{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T02:02:58Z","timestamp":1784685778294,"version":"3.55.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T00:00:00Z","timestamp":1782518400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T00:00:00Z","timestamp":1782518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1007\/s10623-026-01879-x","type":"journal-article","created":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T04:57:42Z","timestamp":1782536262000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cryptanalysis of Gleeok-128"],"prefix":"10.1007","volume":"94","author":[{"given":"Siwei","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peipei","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shengyuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiutao","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zejun","family":"Xiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangyong","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,27]]},"reference":[{"issue":"2","key":"1879_CR1","doi-asserted-by":"publisher","first-page":"545","DOI":"10.46586\/TCHES.V2024.I2.545-587","volume":"2024","author":"R Anand","year":"2024","unstructured":"Anand R., Banik S., Caforio A., Ishikawa T., Isobe T., Liu F., Minematsu K., Rahman M., Sakamoto K.: Gleeok: a family of low-latency PRFs and its applications to authenticated encryption. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2024(2), 545\u2013587 (2024). https:\/\/doi.org\/10.46586\/TCHES.V2024.I2.545-587.","journal-title":"IACR Trans. Cryptogr. Hardw. Embed. Syst."},{"issue":"1","key":"1879_CR2","doi-asserted-by":"publisher","first-page":"4","DOI":"10.13154\/tosc.v2017.i1.4-44","volume":"2017","author":"R Avanzi","year":"2017","unstructured":"Avanzi R.: The QARMA block cipher family\u2014almost MDS matrices over rings with zero divisors, nearly symmetric even-Mansour constructions with non-involutory central rounds, and search heuristics for low-latency S-boxes. IACR Trans. Symmetric Cryptol 2017(1), 4\u201344 (2017). https:\/\/doi.org\/10.13154\/tosc.v2017.i1.4-44.","journal-title":"IACR Trans. Symmetric Cryptol"},{"issue":"1","key":"1879_CR3","doi-asserted-by":"publisher","first-page":"37","DOI":"10.46586\/TOSC.V2021.I1.37-77","volume":"2021","author":"S Banik","year":"2021","unstructured":"Banik S., Isobe T., Liu F., Minematsu K., Sakamoto K.: Orthros: a low-latency PRF. IACR Trans. Symmetric Cryptol. 2021(1), 37\u201377 (2021). https:\/\/doi.org\/10.46586\/TOSC.V2021.I1.37-77.","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"1879_CR4","doi-asserted-by":"publisher","unstructured":"Bar-On A., Dunkelman O., Keller N., Weizman A.: DLCT: a new tool for differential-linear cryptanalysis. In: Ishai Y., Rijmen V. (eds.) Advances in Cryptology\u2014EUROCRYPT 2019\u201438th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings, Part I. Lecture Notes in Computer Science, Darmstadt, Germany, 19\u201323 May 2019, vol. 11476, pp. 313\u2013342. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17653-2_11.","DOI":"10.1007\/978-3-030-17653-2_11"},{"key":"1879_CR5","doi-asserted-by":"publisher","unstructured":"Beierle C., Jean J., K\u00f6lbl S., Leander G., Moradi A., Peyrin T., Sasaki Y., Sasdrich P., Sim S.M.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw M., Katz J. (eds.) Advances in Cryptology\u2014CRYPTO 2016\u201436th Annual International Cryptology Conference, Proceedings, Part II. Lecture Notes in Computer Science, Santa Barbara, CA, USA, 14\u201318 August 2016, vol. 9815, pp. 123\u2013153. Springer, Berlin (2016). https:\/\/doi.org\/10.1007\/978-3-662-53008-5_5.","DOI":"10.1007\/978-3-662-53008-5_5"},{"issue":"3","key":"1879_CR6","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1007\/s00145-016-9237-5","volume":"30","author":"C Blondeau","year":"2017","unstructured":"Blondeau C., Leander G., Nyberg K.: Differential-linear cryptanalysis revisited. J. Cryptol. 30(3), 859\u2013888 (2017).","journal-title":"J. Cryptol."