201371 (2017). https:\/\/doi.org\/10.1016\/J.JCO.2017.03.003","DOI":"10.1016\/J.JCO.2017.03.003"},{"key":"3_CR23","doi-asserted-by":"publisher","unstructured":"Li, W.D., Chen, M.S., Kuo, P.C., Cheng, C.M., Yang, B.Y.: Frobenius Additive Fast Fourier Transform. In: ISSAC 2018, pp. 263\u2013270. ACM, New York, NY, USA (2018). https:\/\/doi.org\/10.1145\/3208976.3208998","DOI":"10.1145\/3208976.3208998"},{"key":"3_CR24","doi-asserted-by":"publisher","unstructured":"Liu, F., Mahzoun, M., Meier, W.: Modelling ciphers with overdefined systems of quadratic equations: application to Friday, Vision, RAIN and Biscuit. In: Chung, K.M., Sasaki, Y. (eds.) ASIACRYPT 2024, Part\u00a0VII. LNCS, vol. 15490, pp. 424\u2013456. Springer, Singapore, Singapore (2024). https:\/\/doi.org\/10.1007\/978-981-96-0941-3_14","DOI":"10.1007\/978-981-96-0941-3_14"},{"key":"3_CR25","doi-asserted-by":"publisher","unstructured":"Liu, F., Mahzoun, M., \u00d8ygarden, M., Meier, W.: Algebraic attacks on RAIN and AIM using equivalent representations. IACR Trans. Symm. Cryptol. 2023(4), 166\u2013186 (2023). https:\/\/doi.org\/10.46586\/tosc.v2023.i4.166-186","DOI":"10.46586\/tosc.v2023.i4.166-186"},{"key":"3_CR26","unstructured":"Lyubashevsky, V., et al.: CRYSTALS-DILITHIUM. Technical Report, National Institute of Standards and Technology (2022). Available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022"},{"key":"3_CR27","doi-asserted-by":"publisher","unstructured":"Nemec, M., Sys, M., Svenda, P., Klinec, D., Matyas, V.: The return of coppersmith\u2019s attack: practical factorization of widely used RSA moduli. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 1631\u20131648. ACM Press (2017). https:\/\/doi.org\/10.1145\/3133956.3133969","DOI":"10.1145\/3133956.3133969"},{"key":"3_CR28","unstructured":"Sage\u00a0Developers, T.: SageMath, the Sage Mathematics Software System (Version 10.7) (2025). https:\/\/www.sagemath.org"},{"key":"3_CR29","unstructured":"Schwabe, P., et al.: CRYSTALS-KYBER. Technical Report, National Institute of Standards and Technology (2022). Available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022"},{"issue":"1","key":"3_CR30","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1109\/TIT.1986.1057137","volume":"32","author":"DH Wiedemann","year":"1986","unstructured":"Wiedemann, D.H.: Solving sparse linear equations over finite fields. IEEE Trans. Inf. Theory 32(1), 54\u201362 (1986). https:\/\/doi.org\/10.1109\/TIT.1986.1057137","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3_CR31","doi-asserted-by":"publisher","unstructured":"Yang, H.S., Zheng, Q.X., Yang, J.: Algebraic cryptanalysis of AO primitives based on polynomial decomposition. In: Hanaoka, G., Yang, B.Y. (eds.) ASIACRYPT 2025, pp. 383\u2013410. Springer Nature Singapore, Singapore (2026). https:\/\/doi.org\/10.1007\/978-981-95-5018-0_13","DOI":"10.1007\/978-981-95-5018-0_13"},{"key":"3_CR32","unstructured":"Zaverucha, G., et al.: Picnic. Technical Report, National Institute of Standards and Technology (2020). Available at https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\/post-quantum-cryptography-standardization\/round-3-submissions"},{"key":"3_CR33","doi-asserted-by":"publisher","unstructured":"Zhang, K., Wang, Q., Yu, Y., Guo, C., Cui, H.: Algebraic attacks on round-reduced rain and full AIM-III. In: Guo, J., Steinfeld, R. (eds.) ASIACRYPT\u00a02023, Part\u00a0III. LNCS, vol. 14440, pp. 285\u2013310. Springer, Singapore (2023). https:\/\/doi.org\/10.1007\/978-981-99-8727-6_10","DOI":"10.1007\/978-981-99-8727-6_10"},{"key":"3_CR34","doi-asserted-by":"publisher","unstructured":"Zhou, W., Labahn, G., Storjohann, A.: Computing minimal nullspace bases. In: ISSAC 12, pp. 366\u2013373. ACM, New York, NY, USA (2012). https:\/\/doi.org\/10.1145\/2442829.2442881","DOI":"10.1145\/2442829.2442881"}],"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\/978-3-032-25333-0_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:41:44Z","timestamp":1778020904000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-25333-0_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032253323","9783032253330"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-25333-0_3","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":"6 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"}}]}}