{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T15:33:39Z","timestamp":1757777619018,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T00:00:00Z","timestamp":1661472000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T00:00:00Z","timestamp":1661472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972457"],"award-info":[{"award-number":["61972457"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"national key r &d program of china","doi-asserted-by":"crossref","award":["2017YFB0802000"],"award-info":[{"award-number":["2017YFB0802000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61902303","U19B2021"],"award-info":[{"award-number":["61902303","U19B2021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Cryptography Development Fund of China","award":["MMJJ20170104","MMJJ20180219"],"award-info":[{"award-number":["MMJJ20170104","MMJJ20180219"]}]},{"name":"Key Research and Development Program of Shaanxi","award":["2020ZDLGY08-04"],"award-info":[{"award-number":["2020ZDLGY08-04"]}]},{"name":"Guangxi Key Laboratory of Cryptography and Information Security","award":["GCIS202125"],"award-info":[{"award-number":["GCIS202125"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["2020JQ-832","2021JM-126"],"award-info":[{"award-number":["2020JQ-832","2021JM-126"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10623-022-01089-1","type":"journal-article","created":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T12:02:48Z","timestamp":1661515368000},"page":"2419-2448","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improved key-recovery attacks on reduced-round WEM-8"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7091-9616","authenticated-orcid":false,"given":"Jun","family":"Liu","sequence":"first","affiliation":[]},{"given":"Dachao","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Yupu","family":"Hu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4152-8923","authenticated-orcid":false,"given":"Jie","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2554-4464","authenticated-orcid":false,"given":"Baocang","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,26]]},"reference":[{"issue":"10","key":"1089_CR1","doi-asserted-by":"publisher","first-page":"996","DOI":"10.1002\/sec.1394","volume":"9","author":"K Bai","year":"2016","unstructured":"Bai K., Wu C.: A secure white-box SM4 implementation. Secur. Commun. Netw. 9(10), 996\u20131006 (2016).","journal-title":"Secur. Commun. Netw."},{"key":"1089_CR2","unstructured":"Bard G.V.: Achieving a log($$n$$) speed up for boolean matrix operations and calculating the complexity of the dense linear algebra step of algebraic stream cipher attacks and of integer factorization methods (2006). http:\/\/eprint.iacr.org\/2006\/163."},{"key":"1089_CR3","first-page":"227","volume-title":"Selected Areas in Cryptography","author":"O Billet","year":"2005","unstructured":"Billet O., Gilbert H., Ech-Chatbi C.: Cryptanalysis of a white box AES implementation. In: Handschuh H., Hasan M.A. (eds.) Selected Areas in Cryptography, pp. 227\u2013240. Springer, Berlin (2005)."},{"key":"1089_CR4","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/3-540-44987-6_24","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2001","author":"A Biryukov","year":"2001","unstructured":"Biryukov A., Shamir A.: Structural cryptanalysis of SASAS. In: Pfitzmann B. (ed.) Advances in Cryptology\u2014EUROCRYPT 2001, pp. 395\u2013405. Springer, Berlin (2001)."},{"key":"1089_CR5","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/978-3-030-03329-3_13","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2018","author":"A Biryukov","year":"2018","unstructured":"Biryukov A., Udovenko A.: Attacks and countermeasures for white-box designs. In: Peyrin T., Galbraith S. (eds.) Advances in Cryptology\u2014ASIACRYPT 2018, pp. 373\u2013402. Springer International Publishing, Cham (2018)."},{"key":"1089_CR6","first-page":"63","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2014","author":"A Biryukov","year":"2014","unstructured":"Biryukov A., Bouillaguet C., Khovratovich D.: Cryptographic schemes based on the ASASA structure: black-box, white-box, and public-key (extended abstract). In: Sarkar P., Iwata T. (eds.) Advances in Cryptology\u2014ASIACRYPT 2014, pp. 63\u201384. Springer, Berlin Heidelberg, Berlin, Heidelberg (2014)."},{"key":"1089_CR7","doi-asserted-by":"crossref","unstructured":"Bogdanov, A., Isobe, T.: White-box cryptography revisited: space-hard ciphers. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 1058\u20131069. ACM, New York (2015)","DOI":"10.1145\/2810103.2813699"},{"key":"1089_CR8","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-662-53887-6_5","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2016","author":"A Bogdanov","year":"2016","unstructured":"Bogdanov A., Isobe T., Tischhauser E.: Towards practical whitebox cryptography: optimizing efficiency and space hardness. In: Cheon J.H., Takagi T. (eds.) Advances in Cryptology\u2014ASIACRYPT 2016, pp. 126\u2013158. Springer, Berlin (2016)."