{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:55:15Z","timestamp":1762005315115,"version":"3.37.3"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T00:00:00Z","timestamp":1622505600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62002370","61772545"],"award-info":[{"award-number":["62002370","61772545"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"Impossible differential attack is one of the most effective cryptanalytic methods for block ciphers. Its key step is to construct impossible differential distinguishers as long as possible. In this paper, we mainly focus on constructing longer impossible differential distinguishers for two kinds of generalized Feistel structures which are \n \n m<\/a:mi>\n <\/a:math>\n <\/jats:inline-formula>-dataline CAST256-like and MARS-like structures. When their round function takes Substitution Permutation \n \n \n \n SP<\/c:mtext>\n <\/c:mrow>\n <\/c:mfenced>\n <\/c:math>\n <\/jats:inline-formula> and Substitution Permutation Substitution \n \n \n \n SPS<\/h:mtext>\n <\/h:mrow>\n <\/h:mfenced>\n <\/h:math>\n <\/jats:inline-formula> types, they are called \n \n \n CAST<\/m:mtext>\n \n \n 256<\/m:mn>\n <\/m:mrow>\n \n SP<\/m:mtext>\n <\/m:mrow>\n <\/m:msub>\n <\/m:mrow>\n \/<\/m:mo>\n \n CAST<\/m:mtext>\n \n \n 256<\/m:mn>\n <\/m:mrow>\n \n SPS<\/m:mtext>\n <\/m:mrow>\n <\/m:msub>\n <\/m:mrow>\n <\/m:math>\n <\/jats:inline-formula> and \n \n \n \n \n MARS<\/o:mtext>\n <\/o:mrow>\n \n SP<\/o:mtext>\n <\/o:mrow>\n <\/o:msub>\n <\/o:mrow>\n \/<\/o:mo>\n \n \n \n MARS<\/o:mtext>\n <\/o:mrow>\n \n SPS<\/o:mtext>\n <\/o:mrow>\n <\/o:msub>\n <\/o:mrow>\n <\/o:math>\n <\/jats:inline-formula>, respectively. For \n \n \n CAST<\/q:mtext>\n \n \n 256<\/q:mn>\n <\/q:mrow>\n \n SP<\/q:mtext>\n <\/q:mrow>\n <\/q:msub>\n <\/q:mrow>\n \/<\/q:mo>\n \n CAST<\/q:mtext>\n \n \n 256<\/q:mn>\n <\/q:mrow>\n \n SPS<\/q:mtext>\n <\/q:mrow>\n <\/q:msub>\n <\/q:mrow>\n <\/q:math>\n <\/jats:inline-formula>, the best known result for the length of the impossible differential distinguisher was \n \n \n \n \n \n \n m<\/s:mi>\n <\/s:mrow>\n \n 2<\/s:mn>\n <\/s:mrow>\n <\/s:msup>\n +<\/s:mo>\n m<\/s:mi>\n <\/s:mrow>\n <\/s:mfenced>\n <\/s:mrow>\n \/<\/s:mo>\n \n \n \n \n \n m<\/s:mi>\n <\/s:mrow>\n \n 2<\/s:mn>\n <\/s:mrow>\n <\/s:msup>\n +<\/s:mo>\n m<\/s:mi>\n \u2212<\/s:mo>\n 1<\/s:mn>\n <\/s:mrow>\n <\/s:mfenced>\n <\/s:mrow>\n <\/s:math>\n <\/jats:inline-formula> rounds, respectively. With the help of the linear layer \n \n P<\/ab:mi>\n <\/ab:math>\n <\/jats:inline-formula>, we can construct \n \n \n \n \n \n \n m<\/cb:mi>\n <\/cb:mrow>\n \n 2<\/cb:mn>\n <\/cb:mrow>\n <\/cb:msup>\n +<\/cb:mo>\n m<\/cb:mi>\n +<\/cb:mo>\n \n \u039b<\/cb:mi>\n \n 0<\/cb:mn>\n <\/cb:mrow>\n <\/cb:msub>\n <\/cb:mrow>\n <\/cb:mfenced>\n <\/cb:mrow>\n \/<\/cb:mo>\n \n \n \n \n \n m<\/cb:mi>\n <\/cb:mrow>\n \n 2<\/cb:mn>\n <\/cb:mrow>\n <\/cb:msup>\n +<\/cb:mo>\n m<\/cb:mi>\n +<\/cb:mo>\n \n \u039b<\/cb:mi>\n \n 1<\/cb:mn>\n <\/cb:mrow>\n <\/cb:msub>\n <\/cb:mrow>\n <\/cb:mfenced>\n <\/cb:mrow>\n <\/cb:math>\n <\/jats:inline-formula>-round impossible differential distinguishers, where \n \n \n \u039b<\/mb:mi>\n \n 0<\/mb:mn>\n <\/mb:mrow>\n <\/mb:msub>\n <\/mb:math>\n <\/jats:inline-formula> and \n \n \n \u039b<\/pb:mi>\n \n 1<\/pb:mn>\n <\/pb:mrow>\n <\/pb:msub>\n <\/pb:math>\n <\/jats:inline-formula> are non-negative numbers if \n \n P<\/sb:mi>\n <\/sb:math>\n <\/jats:inline-formula> satisfies some restricted conditions. For \n \n \n \n MARS<\/ub:mtext>\n <\/ub:mrow>\n \n SPS<\/ub:mtext>\n <\/ub:mrow>\n <\/ub:msub>\n <\/ub:math>\n <\/jats:inline-formula>, the best known result for the length of the impossible differential distinguisher was \n \n \n \n 3<\/wb:mn>\n m<\/wb:mi>\n \u2212<\/wb:mo>\n 1<\/wb:mn>\n <\/wb:mrow>\n <\/wb:mfenced>\n <\/wb:math>\n <\/jats:inline-formula> rounds. We can construct \n \n 3<\/bc:mn>\n m<\/bc:mi>\n <\/bc:math>\n <\/jats:inline-formula>-round impossible differential distinguishers which are 1 round longer than before. To our knowledge, the results in this paper are the best for the two kinds of generalized Feistel structures.