{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:39:24Z","timestamp":1747190364700,"version":"3.40.5"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,9,22]],"date-time":"2020-09-22T00:00:00Z","timestamp":1600732800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&D Program of China","award":["2018YFB0803905"],"award-info":[{"award-number":["2018YFB0803905"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2020,9,22]]},"abstract":"<jats:p>Generalized Feistel structures are widely used in the design of block ciphers. In this paper, we focused on retrieving impossible differentials for two kinds of generalized Feistel structures: CAST256-like structure with Substitution-Permutation (SP) or Substitution-Permutation-Substitution (SPS) round functions (named <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mrow><mml:mrow><mml:mtext>CAST<\/mml:mtext><mml:mn>256<\/mml:mn><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mtext>SP<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mrow><mml:mtext>CAST<\/mml:mtext><mml:mn>256<\/mml:mn><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mtext>SPS<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math>, respectively) and MARS-like structure with SP\/SPS round function (named <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mtext>MARS<\/mml:mtext><\/mml:mrow><mml:mrow><mml:mtext>SP<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msub><mml:mrow><mml:mtext>MARS<\/mml:mtext><\/mml:mrow><mml:mrow><mml:mtext>SPS<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math>, respectively). Known results show that for bijective round function, CAST256-like structures and MARS-like structures have (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:msup><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>) and (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mn>2<\/mml:mn><mml:mi>m<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>) rounds impossible differentials, respectively. By our observation, there existed (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:msup><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>+<\/mml:mo><mml:mi>m<\/mml:mi><\/mml:math>) rounds impossible differentials in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:msub><mml:mrow><mml:mrow><mml:mtext>CAST<\/mml:mtext><mml:mn>256<\/mml:mn><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mtext>SP<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math> and (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mn>3<\/mml:mn><mml:mi>m<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:math>) rounds impossible differentials in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:msub><mml:mrow><mml:mtext>MARS<\/mml:mtext><\/mml:mrow><mml:mrow><mml:mtext>SPS<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math> (this result does not require the P layer to be invertible). When the diffusion layer satisfied some special conditions, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:msub><mml:mrow><mml:mrow><mml:mtext>CAST<\/mml:mtext><mml:mn>256<\/mml:mn><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mtext>SPS<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math> had (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:msup><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>+<\/mml:mo><mml:mi>m<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>) rounds impossible differentials and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:msub><mml:mrow><mml:mtext>MARS<\/mml:mtext><\/mml:mrow><mml:mrow><mml:mtext>SPS<\/mml:mtext><\/mml:mrow><\/mml:msub><\/mml:math> had (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mn>3<\/mml:mn><mml:mi>m<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:math>) rounds impossible differentials.<\/jats:p>","DOI":"10.1155\/2020\/8828504","type":"journal-article","created":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T00:16:22Z","timestamp":1600820182000},"page":"1-9","source":"Crossref","is-referenced-by-count":4,"title":["Impossible Differential Distinguishers of Two Generalized Feistel Structures"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8767-2587","authenticated-orcid":true,"given":"Huili","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"},{"name":"China Electronic Technology Standardization Institute, Beijing 100076, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenping","family":"Ma","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lang","family":"Liao","sequence":"additional","affiliation":[{"name":"Shenzhen Institute of Information Technology, Shenzhen 518172, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yushan","family":"Li","sequence":"additional","affiliation":[{"name":"Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linfeng","family":"Zheng","sequence":"additional","affiliation":[{"name":"Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04722-4"},{"volume":"23","year":"1977","key":"2"},{"volume":"2","journal-title":"Specification Version","year":"2000","key":"4"},{"year":"1998","key":"6"},{"issue":"1","key":"7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10231-016-0559-6","volume":"196","year":"2017","journal-title":"Annali di Matematica Pura ed Applicata (1923)"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-005-0129-3"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s11390-007-9056-0"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1049\/iet-ifs.2010.0174"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.02.029"},{"issue":"6","key":"23","first-page":"870","volume":"27","year":"2005","journal-title":"Journal of Electronics and Information Technology"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/8828504.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/8828504.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/8828504.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T00:16:26Z","timestamp":1600820186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2020\/8828504\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,22]]},"references-count":10,"alternative-id":["8828504","8828504"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8828504","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"type":"print","value":"1939-0114"},{"type":"electronic","value":"1939-0122"}],"subject":[],"published":{"date-parts":[[2020,9,22]]}}}