{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:07:17Z","timestamp":1786979237096,"version":"3.56.0"},"publisher-location":"Singapore","reference-count":32,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819609406","type":"print"},{"value":"9789819609413","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T00:00:00Z","timestamp":1733702400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T00:00:00Z","timestamp":1733702400000},"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\/978-981-96-0941-3_13","type":"book-chapter","created":{"date-parts":[[2024,12,8]],"date-time":"2024-12-08T08:35:44Z","timestamp":1733646944000},"page":"392-423","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Ultrametric Integral Cryptanalysis"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5638-9885","authenticated-orcid":false,"given":"Tim","family":"Beyne","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5982-1984","authenticated-orcid":false,"given":"Michiel","family":"Verbauwhede","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,12,9]]},"reference":[{"key":"13_CR1","doi-asserted-by":"crossref","unstructured":"Tim Beyne. A geometric approach to linear cryptanalysis. In Mehdi Tibouchi and Huaxiong Wang, editors, ASIACRYPT\u00a02021, Part\u00a0I, volume 13090 of LNCS, pages 36\u201366. Springer, Cham, December 2021.","DOI":"10.1007\/978-3-030-92062-3_2"},{"key":"13_CR2","doi-asserted-by":"crossref","unstructured":"Tim Beyne. A geometric approach to symmetric-key cryptanalysis. PhD thesis, KU Leuven, June 2023.","DOI":"10.46586\/tosc.v2023.i4.244-269"},{"key":"13_CR3","doi-asserted-by":"crossref","unstructured":"Tim Beyne and Vincent Rijmen. Differential cryptanalysis in the fixed-key model. In Yevgeniy Dodis and Thomas Shrimpton, editors, CRYPTO\u00a02022, Part\u00a0III, volume 13509 of LNCS, pages 687\u2013716. Springer, Cham, August 2022.","DOI":"10.1007\/978-3-031-15982-4_23"},{"key":"13_CR4","doi-asserted-by":"crossref","unstructured":"Tim Beyne and Michiel Verbauwhede. Integral cryptanalysis using algebraic transition matrices. IACR Transactions on Symmetric Cryptology, 2023(4):244\u2013269, Dec. 2023.","DOI":"10.46586\/tosc.v2023.i4.244-269"},{"key":"13_CR5","unstructured":"Tim Beyne and Michiel Verbauwhede. Ultrametric integral cryptanalysis. Cryptology ePrint Archive, Report 2024\/722, 2024."},{"key":"13_CR6","doi-asserted-by":"crossref","unstructured":"Andrey Bogdanov, Lars\u00a0R. Knudsen, Gregor Leander, Christof Paar, Axel Poschmann, Matthew J.\u00a0B. Robshaw, Yannick Seurin, and C.\u00a0Vikkelsoe. PRESENT: An ultra-lightweight block cipher. In Pascal Paillier and Ingrid Verbauwhede, editors, CHES\u00a02007, volume 4727 of LNCS, pages 450\u2013466. Springer, Berlin, Heidelberg, September 2007.","DOI":"10.1007\/978-3-540-74735-2_31"},{"key":"13_CR7","doi-asserted-by":"crossref","unstructured":"Andrey Bogdanov, Gregor Leander, Kaisa Nyberg, and Meiqin Wang. Integral and multidimensional linear distinguishers with correlation zero. In Xiaoyun Wang and Kazue Sako, editors, ASIACRYPT\u00a02012, volume 7658 of LNCS, pages 244\u2013261. Springer, Berlin, Heidelberg, December 2012.","DOI":"10.1007\/978-3-642-34961-4_16"},{"key":"13_CR8","doi-asserted-by":"crossref","unstructured":"Andrey Bogdanov and Vincent Rijmen. Linear hulls with correlation zero and linear cryptanalysis of block ciphers. DCC, 70(3):369\u2013383, 2014.","DOI":"10.1007\/s10623-012-9697-z"},{"key":"13_CR9","doi-asserted-by":"crossref","unstructured":"Christina Boura and Anne Canteaut. On the influence of the algebraic degree of $$f^{-1}$$ on the algebraic degree of $$g \\circ f$$. IEEE Transactions on Information Theory, 59(1):691\u2013702, 2012.","DOI":"10.1109\/TIT.2012.2214203"},{"key":"13_CR10","doi-asserted-by":"crossref","unstructured":"Christina Boura and Anne Canteaut. Another view of the division property. In Matthew Robshaw and Jonathan Katz, editors, CRYPTO\u00a02016, Part\u00a0I, volume 