{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T06:39:56Z","timestamp":1725518396086},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540859116"},{"type":"electronic","value":"9783540859123"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-85912-3_35","type":"book-chapter","created":{"date-parts":[[2008,9,11]],"date-time":"2008-09-11T13:34:32Z","timestamp":1221140072000},"page":"403-414","source":"Crossref","is-referenced-by-count":25,"title":["New Perfect Nonlinear Multinomials over F $_{p^{2k}}$ for Any Odd Prime p"],"prefix":"10.1007","author":[{"given":"Lilya","family":"Budaghyan","sequence":"first","affiliation":[]},{"given":"Tor","family":"Helleseth","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"35_CR1","doi-asserted-by":"publisher","first-page":"296","DOI":"10.2307\/1990756","volume":"72","author":"A.A. Albert","year":"1952","unstructured":"Albert, A.A.: On nonassociative division algebras. Trans. Amer. Math. Soc.\u00a072, 296\u2013309 (1952)","journal-title":"Trans. Amer. Math. Soc."},{"key":"35_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2140\/pjm.1961.11.1","volume":"11","author":"A.A. Albert","year":"1961","unstructured":"Albert, A.A.: Generalized twisted fields. Pacific J. Math.\u00a011, 1\u20138 (1961)","journal-title":"Pacific J. Math."},{"issue":"1","key":"35_CR3","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/BF00630563","volume":"4","author":"E. Biham","year":"1991","unstructured":"Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. Journal of Cryptology\u00a04(1), 3\u201372 (1991)","journal-title":"Journal of Cryptology"},{"key":"35_CR4","doi-asserted-by":"crossref","unstructured":"Bracken, C., Byrne, E., Markin, N., McGuire, G.: New families of quadratic almost perfect nonlinear trinomials and multinomials. Finite Fields and Applications (to appear, 2008)","DOI":"10.1016\/j.ffa.2007.11.002"},{"issue":"3","key":"35_CR5","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1109\/TIT.2005.864481","volume":"52","author":"L. Budaghyan","year":"2006","unstructured":"Budaghyan, L., Carlet, C., Pott, A.: New Classes of Almost Bent and Almost Perfect Nonlinear Functions. IEEE Trans. Inform. Theory\u00a052(3), 1141\u20131152 (2006)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"35_CR6","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008344232130","volume":"15","author":"C. Carlet","year":"1998","unstructured":"Carlet, C., Charpin, P., Zinoviev, V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Des., Codes Cryptogr.\u00a015(2), 125\u2013156 (1998)","journal-title":"Des., Codes Cryptogr."},{"key":"35_CR7","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1016\/0021-8693(82)90045-X","volume":"75","author":"S.D. Cohen","year":"1982","unstructured":"Cohen, S.D., Ganley, M.J.: Commutative semifields, two-dimensional over their middle nuclei. J. Algebra\u00a075, 373\u2013385 (1982)","journal-title":"J. Algebra"},{"key":"35_CR8","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1023\/A:1008292303803","volume":"10","author":"R.S. Coulter","year":"1997","unstructured":"Coulter, R.S., Matthews, R.W.: Planar functions and planes of Lenz-Barlotti class II. Des., Codes Cryptogr.\u00a010, 167\u2013184 (1997)","journal-title":"Des., Codes Cryptogr."},{"key":"35_CR9","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1016\/j.aim.2007.07.007","volume":"217","author":"R.S. Coulter","year":"2008","unstructured":"Coulter, R.S., Henderson, M.: Commutative presemifields and semifields. Advances in Math.\u00a0217, 282\u2013304 (2008)","journal-title":"Advances in Math."},{"key":"35_CR10","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10623-007-9097-y","volume":"44","author":"R.S. Coulter","year":"2007","unstructured":"Coulter, R.S., Henderson, M., Kosick, P.: Planar polynomials for commutative semifields with specified nuclei. Des. Codes Cryptogr.