{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:44:38Z","timestamp":1775756678985,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T00:00:00Z","timestamp":1718668800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T00:00:00Z","timestamp":1718668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100012320","name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012320","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2024,11]]},"abstract":"Abstract<\/jats:title>\n The concatenation of four Boolean bent functions \n \n $$f=f_1||f_2||f_3||f_4$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n =<\/mml:mo>\n \n f<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n \n |<\/mml:mo>\n |<\/mml:mo>\n <\/mml:mrow>\n \n f<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n \n |<\/mml:mo>\n |<\/mml:mo>\n <\/mml:mrow>\n \n f<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n \n |<\/mml:mo>\n |<\/mml:mo>\n <\/mml:mrow>\n \n f<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is bent if and only if the dual bent condition \n \n $$f_1^* + f_2^* + f_3^* + f_4^* =1$$<\/jats:tex-math>\n \n \n \n f<\/mml:mi>\n 1<\/mml:mn>\n \u2217<\/mml:mo>\n <\/mml:msubsup>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 2<\/mml:mn>\n \u2217<\/mml:mo>\n <\/mml:msubsup>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 3<\/mml:mn>\n \u2217<\/mml:mo>\n <\/mml:msubsup>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 4<\/mml:mn>\n \u2217<\/mml:mo>\n <\/mml:msubsup>\n =<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is satisfied. However, to specify four bent functions satisfying this duality condition is in general quite a difficult task. Commonly, to simplify this problem, certain relations between \n \n $$f_i$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> are assumed, as well as functions \n \n $$f_i$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> of a special shape are considered, e.g., \n \n $$f_i(x,y)=x\\cdot \\pi _i(y)+h_i(y)$$<\/jats:tex-math>\n \n \n \n f<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n =<\/mml:mo>\n x<\/mml:mi>\n \u00b7<\/mml:mo>\n \n \u03c0<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n \n h<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> are Maiorana-McFarland bent functions. In the case when permutations \n \n $$\\pi _i$$<\/jats:tex-math>\n \n \n \u03c0<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> of \n \n $$\\mathbb {F}_2^m$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n m<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> have the \n \n $$(\\mathcal {A}_m)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n A<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> property and Maiorana-McFarland bent functions \n \n $$f_i$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> satisfy the additional condition \n \n $$f_1+f_2+f_3+f_4=0$$<\/jats:tex-math>\n \n \n \n f<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n =<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, the dual bent condition is known to have a relatively simple shape allowing to specify the functions \n \n $$f_i$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> explicitly. In this paper, we generalize this result for the case when Maiorana-McFarland bent functions \n \n $$f_i$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> satisfy the condition \n \n $$f_1(x,y)+f_2(x,y)+f_3(x,y)+f_4(x,y)=s(y)$$<\/jats:tex-math>\n \n \n \n f<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n \n f<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n =<\/mml:mo>\n s<\/mml:mi>\n \n (<\/mml:mo>\n y<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and provide a construction of new permutations with the \n \n $$(\\mathcal {A}_m)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n A<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> property from the old ones. Combining these two results, we obtain a recursive construction method of bent functions satisfying the dual bent condition. Moreover, we provide a generic condition on the Maiorana-McFarland bent functions \n \n $$f_1,f_2,f_3,f_4$$<\/jats:tex-math>\n \n \n \n f<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n f<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n f<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n f<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> stemming from the permutations of \n \n $$\\mathbb {F}_2^m$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n m<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> with