},{"key":"1089_CR9","doi-asserted-by":"crossref","unstructured":"Bos J.W., Hubain C., Michiels W., Teuwen P.: Differential computation analysis: hiding your white-box designs is not enough. In: Gierlichs B., Poschmann A.Y. (eds.) Cryptographic Hardware and Embedded Systems\u2013CHES 2016, pp. 215\u2013236. Springer, Berlin (2016).","DOI":"10.1007\/978-3-662-53140-2_11"},{"key":"1089_CR10","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/978-3-319-52153-4_17","volume-title":"Topics in Cryptology\u2014CT-RSA 2017","author":"J Cho","year":"2017","unstructured":"Cho J., Choi K.Y., Dinur I., Dunkelman O., Keller N., Moon D., Veidberg A.: WEM: a new family of white-box block ciphers based on the Even-Mansour construction. In: Handschuh H. (ed.) Topics in Cryptology\u2014CT-RSA 2017, pp. 293\u2013308. Springer International Publishing, Cham (2017)."},{"key":"1089_CR11","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1007\/3-540-36492-7_17","volume-title":"Selected Areas in Cryptography","author":"S Chow","year":"2003","unstructured":"Chow S., Eisen P., Johnson H., Van Oorschot P.C.: White-box cryptography and an AES implementation. In: Nyberg K., Heys H. (eds.) Selected Areas in Cryptography, pp. 250\u2013270. Springer, Berlin (2003)."},{"key":"1089_CR12","first-page":"1","volume-title":"Digital Rights Management","author":"S Chow","year":"2003","unstructured":"Chow S., Eisen P., Johnson H., Van Oorschot P.C.: A white-box DES implementation for DRM applications. In: Feigenbaum J. (ed.) Digital Rights Management, pp. 1\u201315. Springer, Berlin (2003)."},{"key":"1089_CR13","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/11832072_6","volume-title":"Security and Cryptography for Networks","author":"J Daemen","year":"2006","unstructured":"Daemen J., Rijmen V.: Understanding two-round differentials in AES. In: De Prisco R., Yung M. (eds.) Security and Cryptography for Networks, pp. 78\u201394. Springer, Berlin (2006)."},{"key":"1089_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-60769-5","volume-title":"The Design of Rijndael: The Advanced Encryption Standard (AES)","author":"J Daemen","year":"2020","unstructured":"Daemen J., Rijmen V.: The Design of Rijndael: The Advanced Encryption Standard (AES). Springer, Berlin (2020)."},{"key":"1089_CR15","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/BFb0052343","volume-title":"Fast Software Encryption","author":"J Daemen","year":"1997","unstructured":"Daemen J., Knudsen L., Rijmen V.: The block cipher Square. In: Biham E. (ed.) Fast Software Encryption, pp. 149\u2013165. Springer, Berlin (1997)."},{"issue":"3","key":"1089_CR16","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s001459900025","volume":"10","author":"S Even","year":"1997","unstructured":"Even S., Mansour Y.: A construction of a cipher from a single pseudorandom permutation. J. Cryptol. 10(3), 151\u2013161 (1997).","journal-title":"J. Cryptol."},{"key":"1089_CR17","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/978-3-662-53887-6_6","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2016","author":"PA Fouque","year":"2016","unstructured":"Fouque P.A., Karpman P., Kirchner P., Minaud B.: Efficient and provable white-box primitives. In: Cheon J.H., Takagi T. (eds.) Advances in Cryptology\u2014ASIACRYPT 2016, pp. 159\u2013188. Springer, Berlin (2016)."},{"key":"1089_CR18","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/978-3-662-47989-6_23","volume-title":"Advances in Cryptology\u2014CRYPTO 2015","author":"H Gilbert","year":"2015","unstructured":"Gilbert H., Pl\u00fbt J., Treger J.: Key-recovery attack on the ASASA cryptosystem with expanding s-boxes. In: Gennaro R., Robshaw M. (eds.) Advances in Cryptology\u2014CRYPTO 2015, pp. 475\u2013490. Springer, Berlin (2015)."},{"issue":"3","key":"1089_CR19","doi-asserted-by":"publisher","first-page":"454","DOI":"10.46586\/tches.v2020.i3.454-482","volume":"2020","author":"L Goubin","year":"2020","unstructured":"Goubin L., Rivain M., Wang J.: Defeating state-of-the-art white-box countermeasures with advanced gray-box attacks. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2020(3), 454\u2013482 (2020).","journal-title":"IACR Trans. Cryptogr. Hardw. Embed. Syst."},{"key":"1089_CR20","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/978-3-319-76953-0_13","volume-title":"Topics in Cryptology\u2014CT-RSA 2018","author":"L Grassi","year":"2018","unstructured":"Grassi L.: Mixcolumns properties and attacks on (round-reduced) AES with a single secret s-box. In: Smart N.P. (ed.) Topics in Cryptology\u2014CT-RSA 2018, pp. 243\u2013263. Springer International Publishing, Cham (2018)."},{"key":"1089_CR21","doi-asserted-by":"crossref","unstructured":"Grassi L., Rechberger C., Ronjom S.: Subspace trail cryptanalysis and its applications to AES. IACR Trans. Symmetric Cryptol. 