{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T09:02:32Z","timestamp":1772442152464,"version":"3.50.1"},"reference-count":26,"publisher":"Institute of Electronics, Information and Communications Engineers (IEICE)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEICE Trans. Fundamentals"],"published-print":{"date-parts":[[2022,8,1]]},"DOI":"10.1587\/transfun.2021eap1167","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T22:09:22Z","timestamp":1645481362000},"page":"1134-1146","source":"Crossref","is-referenced-by-count":3,"title":["On Cryptographic Parameters of Permutation Polynomials of the form &lt;i&gt;x&lt;sup&gt;r&lt;\/sup&gt;h&lt;\/i&gt;(&lt;i&gt;x&lt;\/i&gt;&lt;sup&gt;(2&lt;i&gt;&lt;sup&gt;n&lt;\/sup&gt;&lt;\/i&gt;-1)\/&lt;i&gt;d&lt;\/i&gt;&lt;\/sup&gt;)"],"prefix":"10.1587","volume":"E105.A","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0103-2920","authenticated-orcid":false,"given":"Jaeseong","family":"JEONG","sequence":"first","affiliation":[{"name":"Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2234-8572","authenticated-orcid":false,"given":"Chang Heon","family":"KIM","sequence":"additional","affiliation":[{"name":"Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1678-8480","authenticated-orcid":false,"given":"Namhun","family":"KOO","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, Ewha Womans University"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3336-0817","authenticated-orcid":false,"given":"Soonhak","family":"KWON","sequence":"additional","affiliation":[{"name":"Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University"}]},{"given":"Sumin","family":"LEE","sequence":"additional","affiliation":[{"name":"Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University"}]}],"member":"532","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] A. Akbary and Q. Wang, \u201cOn polynomials of the form <i>x<sup>r<\/sup>f<\/i>(<i>x<\/i><sup>(<i>q<\/i>-1)\/<i>l<\/i><\/sup>),\u201d International Journal of Mathematics and Mathematical Sciences, vol.2007, Article ID 23408, 2007. https:\/\/doi.org\/10.1155\/2007\/23408 10.1155\/2007\/23408","DOI":"10.1155\/2007\/23408"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] S. Bhattacharya and S. Sarkar, \u201cOn some permutation binomials and trinomials over \ud835\udd3d<sub>2<\/sub><i>n<\/i>,\u201d Des. Codes Cryptogr., vol.82, pp.149-160, 2017. https:\/\/doi.org\/10.1007\/s10623-016-0229-0 10.1007\/s10623-016-0229-0","DOI":"10.1007\/s10623-016-0229-0"},{"key":"3","doi-asserted-by":"crossref","unstructured":"[3] C. Boura and A. Canteaut, \u201cOn the boomerang uniformity of cryptographic Sboxes,\u201d IACR Trans. Symmetric Cryptology, vol.2018, no.3, pp.290-310, 2018. https:\/\/doi.org\/10.13154\/tosc.v2018.i3.290-310 10.13154\/tosc.v2018.i3.290-310","DOI":"10.46586\/tosc.v2018.i3.290-310"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] C. Boura, A. Canteaut, J. Jean, and V. Suder, \u201cTwo notions of differential equivalence on Sboxes,\u201d Des. Codes Cryptogr., vol.87, pp.185-202, 2019. https:\/\/doi.org\/10.1007\/s10623-018-0496-z 10.1007\/s10623-018-0496-z","DOI":"10.1007\/s10623-018-0496-z"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] K.A. Browning, J.F. Dillon, M.T. McQuistan, and A.J. Wolfe, \u201cAn APN permutation in dimension six,\u201d 9th, International conference on finite fields and applications; Finite fields: theory and applications, Dublin, in Comtemporary Mathematics, vol.518, pp.33-42, 2010. http:\/\/doi.org\/10.1090\/conm\/518","DOI":"10.1090\/conm\/518\/10194"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] C. Carlet, P. Charpin, and V. Zinoviev, \u201cCodes, bent functions, and permutations suitable for DES-like cryptosystems,\u201d Des. Codes Cryptogr., vol.15, no.2, pp.125-156, 1998. https:\/\/doi.org\/10.1023\/A:1008344232130 