the \n \n $$(\\mathcal {A}_m)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n A<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> property, such that the concatenation \n \n $$f=f_1||f_2||f_3||f_4$$<\/jats:tex-math>\n \n \n f<\/mml:mi>\n =<\/mml:mo>\n \n f<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n \n |<\/mml:mo>\n |<\/mml:mo>\n <\/mml:mrow>\n \n f<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n \n |<\/mml:mo>\n |<\/mml:mo>\n <\/mml:mrow>\n \n f<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n \n |<\/mml:mo>\n |<\/mml:mo>\n <\/mml:mrow>\n \n f<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> does not belong, up to equivalence, to the Maiorana-McFarland class. Using monomial permutations \n \n $$\\pi _i$$<\/jats:tex-math>\n \n \n \u03c0<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> of \n \n $$\\mathbb {F}_{2^m}$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n \n 2<\/mml:mn>\n m<\/mml:mi>\n <\/mml:msup>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> with the \n \n $$(\\mathcal {A}_m)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n A<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> property and monomial functions \n \n $$h_i$$<\/jats:tex-math>\n \n \n h<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> on \n \n $$\\mathbb {F}_{2^m}$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n \n 2<\/mml:mn>\n m<\/mml:mi>\n <\/mml:msup>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, we provide explicit constructions of such bent functions; a particular case of our result shows how one can construct bent functions from APN permutations, when m<\/jats:italic> is odd. Finally, with our construction method, we explain how one can construct homogeneous cubic bent functions, noticing that only very few design methods of these objects are known.<\/jats:p>","DOI":"10.1007\/s12095-024-00724-z","type":"journal-article","created":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T07:03:26Z","timestamp":1718694206000},"page":"1235-1256","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bent functions satisfying the dual bent condition and permutations with the $$(\\mathcal {A}_m)$$ property"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0461-4793","authenticated-orcid":false,"given":"Alexandr","family":"Polujan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6343-8796","authenticated-orcid":false,"given":"Enes","family":"Pasalic","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sadmir","family":"Kudin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6804-6975","authenticated-orcid":false,"given":"Fengrong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"724_CR1","doi-asserted-by":"publisher","unstructured":"Anbar, N., Kudin, S., Meidl, W., Pasalic, E., Polujan, A.: Vectorial negabent concepts: Similarities, differences, and generalizations (2024). https:\/\/doi.org\/10.48550\/arXiv.2402.05677","DOI":"10.48550\/arXiv.2402.05677"},{"issue":"8","key":"724_CR2","doi-asserted-by":"publisher","first-page":"2004","DOI":"10.1109\/TIT.2003.814476","volume":"49","author":"A Canteaut","year":"2003","unstructured":"Canteaut, A., Charpin, P.: Decomposing bent functions. IEEE Trans. Inf. Theory 49(8), 2004\u20132019 (2003). https:\/\/doi.org\/10.1109\/TIT.2003.814476","journal-title":"IEEE Trans. Inf. Theory"},{"key":"724_CR3","doi-asserted-by":"publisher","unstructured":"Carlet, C.: Two new classes of bent functions. In: Helleseth T. (ed.) Advances in Cryptology \u2014 EUROCRYPT \u201993, pp. 77\u2013101. Springer Berlin Heidelberg, Berlin, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48285-7_8","DOI":"10.1007\/3-540-48285-7_8"},{"key":"724_CR4","doi-asserted-by":"publisher","unstructured":"Carlet, C.: On the secondary constructions of resilient and bent functions. In:\u00a0Feng,K.,\u00a0Niederreiter, H.,\u00a0Xing, C. (eds.) Coding, Cryptography and Combinatorics, pp. 3\u201328. Birkh\u00e4user Basel, Basel (2004). https:\/\/doi.org\/10.1007\/978-3-0348-7865-4_1","DOI":"10.1007\/978-3-0348-7865-4_1"},{"key":"724_CR5","doi-asserted-by":"publisher","unstructured":"Carlet, C.: Boolean functions for cryptography and coding theory. Cambridge University Press (2021). https:\/\/doi.org\/10.1017\/9781108606806","DOI":"10.1017\/9781108606806"},{"issue":"1","key":"724_CR6","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10623-015-0145-8","volume":"78","author":"C Carlet","year":"2016","unstructured":"Carlet, C., Mesnager, S.: Four decades of research on bent functions. Designs, Codes Cryptography 78(1), 5\u201350 (2016). https:\/\/doi.org\/10.1007\/s10623-015-0145-8","journal-title":"Designs, Codes Cryptography"},{"issue":"6","key":"724_CR7","doi-asserted-by":"publisher","first-page":"1275","DOI":"10.1007\/s12095-019-00395-1","volume":"11","author":"N Cepak","year":"2019","unstructured":"Cepak, N., Pasalic, E., Muratovi\u0107-Ribi\u0107, A.: Frobenius linear translators giving rise to new infinite classes of permutations and bent functions. Cryptography Commun. 