\u00a044, 275\u2013286 (2007)","journal-title":"Des. Codes Cryptogr."},{"key":"35_CR11","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/BF01111042","volume":"103","author":"P. Dembowski","year":"1968","unstructured":"Dembowski, P., Ostrom, T.: Planes of order n with collineation groups of order n\n 2. Math. Z.\u00a0103, 239\u2013258 (1968)","journal-title":"Math. Z."},{"key":"35_CR12","doi-asserted-by":"publisher","first-page":"514","DOI":"10.2307\/1986243","volume":"7","author":"L.E. Dickson","year":"1906","unstructured":"Dickson, L.E.: On commutative linear algebras in which division is always uniquely possible. Trans. Amer. Math. Soc.\u00a07, 514\u2013522 (1906)","journal-title":"Trans. Amer. Math. Soc."},{"key":"35_CR13","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1215\/S0012-7094-35-00112-0","volume":"1","author":"L.E. Dickson","year":"1935","unstructured":"Dickson, L.E.: Linear algebras with associativity not assumed. Duke Math. J.\u00a01, 113\u2013125 (1935)","journal-title":"Duke Math. J."},{"key":"35_CR14","doi-asserted-by":"publisher","first-page":"1526","DOI":"10.1016\/j.jcta.2005.10.006","volume":"133","author":"C. Ding","year":"2006","unstructured":"Ding, C., Yuan, J.: A new family of skew Paley-Hadamard difference sets. J. Comb. Theory Ser.\u00a0A.\u00a0133, 1526\u20131535 (2006)","journal-title":"J. Comb. Theory Ser.\u00a0A."},{"key":"35_CR15","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/S0195-6698(81)80041-8","volume":"2","author":"M.J. Ganley","year":"1981","unstructured":"Ganley, M.J.: Central weak nucleus semifields. European J. Combin.\u00a02, 339\u2013347 (1981)","journal-title":"European J. Combin."},{"key":"35_CR16","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1109\/18.748997","volume":"45","author":"T. Helleseth","year":"1999","unstructured":"Helleseth, T., Rong, C., Sandberg, D.: New families of almost perfect nonlinear power mappings. IEEE Trans. Inf. Theory\u00a045, 475\u2013485 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"35_CR17","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s002000050073","volume":"8","author":"T. Helleseth","year":"1997","unstructured":"Helleseth, T., Sandberg, D.: Some power mappings with low differential uniformity. Applic. Alg. Eng., Commun. Comput.\u00a08, 363\u2013370 (1997)","journal-title":"Applic. Alg. Eng., Commun. Comput."},{"key":"35_CR18","unstructured":"Minami, K., Nakagawa, N.: On planar functions of elementary abelian p-group type (submitted)"},{"key":"35_CR19","unstructured":"Nakagawa, N.: On functions of finite fields, \n \n http:\/\/www.math.is.tohoku.ac.jp\/~taya\/sendaiNC\/2006\/report\/nakagawa.pdf"},{"key":"35_CR20","unstructured":"Ness, G.J.: Correlation of sequences of different lengths and related topics. PhD dissertation. University of Bergen, Norway (2007)"},{"key":"35_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/3-540-48285-7_6","volume-title":"Advances in Cryptology - EUROCRYPT \u201993","author":"K. Nyberg","year":"1994","unstructured":"Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol.\u00a0765, pp. 55\u201364. Springer, Heidelberg (1994)"},{"key":"35_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1005244202633","volume":"82","author":"T. Penttila","year":"2000","unstructured":"Penttila, T., Williams, B.: Ovoids of parabolic spaces. Geom. Dedicata\u00a082, 1\u201319 (2000)","journal-title":"Geom. Dedicata"}],"container-title":["Lecture Notes in Computer Science","Sequences and Their Applications - SETA 2008"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-85912-3_35.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T11:54:40Z","timestamp":1619524480000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-85912-3_35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540859116","9783540859123"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-85912-3_35","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[]}}