9814 of LNCS, pages 654\u2013682. Springer, Berlin, Heidelberg, August 2016.","DOI":"10.1007\/978-3-662-53018-4_24"},{"key":"13_CR11","doi-asserted-by":"crossref","unstructured":"Anne Canteaut and Marion Videau. Degree of composition of highly nonlinear functions and applications to higher order differential cryptanalysis. In Lars\u00a0R. Knudsen, editor, EUROCRYPT\u00a02002, volume 2332 of LNCS, pages 518\u2013533. Springer, Berlin, Heidelberg, April\u00a0\/\u00a0May 2002.","DOI":"10.1007\/3-540-46035-7_34"},{"key":"13_CR12","doi-asserted-by":"crossref","unstructured":"Claude Carlet. Two new classes of Bent functions. In Tor Helleseth, editor, EUROCRYPT\u201993, volume 765 of LNCS, pages 77\u2013101. Springer, Berlin, Heidelberg, May 1994.","DOI":"10.1007\/3-540-48285-7_8"},{"key":"13_CR13","doi-asserted-by":"crossref","unstructured":"Claude Carlet. Boolean functions for cryptography and coding theory.Cambridge University Press, 2021.","DOI":"10.1017\/9781108606806"},{"key":"13_CR14","doi-asserted-by":"crossref","unstructured":"Joan Daemen, Ren\u00e9 Govaerts, and Joos Vandewalle. Correlation matrices. In Bart Preneel, editor, FSE\u201994, volume 1008 of LNCS, pages 275\u2013285. Springer, Berlin, Heidelberg, December 1995.","DOI":"10.1007\/3-540-60590-8_21"},{"key":"13_CR15","doi-asserted-by":"crossref","unstructured":"Joan Daemen, Lars\u00a0R. Knudsen, and Vincent Rijmen. The block cipher Square. In Eli Biham, editor, FSE\u201997, volume 1267 of LNCS, pages 149\u2013165. Springer, Berlin, Heidelberg, January 1997.","DOI":"10.1007\/BFb0052343"},{"key":"13_CR16","unstructured":"Richard Dedekind. Ideale in Normalk\u00f6rpern. In Robert Fricke, Emmy Noether, and \u00d8ystein Ore, editors, Gesammelte mathematische Werke. 1930."},{"key":"13_CR17","doi-asserted-by":"crossref","unstructured":"Brandon Dravie, J\u00e9r\u00e9my Parriaux, Philippe Guillot, and Gilles Mill\u00e9rioux.Matrix representations of vectorial boolean functions and eigenanalysis.Cryptography and Communications, 8:555\u2013577, 2016.","DOI":"10.1007\/s12095-015-0160-7"},{"key":"13_CR18","unstructured":"Hosein Hadipour, Simon Gerhalter, Sadegh Sadeghi, and Maria Eichlseder. Improved search for integral, impossible-differential and zero-correlation attacks: Application to Ascon, ForkSKINNY, SKINNY, MANTIS, PRESENT and QARMAv2. Cryptology ePrint Archive, Paper 2023\/1701, 2023. https:\/\/eprint.iacr.org\/2023\/1701."},{"key":"13_CR19","doi-asserted-by":"crossref","unstructured":"Yonglin Hao, Gregor Leander, Willi Meier, Yosuke Todo, and Qingju Wang. Modeling for three-subset division property without unknown subset - improved cube attacks against Trivium and Grain-128AEAD. In Anne Canteaut and Yuval Ishai, editors, EUROCRYPT\u00a02020, Part\u00a0I, volume 12105 of LNCS, pages 466\u2013495. Springer, Cham, May 2020.","DOI":"10.1007\/978-3-030-45721-1_17"},{"key":"13_CR20","doi-asserted-by":"crossref","unstructured":"Phil Hebborn, Gregor Leander, and Aleksei Udovenko. Mathematical aspects of division property. Cryptography and Communications, pages 1\u201344, 2023.","DOI":"10.1007\/s12095-022-00622-2"},{"key":"13_CR21","doi-asserted-by":"crossref","unstructured":"Kai Hu, Siwei Sun, Meiqin Wang, and Qingju Wang. An algebraic formulation of the division property: Revisiting degree evaluations, cube attacks, and key-independent sums. In Shiho Moriai and Huaxiong Wang, editors, ASIACRYPT\u00a02020, Part\u00a0I, volume 12491 of LNCS, pages 446\u2013476. Springer, Cham, December 2020.","DOI":"10.1007\/978-3-030-64837-4_15"},{"key":"13_CR22","doi-asserted-by":"crossref","unstructured":"Nicholas\u00a0M. Katz. On a theorem of Ax. American Journal of Mathematics, 93(2):485\u2013499, 1971.","DOI":"10.2307\/2373389"},{"key":"13_CR23","doi-asserted-by":"crossref","unstructured":"Lars\u00a0R. Knudsen. Truncated and higher order differentials. In Bart Preneel, editor, FSE\u201994, volume 1008 of LNCS, pages 196\u2013211. Springer, Berlin, Heidelberg, December 1995.","DOI":"10.1007\/3-540-60590-8_16"},{"key":"13_CR24","doi-asserted-by":"crossref","unstructured":"Lars\u00a0R. Knudsen and David Wagner. Integral cryptanalysis. In Joan Daemen and Vincent Rijmen, editors, FSE\u00a02002, volume 2365 of LNCS, pages 112\u2013127. Springer, Berlin, Heidelberg, February 2002.","DOI":"10.1007\/3-540-45661-9_9"},{"key":"13_CR25","unstructured":"Florence\u00a0J. MacWilliams and Neil J.