<\/jats:p>","DOI":"10.1155\/2021\/5582711","type":"journal-article","created":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T22:06:34Z","timestamp":1622585194000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Revisiting Impossible Differential Distinguishers of Two Generalized Feistel Structures"],"prefix":"10.1155","volume":"2021","author":[{"given":"Xuan","family":"Shen","sequence":"first","affiliation":[{"name":"College of Information and Communication, National University of Defense Technology, Wuhan 430010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7013-6657","authenticated-orcid":true,"given":"Jun","family":"He","sequence":"additional","affiliation":[{"name":"College of Information and Communication, National University of Defense Technology, Wuhan 430010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","article-title":"The design of Rijndael: AES-the advanced encryption standard","volume-title":"Information Security and Cryptography","author":"J. Daemen","year":"2002"},{"volume-title":"Federal Information Processing Standards Publication 46","year":"1977","author":"Data Encryption Standard","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/bfb0034838"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1587\/transfun.e96.a.2"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1049\/iet-ifs.2016.0448"},{"key":"6","doi-asserted-by":"crossref","DOI":"10.17487\/rfc2612","article-title":"The CAST-256 encryption algorithm","volume-title":"Network Working Group","author":"C. Adams","year":"1999"},{"key":"7","article-title":"MARS-a candidate cipher for AES","volume":"268","author":"C. Burwick","year":"1998","journal-title":"NIST AES Proposal"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-016-0477-8"},{"article-title":"Deal\u2014a 128-bit block cipher","year":"1998","author":"L. R. Knudsen","key":"9"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-005-0129-3"},{"first-page":"239","article-title":"New results on impossible differential cryptanalysis of reduced AES","author":"W. Zhang","key":"11"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s11390-007-9056-0"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24582-7_6"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.08.051"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-34931-7_17"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-56617-7_7"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1049\/cje.2018.04.002"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/8828504"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1049\/iet-ifs.2014.0183"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-49890-3_8"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53008-5_5"},{"issue":"8","key":"22","first-page":"2337","article-title":"Truncated impossible differential cryptanalysis of Midori-64","volume":"30","author":"M. Li","year":"2019","journal-title":"Journal of Software"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2021\/5582711.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2021\/5582711.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2021\/5582711.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,3]],"date-time":"2021-07-03T08:57:19Z","timestamp":1625302639000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2021\/5582711\/"}},"subtitle":[],"editor":[{"given":"Stelvio","family":"Cimato","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,6,1]]},"references-count":22,"alternative-id":["5582711","5582711"],"URL":"https:\/\/doi.org\/10.1155\/2021\/5582711","relation":{},"ISSN":["1939-0122","1939-0114"],"issn-type":[{"type":"electronic","value":"1939-0122"},{"type":"print","value":"1939-0114"}],"subject":[],"published":{"date-parts":[[2021,6,1]]}}}