},{"key":"1879_CR7","doi-asserted-by":"publisher","unstructured":"Borghoff J., Canteaut A., G\u00fcneysu T., Kavun E.B., Knezevic M., Knudsen L.R., Leander G., Nikov V., Paar C., Rechberger C., Rombouts P., Thomsen S.S., Yal\u00e7in T.: PRINCE\u2014a low-latency block cipher for pervasive computing applications\u2014extended abstract. In: Wang X., Sako K. (eds.) Advances in Cryptology\u2014ASIACRYPT 2012, Proceedings. Lecture Notes in Computer Science, Beijing, China, 2\u20136 December 2012, vol. 7658, pp. 208\u2013225. Springer, Berlin (2012). https:\/\/doi.org\/10.1007\/978-3-642-34961-4_14.","DOI":"10.1007\/978-3-642-34961-4_14"},{"key":"1879_CR8","doi-asserted-by":"publisher","unstructured":"Boura C., Canteaut A., Canni\u00e8re C.D.: Higher-order differential properties of keccak and Luffa. In: Joux A. (ed.) Fast Software Encryption\u201418th International Workshop, FSE 2011, Revised Selected Papers. Lecture Notes in Computer Science, Lyngby, Denmark, 13\u201316 February 2011, vol. 6733, pp. 252\u2013269. Springer, Berlin (2011). https:\/\/doi.org\/10.1007\/978-3-642-21702-9_15.","DOI":"10.1007\/978-3-642-21702-9_15"},{"issue":"1","key":"1879_CR9","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1109\/TIT.2012.2214203","volume":"59","author":"C Boura","year":"2013","unstructured":"Boura C., Canteaut A.: On the influence of the algebraic degree of $${\\text{ f }}^{{-1}}$$ on the algebraic degree of G $$\\circ $$ F. IEEE Trans. Inf. Theory 59(1), 691\u2013702 (2013). https:\/\/doi.org\/10.1109\/TIT.2012.2214203.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"1879_CR10","doi-asserted-by":"publisher","first-page":"7702","DOI":"10.1109\/TIT.2020.3017494","volume":"66","author":"C Carlet","year":"2020","unstructured":"Carlet C.: Graph indicators of vectorial functions and bounds on the algebraic degree of composite functions. IEEE Trans. Inf. Theory 66(12), 7702\u20137716 (2020). https:\/\/doi.org\/10.1109\/TIT.2020.3017494.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"1879_CR11","doi-asserted-by":"publisher","first-page":"411","DOI":"10.46586\/TOSC.V2021.I1.411-442","volume":"2021","author":"S Chen","year":"2021","unstructured":"Chen S., Xiang Z., Zeng X., Zhang S.: On the relationships between different methods for degree evaluation. IACR Trans. Symmetric Cryptol. 2021(1), 411\u2013442 (2021). https:\/\/doi.org\/10.46586\/TOSC.V2021.I1.411-442.","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"1879_CR12","doi-asserted-by":"publisher","unstructured":"Daemen J., Knudsen L.R., Rijmen V.: The block cipher square. In: Biham E. (ed.) Fast Software Encryption, 4th International Workshop, FSE \u201997, Proceedings. Lecture Notes in Computer Science, Haifa, Israel, 20\u201322 January 1997, vol. 1267, pp. 149\u2013165. Springer, Berlin (1997). https:\/\/doi.org\/10.1007\/BFB0052343.","DOI":"10.1007\/BFB0052343"},{"key":"1879_CR13","unstructured":"Feng X., Tian Y., Wang Y., Xu S., Zhang A.: Full linear integer inequality characterization of sets over $$\\text{ Z}^{n}_{2}$$. ChinaXiv (2022). arXiv:2022.10000V2."},{"key":"1879_CR14","doi-asserted-by":"publisher","unstructured":"Hadipour H., Derbez P., Eichlseder M.: Revisiting differential-linear attacks via a boomerang perspective with application to AES, Ascon, CLEFIA, SKINNY, PRESENT, KNOT, TWINE, WARP, LBlock, Simeck, and SERPENT. In: Reyzin L., Stebila D. (eds.) Advances in Cryptology\u2014CRYPTO 2024\u201444th Annual International Cryptology Conference, Proceedings, Part IV. Lecture Notes in Computer Science, Santa Barbara, CA, USA, 18\u201322 August 2024, vol. 14923, pp. 38\u201372. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-68385-5_2.","DOI":"10.1007\/978-3-031-68385-5_2"},{"key":"1879_CR15","doi-asserted-by":"publisher","unstructured":"Hebborn P., Lambin B., Leander G., Todo Y.: Lower bounds on the degree of block ciphers. In: Moriai S., Wang H. (eds.) Advances in Cryptology\u2014ASIACRYPT 2020\u201426th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part I. Lecture Notes in Computer Science, Daejeon, South Korea, 7\u201311 December 2020, vol. 12491, pp. 537\u2013566. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64837-4_18.","DOI":"10.1007\/978-3-030-64837-4_18"},{"key":"1879_CR16","doi-asserted-by":"publisher","unstructured":"Hu K., Sun S., Wang M., Wang Q.: An algebraic formulation of the division property: revisiting degree evaluations, cube attacks, and key-independent sums. In: Moriai S., Wang H. (eds.) Advances in Cryptology\u2014ASIACRYPT 2020\u201426th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part I. Lecture Notes in Computer Science, Daejeon, South Korea, 7\u201311 December 2020, vol. 12491, pp. 446\u2013476. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64837-4_15.","DOI":"10.1007\/978-3-030-64837-4_15"},{"key":"1879_CR17","doi-asserted-by":"publisher","unstructured":"Knudsen L.R., Wagner D.A.: Integral cryptanalysis. In: Daemen J., Rijmen V. (eds.) Fast Software Encryption, 9th International Workshop, FSE 2002, Revised Papers. Lecture Notes in Computer Science, Leuven, Belgium, 4\u20136 February 2002, vol. 2365, pp. 112\u2013127. Springer, Berlin (2002). https:\/\/doi.org\/10.1007\/3-540-45661-9_9.","DOI":"10.1007\/3-540-45661-9_9"},{"key":"1879_CR18","doi-asserted-by":"publisher","unstructured":"Langford S.K., Hellman M.E.: Differential-linear cryptanalysis. In: Desmedt Y. (ed.) Advances in Cryptology\u2014CRYPTO \u201994, 14th Annual International Cryptology Conference, Proceedings. Lecture Notes in Computer Science, Santa Barbara, California, USA, 21\u201325 August 1994, vol. 839, pp. 17\u201325. Springer, Berlin (1994). https:\/\/doi.org\/10.1007\/3-540-48658-5_3.","DOI":"10.1007\/3-540-48658-5_3"},{"key":"1879_CR19","doi-asserted-by":"publisher","unstructured":"Liu M.: Degree evaluation of NFSR-based cryptosystems. In: Katz J., Shacham H. (eds.) Advances in Cryptology\u2014CRYPTO 2017\u201437th Annual International Cryptology Conference, Proceedings, Part III. Lecture Notes in Computer Science, Santa Barbara, CA, USA, 20\u201324 August 2017, vol. 10403, pp. 227\u2013249. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63697-9_8.","DOI":"10.1007\/978-3-319-63697-9_8"},{"key":"1879_CR20","doi-asserted-by":"publisher","unstructured":"Matsui M.: Linear cryptanalysis method for DES cipher. In: Helleseth T. (ed.) Advances in Cryptology\u2014EUROCRYPT \u201993, Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science, Lofthus, Norway, 23\u201327 May 1993, vol. 765, pp. 386\u2013397. Springer, Berlin (1993). https:\/\/doi.org\/10.1007\/3-540-48285-7_33.","DOI":"10.1007\/3-540-48285-7_33"},{"key":"1879_CR21","doi-asserted-by":"publisher","unstructured":"Peng T., Zhang W., Weng J., Ding T.: New approaches for estimating the bias of differential-linear distinguishers. In: Reyzin L., Stebila D. (eds.) Advances in Cryptology\u2014CRYPTO 2024\u201444th Annual International Cryptology Conference, Proceedings, Part IV. Lecture Notes in Computer Science, Santa Barbara, CA, USA, 18\u201322 August 2024, vol. 14923, pp. 174\u2013205. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-68385-5_6.","DOI":"10.1007\/978-3-031-68385-5_6"},{"key":"1879_CR22","doi-asserted-by":"publisher","unstructured":"Sasaki Y., Todo Y.: New algorithm for modeling S-box in MILP based differential and division trail search. In: Farshim P., Simion E. (eds.) Innovative Security Solutions for Information Technology and Communications\u201410th International Conference, SecITC 2017, Revised Selected Papers. Lecture Notes in Computer Science, Bucharest, Romania, 8\u20139 June 2017, vol. 10543, pp. 150\u2013165. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-69284-5_11.","DOI":"10.1007\/978-3-319-69284-5_11"},{"key":"1879_CR23","doi-asserted-by":"publisher","unstructured":"Sun S., Hu L., Wang P., Qiao K., Ma X., Song L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES (L) and other bit-oriented block ciphers. In: Sarkar P., Iwata T. (eds.) Advances in Cryptology\u2014ASIACRYPT 2014\u201420th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part I. Lecture Notes in Computer Science, Kaoshiung, Taiwan, ROC, 7\u201311 December 2014. vol. 8873, pp. 158\u2013178. Springer, Berlin (2014). https:\/\/doi.org\/10.1007\/978-3-662-45611-8_9.","DOI":"10.1007\/978-3-662-45611-8_9"},{"key":"1879_CR24","doi-asserted-by":"publisher","unstructured":"Todo Y.: Structural evaluation by generalized integral property. In: Oswald E., Fischlin M. (eds.) Advances in Cryptology\u2014EUROCRYPT 2015\u201434th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings, Part I. Lecture Notes in Computer Science, Sofia, Bulgaria, 26\u201330 April 2015, vol. 9056, pp. 287\u2013314. Springer, Berlin (2015). https:\/\/doi.org\/10.1007\/978-3-662-46800-5_12.","DOI":"10.1007\/978-3-662-46800-5_12"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01879-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-026-01879-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01879-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T01:41:30Z","timestamp":1784684490000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-026-01879-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,27]]},"references-count":24,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["1879"],"URL":"https:\/\/doi.org\/10.1007\/s10623-026-01879-x","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,27]]},"assertion":[{"value":"30 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"145"}}