2016(2), 192\u2013225 (2016)","DOI":"10.46586\/tosc.v2016.i2.192-225"},{"issue":"17","key":"1089_CR22","doi-asserted-by":"publisher","first-page":"1458","DOI":"10.1049\/el:19990979","volume":"35","author":"Y Hu","year":"1999","unstructured":"Hu Y., Zhang Y., Xiao G.: Integral cryptanalysis of SAFER+. Electron. Lett. 35(17), 1458\u20131459 (1999).","journal-title":"Electron. Lett."},{"key":"1089_CR23","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1007\/3-540-45661-9_9","volume-title":"Fast Software Encryption","author":"L Knudsen","year":"2002","unstructured":"Knudsen L., Wagner D.: Integral cryptanalysis. In: Daemen J., Rijmen V. (eds.) Fast Software Encryption, pp. 112\u2013127. Springer, Berlin (2002)."},{"key":"1089_CR24","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/978-3-030-40186-3_6","volume-title":"Topics in Cryptology\u2014CT-RSA 2020","author":"J Kwon","year":"2020","unstructured":"Kwon J., Lee B., Lee J., Moon D.: FPL: white-box secure block cipher using parallel table look-ups. In: Jarecki S. (ed.) Topics in Cryptology\u2014CT-RSA 2020, pp. 106\u2013128. Springer International Publishing, Cham (2020)."},{"issue":"2","key":"1089_CR25","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1007\/s11390-017-1727-x","volume":"32","author":"T Lin","year":"2017","unstructured":"Lin T., Lai X., Xue W., Jia Y.: A new Feistel-type white-box encryption scheme. J. Comput. Sci. Technol. 32(2), 386\u2013395 (2017).","journal-title":"J. Comput. Sci. Technol."},{"key":"1089_CR26","first-page":"1","volume-title":"Fast Software Encryption","author":"S Lucks","year":"2002","unstructured":"Lucks S.: The saturation attack\u2014a bait for Twofish. In: Matsui M. (ed.) Fast Software Encryption, pp. 1\u201315. Springer, Berlin (2002)."},{"issue":"3","key":"1089_CR27","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1007\/s00145-017-9272-x","volume":"31","author":"B Minaud","year":"2018","unstructured":"Minaud B., Derbez P., Fouque P.A., Karpman P.: Key-recovery attacks on ASASA. J. Cryptol. 31(3), 845\u2013884 (2018).","journal-title":"J. Cryptol."},{"key":"1089_CR28","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/978-3-319-70694-8_8","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2017","author":"S R\u00f8njom","year":"2017","unstructured":"R\u00f8njom S., Bardeh N.G., Helleseth T.: Yoyo tricks with AES. In: Takagi T., Peyrin T. (eds.) Advances in Cryptology\u2014ASIACRYPT 2017, pp. 217\u2013243. Springer International Publishing, Cham (2017)."},{"issue":"2","key":"1089_CR29","doi-asserted-by":"publisher","first-page":"61","DOI":"10.46586\/tches.v2021.i2.61-105","volume":"2021","author":"O Seker","year":"2021","unstructured":"Seker O., Eisenbarth T., Liskiewicz M.: A white-box masking scheme resisting computational and algebraic attacks. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2021(2), 61\u2013105 (2021).","journal-title":"IACR Trans. Cryptogr. Hardw. Embed. Syst."},{"key":"1089_CR30","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1007\/978-3-662-53018-4_22","volume-title":"Advances in Cryptology\u2014CRYPTO 2016","author":"B Sun","year":"2016","unstructured":"Sun B., Liu M., Guo J., Qu L., Rijmen V.: New insights on AES-like SPN ciphers. In: Robshaw M., Katz J. (eds.) Advances in Cryptology\u2014CRYPTO 2016, pp. 605\u2013624. Springer, Berlin (2016)."},{"key":"1089_CR31","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/978-3-662-48116-5_9","volume-title":"Fast Software Encryption","author":"T Tiessen","year":"2015","unstructured":"Tiessen T., Knudsen L.R., K\u00f6lbl S., Lauridsen M.M.: Security of the AES with a secret s-box. In: Leander G. (ed.) Fast Software Encryption, pp. 175\u2013189. Springer, Berlin (2015)."},{"key":"1089_CR32","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1007\/978-3-540-77360-3_17","volume-title":"Selected Areas in Cryptography","author":"B Wyseur","year":"2007","unstructured":"Wyseur B., Michiels W., Gorissen P., Preneel B.: Cryptanalysis of white-box DES implementations with arbitrary external encodings. In: Adams C., Miri A., Wiener M. (eds.) Selected Areas in Cryptography, pp. 264\u2013277. Springer, Berlin (2007)."},{"key":"1089_CR33","doi-asserted-by":"crossref","unstructured":"Xiao Y., Lai X.: A secure implementation of white-box AES. In: 2009 2nd International Conference on Computer Science and Its Applications, pp. 1\u20136. IEEE, New Jersey (2009).","DOI":"10.1109\/CSA.2009.5404239"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01089-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-022-01089-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01089-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T03:42:39Z","timestamp":1663645359000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-022-01089-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,26]]},"references-count":33,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["1089"],"URL":"https:\/\/doi.org\/10.1007\/s10623-022-01089-1","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2022,8,26]]},"assertion":[{"value":"30 June 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}