11(6), 1275\u20131295 (2019). https:\/\/doi.org\/10.1007\/s12095-019-00395-1","journal-title":"Cryptography Commun."},{"issue":"1","key":"724_CR8","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1023\/A:1016509410000","volume":"26","author":"C Charnes","year":"2002","unstructured":"Charnes, C., R\u00f6tteler, M., Beth, T.: Homogeneous bent functions, invariants, and designs. Designs, Codes Cryptography 26(1), 139\u2013154 (2002). https:\/\/doi.org\/10.1023\/A:1016509410000","journal-title":"Designs, Codes Cryptography"},{"key":"724_CR9","doi-asserted-by":"publisher","unstructured":"Charpin, P., Kyureghyan, G.M.: Monomial functions with linear structure and permutation polynomials. In: Finite fields: theory and applications, Contemp. Math., vol. 518, pp. 99\u2013111. Amer. Math. Soc., Providence, RI (2010). https:\/\/doi.org\/10.1090\/conm\/518\/10199","DOI":"10.1090\/conm\/518\/10199"},{"key":"724_CR10","doi-asserted-by":"publisher","unstructured":"Dillon, J.F.: Elementary Hadamard difference sets. Ph.D. thesis, University of Maryland (1974). https:\/\/doi.org\/10.13016\/M2MS3K194","DOI":"10.13016\/M2MS3K194"},{"issue":"10","key":"724_CR11","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.1007\/s10623-020-00760-9","volume":"88","author":"S Hod\u017ei\u0107","year":"2020","unstructured":"Hod\u017ei\u0107, S., Pasalic, E., Wei, Y.: A general framework for secondary constructions of bent and plateaued functions. Designs, Codes Cryptography 88(10), 2007\u20132035 (2020). https:\/\/doi.org\/10.1007\/s10623-020-00760-9","journal-title":"Designs, Codes Cryptography"},{"issue":"10","key":"724_CR12","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.1007\/s10623-020-00760-9","volume":"88","author":"S Hod\u017ei\u0107","year":"2020","unstructured":"Hod\u017ei\u0107, S., Pasalic, E., Wei, Y.: A general framework for secondary constructions of bent and plateaued functions. Designs, Codes Cryptography 88(10), 2007\u20132035 (2020). https:\/\/doi.org\/10.1007\/s10623-020-00760-9","journal-title":"Designs, Codes Cryptography"},{"issue":"11","key":"724_CR13","doi-asserted-by":"publisher","first-page":"7554","DOI":"10.1109\/TIT.2019.2910808","volume":"65","author":"S Hod\u017ei\u0107","year":"2019","unstructured":"Hod\u017ei\u0107, S., Pasalic, E., Zhang, W.: Generic constructions of five-valued spectra boolean functions. IEEE Trans. Inf. Theory 65(11), 7554\u20137565 (2019). https:\/\/doi.org\/10.1109\/TIT.2019.2910808","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"724_CR14","doi-asserted-by":"publisher","first-page":"4397","DOI":"10.1109\/TIT.2014.2320974","volume":"60","author":"S Mesnager","year":"2014","unstructured":"Mesnager, S.: Several new infinite families of bent functions and their duals. IEEE Trans. Inf. Theory 60(7), 4397\u20134407 (2014). https:\/\/doi.org\/10.1109\/TIT.2014.2320974","journal-title":"IEEE Trans. Inf. Theory"},{"key":"724_CR15","doi-asserted-by":"publisher","unstructured":"Mesnager, S.: Bent Functions: Fundamentals and Results, 1st edn. Springer Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-32595-8","DOI":"10.1007\/978-3-319-32595-8"},{"issue":"2","key":"724_CR16","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s12095-015-0144-7","volume":"8","author":"S Mesnager","year":"2016","unstructured":"Mesnager, S.: Further constructions of infinite families of bent functions from new permutations and their duals. Cryptography Commun. 8(2), 229\u2013246 (2016). https:\/\/doi.org\/10.1007\/s12095-015-0144-7","journal-title":"Cryptography Commun."