10.1023\/A:1008344232130","DOI":"10.1023\/A:1008344232130"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] P. Charpin, and G.M. Kyureghyan, \u201cOn sets determining the differential spectrum of mappings,\u201d International Journal of Information and Coding Theory, vol.4, no.2-3, pp.170-184, 2017, a recent revised version is available at https:\/\/hal.inria.fr\/hal-01406589v3. https:\/\/doi.org\/10.1504\/IJICOT.2017.083844 10.1504\/IJICOT.2017.083844","DOI":"10.1504\/IJICOT.2017.083844"},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] C. Cid, T. Huang, T. Peyrin, Y. Sasaki, and L. Song, \u201cBoomerang connectivity table: A new cryptanalysis tool,\u201d Advances in Cryptology \u2014 EUROCRYPT 2018, J. Nielsen and V. Rijmen, eds., Lecture Notes in Computer Science, vol.10821, pp.683-714, Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-319-78375-8_22 10.1007\/978-3-319-78375-8_22","DOI":"10.1007\/978-3-319-78375-8_22"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] S. Fu and X. Feng, \u201cInvolutory differentially 4-uniform permutations from known constructions,\u201d Des. Codes Cryptogr., vol.87, pp.31-56, 2019. https:\/\/doi.org\/10.1007\/s10623-018-0482-5 10.1007\/s10623-018-0482-5","DOI":"10.1007\/s10623-018-0482-5"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] R. Gupta and R.K. Sharma, \u201cSome new classes of permutation trinomials over finite fields with even characteristic,\u201d Finite Fields Appl., vol.41, pp.89-96, 2016. http:\/\/dx.doi.org\/10.1016\/j.ffa.2016.05.004 10.1016\/j.ffa.2016.05.004","DOI":"10.1016\/j.ffa.2016.05.004"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] X. Hou, \u201cDetermination of a type of permutation trinomials over finite fields, II,\u201d Finite Fields Appl., vol.35, pp.16-35, 2015 http:\/\/dx.doi.org\/10.1016\/j.ffa.2015.03.002 10.1016\/j.ffa.2015.03.002","DOI":"10.1016\/j.ffa.2015.03.002"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] X. Hou and S.D. Lappano, \u201cDetermination of a type of permutation binomials over finite fields,\u201d J. Number Theory, vol.147, pp.14-23, 2015. http:\/\/dx.doi.org\/10.1016\/j.jnt.2014.06.021 10.1016\/j.jnt.2014.06.021","DOI":"10.1016\/j.jnt.2014.06.021"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] N. Li and T. Helleseth, \u201cSeveral classes of permutation trinomials from Niho exponents,\u201d Cryptogr. Commun., vol.9, pp.693-705, 2017. https:\/\/doi.org\/10.1007\/s12095-016-0210-9 10.1007\/s12095-016-0210-9","DOI":"10.1007\/s12095-016-0210-9"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] N. Li and T. Helleseth, \u201cNew permutation trinomials from Niho exponents over finite fields with even characteristic,\u201d Cryptogr. Commun., vol.11, pp.129-136, 2019. https:\/\/doi.org\/10.1007\/s12095-018-0321-6 10.1007\/s12095-018-0321-6","DOI":"10.1007\/s12095-018-0321-6"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] K. Li, L. Qu, and X. Chen, \u201cNew classes of permutation binomials and permutation trinomials over finite fields,\u201d Finite Fields Appl., vol.43, pp.69-85, 2017. https:\/\/doi.org\/10.1016\/j.ffa.2016.09.002 10.1016\/j.ffa.2016.09.002","DOI":"10.1016\/j.ffa.2016.09.002"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] K. Li, L. Qu, B. Sun, and C. Li, \u201cNew results about the boomerang uniformity of permutation polynomials,\u201d IEEE Trans. Inf. Theory, vol.65, pp.7542-7553, 2019. http:\/\/dx.doi.org\/10.1109\/TIT.2019.2918531 10.1109\/TIT.2019.2918531","DOI":"10.1109\/TIT.2019.2918531"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] K. Li, L. Qu, and Q. Wang, \u201cNew constructions of permutation polynomials of the form <i>x<sup>r<\/sup>hx<\/i>(<i>x<\/i><sup><i>q<\/i>-1<\/sup>) over F<sub><i>q<\/i><sup>2<\/sup><\/sub>,\u201d Des. Codes Cryptogr., vol.86, no.10, pp.2379-2405, 2019. https:\/\/doi.org\/10.1007\/s10623-017-0452-3 10.1007\/s10623-017-0452-3","DOI":"10.1007\/s10623-017-0452-3"},{"key":"18","doi-asserted-by":"publisher","unstructured":"[18] K. Li, L. Qu, and