\u00a0A. Sloane. The theory of error-correcting codes, volume\u00a016. Elsevier, 1977."},{"key":"13_CR26","doi-asserted-by":"crossref","unstructured":"Gian\u00a0Carlo Rota. On the foundations of combinatorial theory I. Theory of M\u00f6bius functions. Zeitschrift f\u00fcr Wahrscheinlichkeitstheorie und Verwandte Gebiete, 2(4):340\u2013368, Jan 1964.","DOI":"10.1007\/BF00531932"},{"key":"13_CR27","doi-asserted-by":"crossref","unstructured":"Benjamin Steinberg. Representation theory of finite monoids. Springer Cham, 2016.","DOI":"10.1007\/978-3-319-43932-7"},{"key":"13_CR28","doi-asserted-by":"crossref","unstructured":"Bing Sun, Zhiqiang Liu, Vincent Rijmen, Ruilin Li, Lei Cheng, Qingju Wang, Hoda AlKhzaimi, and Chao Li. Links among impossible differential, integral and zero correlation linear cryptanalysis. In Rosario Gennaro and Matthew J.\u00a0B. Robshaw, editors, CRYPTO\u00a02015, Part\u00a0I, volume 9215 of LNCS, pages 95\u2013115. Springer, Berlin, Heidelberg, August 2015.","DOI":"10.1007\/978-3-662-47989-6_5"},{"key":"13_CR29","doi-asserted-by":"crossref","unstructured":"Yosuke Todo. Structural evaluation by generalized integral property. In Elisabeth Oswald and Marc Fischlin, editors, EUROCRYPT\u00a02015, Part\u00a0I, volume 9056 of LNCS, pages 287\u2013314. Springer, Berlin, Heidelberg, April 2015.","DOI":"10.1007\/978-3-662-46800-5_12"},{"key":"13_CR30","doi-asserted-by":"crossref","unstructured":"Yosuke Todo and Masakatu Morii. Bit-based division property and application to simon family. In Thomas Peyrin, editor, FSE\u00a02016, volume 9783 of LNCS, pages 357\u2013377. Springer, Berlin, Heidelberg, March 2016.","DOI":"10.1007\/978-3-662-52993-5_18"},{"key":"13_CR31","doi-asserted-by":"crossref","unstructured":"SenPeng Wang, Bin Hu, Jie Guan, Kai Zhang, and Tairong Shi. MILP-aided method of searching division property using three subsets and applications. In Steven\u00a0D. Galbraith and Shiho Moriai, editors, ASIACRYPT\u00a02019, Part\u00a0III, volume 11923 of LNCS, pages 398\u2013427. Springer, Cham, December 2019.","DOI":"10.1007\/978-3-030-34618-8_14"},{"key":"13_CR32","doi-asserted-by":"crossref","unstructured":"Zejun Xiang, Wentao Zhang, Zhenzhen Bao, and Dongdai Lin. Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers.In Jung\u00a0Hee Cheon and Tsuyoshi Takagi, editors, ASIACRYPT\u00a02016, Part\u00a0I, volume 10031 of LNCS, pages 648\u2013678. Springer, Berlin, Heidelberg, December 2016.","DOI":"10.1007\/978-3-662-53887-6_24"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-96-0941-3_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,8]],"date-time":"2024-12-08T09:02:46Z","timestamp":1733648566000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-96-0941-3_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,9]]},"ISBN":["9789819609406","9789819609413"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-981-96-0941-3_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,9]]},"assertion":[{"value":"9 December 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ASIACRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on the Theory and Application of Cryptology and Information Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Kolkata","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"India","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"asiacrypt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/asiacrypt.iacr.org\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}