},{"key":"724_CR17","doi-asserted-by":"publisher","unstructured":"Mesnager, S., Cohen, G., Madore, D.: On existence (based on an arithmetical problem) and constructions of bent functions. In:\u00a0Groth, J. (ed.) Cryptography and Coding, pp. 3\u201319. Springer International Publishing, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-27239-9_1","DOI":"10.1007\/978-3-319-27239-9_1"},{"issue":"7","key":"724_CR18","doi-asserted-by":"publisher","first-page":"2365","DOI":"10.1007\/s10623-023-01204-w","volume":"91","author":"E Pasalic","year":"2023","unstructured":"Pasalic, E., Bapi\u0107, A., Zhang, F., Wei, Y.: Explicit infinite families of bent functions outside the completed Maiorana-McFarland class. Designs, Codes Cryptography 91(7), 2365\u20132393 (2023). https:\/\/doi.org\/10.1007\/s10623-023-01204-w","journal-title":"Designs, Codes Cryptography"},{"issue":"6","key":"724_CR19","doi-asserted-by":"publisher","first-page":"4464","DOI":"10.1109\/TIT.2024.3352824","volume":"70","author":"E Pasalic","year":"2024","unstructured":"Pasalic, E., Polujan, A., Kudin, S., Zhang, F.: Design and analysis of bent functions using $$\\cal{M} $$-subspaces. IEEE Trans. Inf. Theory 70(6), 4464\u20134477 (2024). https:\/\/doi.org\/10.1109\/TIT.2024.3352824","journal-title":"IEEE Trans. Inf. Theory"},{"key":"724_CR20","doi-asserted-by":"publisher","unstructured":"Polujan, A.: Boolean and vectorial functions: a design-theoretic point of view. Ph.D. thesis, Otto-von-Guericke-Universit\u00e4t Magdeburg, Fakult\u00e4t f\u00fcr Mathematik (2021). https:\/\/doi.org\/10.25673\/37956","DOI":"10.25673\/37956"},{"key":"724_CR21","unstructured":"Polujan, A., Pasalic, E., Kudin, S., Zhang, F.: On bent functions satisfying the dual bent condition. In: The 8th International Workshop on Boolean Functions and their Applications (2023). https:\/\/boolean.w.uib.no\/bfa-2023\/"},{"issue":"9","key":"724_CR22","doi-asserted-by":"publisher","first-page":"1701","DOI":"10.1007\/s10623-019-00712-y","volume":"88","author":"AA Polujan","year":"2020","unstructured":"Polujan, A.A., Pott, A.: Cubic bent functions outside the completed Maiorana-McFarland class. Designs, Codes Cryptography 88(9), 1701\u20131722 (2020). https:\/\/doi.org\/10.1007\/s10623-019-00712-y","journal-title":"Designs, Codes Cryptography"},{"key":"724_CR23","doi-asserted-by":"publisher","unstructured":"Preneel, B., Van\u00a0Leekwijck, W., Van\u00a0Linden, L., Govaerts, R., Vandewalle, J.: Propagation characteristics of boolean functions. In: Damg\u00e5rd, I.B. (ed.) Advances in Cryptology \u2014 EUROCRYPT \u201990, pp. 161\u2013173. Springer Berlin Heidelberg, Berlin, Heidelberg (1991). https:\/\/doi.org\/10.1007\/3-540-46877-3_14","DOI":"10.1007\/3-540-46877-3_14"},{"key":"724_CR24","doi-asserted-by":"publisher","unstructured":"Rothaus, O.: On \u201cbent\u201d functions. Journal of Combinatorial Theory, Series A 20(3), 300\u2013305 (1976). https:\/\/doi.org\/10.1016\/0097-3165(76)90024-8","DOI":"10.1016\/0097-3165(76)90024-8"},{"key":"724_CR25","doi-asserted-by":"publisher","unstructured":"Seberry, J., Zhang, X.M., Zheng, Y.: Pitfalls in designing substitution boxes. In: Desmedt, Y.G. (ed.) Advances in Cryptology \u2014 CRYPTO \u201994, pp. 383\u2013396. Springer Berlin Heidelberg, Berlin, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48658-5_35","DOI":"10.1007\/3-540-48658-5_35"},{"key":"724_CR26","doi-asserted-by":"publisher","unstructured":"Tokareva, N.: On the number of bent functions from iterative constructions: lower bounds and hypotheses (2011). https:\/\/doi.org\/10.3934\/amc.2011.5.609","DOI":"10.3934\/amc.2011.5.609"},{"key":"724_CR27","doi-asserted-by":"publisher","unstructured":"Zhang, F., Pasalic, E., Bapi\u0107, A., Wang, B.: Constructions of several special classes of cubic bent functions outside the completed Maiorana-McFarland class. Inf. Comput. 297, 105149 (2024). https:\/\/doi.org\/10.1016\/j.ic.2024.105149","DOI":"10.1016\/j.ic.2024.105149"},{"issue":"3","key":"724_CR28","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1007\/s10623-021-00996-z","volume":"90","author":"H Zhao","year":"2022","unstructured":"Zhao, H., Wei, Y., Zhang, F., Pasalic, E., Cepak, N.: Two secondary constructions of bent functions without initial conditions. Des. Codes Cryptogr. 90(3), 653\u2013679 (2022). https:\/\/doi.org\/10.1007\/s10623-021-00996-z","journal-title":"Des. Codes Cryptogr."}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-024-00724-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-024-00724-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-024-00724-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T16:28:03Z","timestamp":1737476883000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-024-00724-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,18]]},"references-count":28,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["724"],"URL":"https:\/\/doi.org\/10.1007\/s12095-024-00724-z","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,18]]},"assertion":[{"value":"15 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}]}}