Q. Wang, \u201cCompositional inverses of permutation polynomials of the form <i>x<sup>r<\/sup>h<\/i>(<i>x<sup>s<\/sup><\/i>) over finite fields,\u201d Cryptogr. Commun., vol.11, pp.279-298, 2019. https:\/\/doi.org\/10.1007\/s12095-018-0292-7 10.1007\/s12095-018-0292-7","DOI":"10.1007\/s12095-018-0292-7"},{"key":"19","doi-asserted-by":"publisher","unstructured":"[19] S. Mesnager, C. Tang, and M. Xiong, \u201cOn the boomerang uniformity of quadratic permutations,\u201d Des. Codes Cryptogr., vol.88, pp.2233-2246, 2020. DOI : 10.1007\/s10623-020-00775-2","DOI":"10.1007\/s10623-020-00775-2"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[20] K. Nyberg, \u201cDifferentially uniform mappings for cryptography,\u201d Advances in Cryptology \u2014 EUROCRYPT&apos;93, T. Helleseth, ed., Lecture Notes in Computer Science, vol.765, pp.55-64, Springer, Berlin, Heidelberg, 1994. https:\/\/doi.org\/10.1007\/3-540-48285-7_6 10.1007\/3-540-48285-7_6","DOI":"10.1007\/3-540-48285-7_6"},{"key":"21","doi-asserted-by":"publisher","unstructured":"[21] Y.H. Park and J.B. Lee, \u201cPermutation polynomial and group permutation polynomials,\u201d Bull. Aust. Math. Soc., vol.63, pp.67-74, 2001. https:\/\/doi.org\/10.1017\/S0004972700019110 10.1017\/S0004972700019110","DOI":"10.1017\/S0004972700019110"},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] D. Wagner, \u201cThe boomerang attack,\u201d Fast Software Encryption 1999, L. Knudsen, ed., Lecture Notes in Computer Science, vol.1636, pp.156-170, Springer, Berlin, Heidelberg, 1999. https:\/\/doi.org\/10.1007\/3-540-48519-8_12 10.1007\/3-540-48519-8_12","DOI":"10.1007\/3-540-48519-8_12"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] D. Wan and R. Lidl, \u201cPermutation polynomials of the form <i>x<sup>r<\/sup>f<\/i>(<i>x<\/i><sup>(<i>q<\/i>-1)\/<i>d<\/i><\/sup>) and their group structure,\u201d Monalshefte f\u00fcr Mathematik, vol.112, pp.149-163, Springer, 1991. https:\/\/doi.org\/10.1007\/BF01525801 10.1007\/BF01525801","DOI":"10.1007\/BF01525801"},{"key":"24","doi-asserted-by":"publisher","unstructured":"[25] Q. Wang, \u201cCyclotomy and permutation polynomials of large indices,\u201d Finite Fields Appl., vol.22, pp.57-69, 2013. https:\/\/doi.org\/10.1016\/j.ffa.2013.02.005 10.1016\/j.ffa.2013.02.005","DOI":"10.1016\/j.ffa.2013.02.005"},{"key":"25","doi-asserted-by":"publisher","unstructured":"[26] X. Zhu, X. Zeng, and Y. Chen, \u201cSome binomial and trinomial differentially 4-uniform permutation polynomials,\u201d International Journal of Foundations of Computer Science, vol.26, no.4, pp.487-497, 2015. https:\/\/doi.org\/10.1142\/S0129054115500276 10.1142\/S0129054115500276","DOI":"10.1142\/S0129054115500276"},{"key":"26","doi-asserted-by":"publisher","unstructured":"[27] M.E. Zieve, \u201cOn some permutation polynomial over \ud835\udd3d<i><sub>q<\/sub><\/i> of the form <i>x<sup>r<\/sup>h<\/i>(<i>x<\/i><sup>(<i>q<\/i>-1)\/<i>d<\/i><\/sup>),\u201d Proc. Am. Math. Soc., vol.137, pp.2207-2216, 2009. https:\/\/doi.org\/10.1090\/S0002-9939-08-09767-0 10.1090\/S0002-9939-08-09767-0","DOI":"10.1090\/S0002-9939-08-09767-0"}],"container-title":["IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E105.A\/8\/E105.A_2021EAP1167\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,6]],"date-time":"2022-08-06T03:28:38Z","timestamp":1659756518000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E105.A\/8\/E105.A_2021EAP1167\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,1]]},"references-count":26,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2022]]}},"URL":"https:\/\/doi.org\/10.1587\/transfun.2021eap1167","relation":{},"ISSN":["0916-8508","1745-1337"],"issn-type":[{"value":"0916-8508","type":"print"},{"value":"1745-1337","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,1]]},"article-number":"2021EAP1167"}}