{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T05:10:18Z","timestamp":1695964218991},"reference-count":7,"publisher":"Wiley","issue":"9","license":[{"start":{"date-parts":[[2007,3,22]],"date-time":"2007-03-22T00:00:00Z","timestamp":1174521600000},"content-version":"vor","delay-in-days":4828,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp;amp; Computers in Japan"],"published-print":{"date-parts":[[1994,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The permutation from {0, 1}<jats:sup><jats:italic>2n<\/jats:italic><\/jats:sup> to {0, 1}<jats:sup><jats:italic>2n<\/jats:italic><\/jats:sup> represented by <jats:italic>S(f)<\/jats:italic> in DES (Data Encryption Standard) is used as the basic operation. Let <jats:italic>f<\/jats:italic> be a function from {0, 1}<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> to {0, 1}<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> and \u2295 denote bitwise exclusive or. Then <jats:italic>S(f)<\/jats:italic> is defined <jats:italic>S(f)(L.R) = R.[L\u2295f(R)]<\/jats:italic> where <jats:italic>L, R \u03f5<\/jats:italic> {0, 1}<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>, Moreover, let <jats:italic>S(f<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>) denote the composition of <jats:italic>S(f<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>S(f<\/jats:italic><jats:sub>1<\/jats:sub>) and <jats:italic>S(f<\/jats:italic><jats:sub>o<\/jats:sub>), and {<jats:italic>S(f<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>)} denote a set of <jats:italic>S(f<\/jats:italic><jats:sub>2<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>) obtained when f<jats:sub>o<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>f<\/jats:italic><jats:sub>2<\/jats:sub> are chosen randomly from a set of pseudorandom functions. Luby et al. have shown that {<jats:italic>S(f<\/jats:italic><jats:sub>2<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>)} is pseudorandom.<\/jats:p><jats:p>This paper investigates the case in which there are two different pseudorandom functions and shows that while {{<jats:italic>S(f<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>1,<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>)} and {<jats:italic>S(f<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>)} are pseudorandom, {<jats:italic>S(f<\/jats:italic><jats:sub>o<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>o<\/jats:sub>)} is not.<\/jats:p>","DOI":"10.1002\/scj.4690250903","type":"journal-article","created":{"date-parts":[[2007,7,8]],"date-time":"2007-07-08T03:22:33Z","timestamp":1183864953000},"page":"32-40","source":"Crossref","is-referenced-by-count":1,"title":["Construction of pseudorandom permutations"],"prefix":"10.1002","volume":"25","author":[{"given":"Yasuhiro","family":"Ohnishi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akira","family":"Maruoka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,22]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/6490.6503"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"A. C.Yao. Theory and Applications of Trapdoor Functions Proc. 23rd IEEE Symposium on Foundations of Computer Science pp.80\u201391(1982).","DOI":"10.1109\/SFCS.1982.45"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0213053"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0217022"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"Y.Zheng T.MatsumotoandH.Imai.Impossibility and optimality results on constructing pseudorandom permutations Advances in Cryptology\u2010EURO CRYPTO '89 pp.412\u2013422(1989).","DOI":"10.1007\/3-540-46885-4_41"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"L. A.Levin.One\u2010way function and pseudorandom generators Proceedings of the 17th ACM Symposium on Theory of Computing pp.363\u2013365(1985).","DOI":"10.1145\/22145.22185"},{"key":"e_1_2_1_8_2","first-page":"38","article-title":"Public\u2010key cryptosystems","volume":"22","author":"Doi N.","year":"1981","journal-title":"Journal of Society for Information Processing"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690250903","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690250903","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T11:47:50Z","timestamp":1695901670000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690250903"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":7,"journal-issue":{"issue":"9","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["10.1002\/scj.4690250903"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690250903","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,1]]}}}