{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T18:23:48Z","timestamp":1746815028947},"reference-count":13,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":6988,"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":[[1988,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper proposes a new public\u2010key cryptosystem based on the difficulty of solving a system of nonlinear equations. The proposed cryptosystem has the following features: <jats:list list-type=\"explicit-label\">\n<jats:list-item><jats:p>The public\u2010key is a nonlinear transform from a plaintext to a ciphertext in the form of rational functions.<\/jats:p><\/jats:list-item>\n<jats:list-item><jats:p>The complexity of both encryption and decryption is <jats:italic>O<\/jats:italic>(<jats:italic>m<\/jats:italic><jats:sup>2<\/jats:sup>), where <jats:italic>m<\/jats:italic> is the plaintext length.<\/jats:p><\/jats:list-item>\n<jats:list-item><jats:p>Digital signature is possible.<\/jats:p><\/jats:list-item>\n<\/jats:list><\/jats:p><jats:p>The two previously proposed systems based on the matrix decomposition and the squared matrix are special cases of the proposed system. The reliability of the cryptosystem when nonlinearity is limited to the polynomial form is discussed. Next, a publickey cryptosystem based on the difficulty of solving a system of nonlinear equations with rational functions is proposed, its decryption algorithm is studied, and the conditions for this cryptosystem to ensure reliability are derived. Finally, the computational complexity of encryption and decryption, the description volume of public and secret keys, and the possibility of digital signature are studied.<\/jats:p>","DOI":"10.1002\/scj.4690190202","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T14:48:25Z","timestamp":1183819705000},"page":"10-18","source":"Crossref","is-referenced-by-count":7,"title":["A public\u2010key cryptosystem based on the difficulty of solving a system of nonlinear equations"],"prefix":"10.1002","volume":"19","author":[{"given":"Shigeo","family":"Tsujii","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshiya","family":"Itoh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Atsushi","family":"Fujioka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaoru","family":"Kurosawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tsutomu","family":"Matsumoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1976.1055638"},{"key":"e_1_2_1_3_2","volume-title":"Nikkei","author":"Davis D. W.","year":"1985"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/359340.359342"},{"key":"e_1_2_1_5_2","unstructured":"Tsujii. A public\u2010key cryptosystem based on the difficulty of solving a system of nonlinear equations 8th Symposium of study group on information theory and its application pp.156\u2013157(Dec.1985)."},{"issue":"12","key":"e_1_2_1_6_2","article-title":"A method of public\u2010key cryptosystem using decomposition of matrix","volume":"85","author":"Tsujii","year":"1985","journal-title":"Technical Paper of I.E.C.E., Japan"},{"issue":"42","key":"e_1_2_1_7_2","article-title":"A method of public\u2010key cryptosystem using decomposition of matrix (No. 2)","volume":"85","author":"Tsujii","year":"1985","journal-title":"Technical Paper of I.E.C.E., Japan"},{"key":"e_1_2_1_8_2","unstructured":"TsujiiandMatsumoto. Study on publickey cryptosystem using matrix decomposition 8th Symposium of study group on information theory and its application pp.66\u201369(Dec.1985)."},{"issue":"73","key":"e_1_2_1_9_2","article-title":"A public\u2010key cryptosystem using decomposition of a matrix over finite field","volume":"85","author":"Tsujii","year":"1986","journal-title":"Technical Paper of I.E.C.E., Japan"},{"issue":"28","key":"e_1_2_1_10_2","article-title":"Asymmetric cryptosystems based on obscure representations over finite non\u2010commutative groups","volume":"85","author":"Matsumoto","year":"1985","journal-title":"Technical Paper of I.E.C.E., Japan"},{"issue":"50","key":"e_1_2_1_11_2","article-title":"A high\u2010speed asymmetric cryptosystem with obscrue public\u2010keys","volume":"84","author":"Matsumoto","year":"1984","journal-title":"Techncial Paper of I.E.C.E., Japan"},{"key":"e_1_2_1_12_2","unstructured":"Tsujii Matsumoto Kurosawa ItohandFujioka. A public\u2010key cryptosystem based on the difficulty of solving a system of nonlinear equations 3rd CIS Symposium (Feb.1986)."},{"key":"e_1_2_1_13_2","unstructured":"OkamotoandNakamura. Evaluation of recently proposed public\u2010key encryption systems 3rd CIS Symposium (Feb.1986)."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0211038"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690190202","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690190202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T07:58:36Z","timestamp":1697961516000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690190202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,2]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1988,2]]}},"alternative-id":["10.1002\/scj.4690190202"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690190202","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,2]]}}}