{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T01:02:29Z","timestamp":1767142949145,"version":"build-2238731810"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFA1000600"],"award-info":[{"award-number":["2021YFA1000600"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62072162"],"award-info":[{"award-number":["62072162"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201193"],"award-info":[{"award-number":["12201193"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Hubei Province of China","award":["2021CFA079"],"award-info":[{"award-number":["2021CFA079"]}]},{"name":"Innovation Group Project of the Natural Science Foundation of Hubei Province of China","award":["2023AFA021"],"award-info":[{"award-number":["2023AFA021"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s40314-024-02979-x","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T02:04:13Z","timestamp":1730426653000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Further explorations in the second-order zero differential spectra of power functions over finite fields"],"prefix":"10.1007","volume":"44","author":[{"given":"Yuying","family":"Man","sequence":"first","affiliation":[]},{"given":"Zhen","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Nian","family":"Li","sequence":"additional","affiliation":[]},{"given":"Xiangyong","family":"Zeng","sequence":"additional","affiliation":[]},{"given":"Yuxuan","family":"Lu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,1]]},"reference":[{"issue":"1","key":"2979_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/BF00630563","volume":"4","author":"E Biham","year":"1991","unstructured":"Biham E, Shamir A (1991) Differential cryptanalysis of DES-like cryptosystems. J Cryptol 4(1):3\u201372","journal-title":"J Cryptol"},{"issue":"2","key":"2979_CR2","first-page":"149","volume":"1","author":"C Blondeau","year":"2010","unstructured":"Blondeau C, Canteaut A, Charpin P (2010) Differential properties of power functions. Int J Inf Coding Theory 1(2):149\u2013170","journal-title":"Int J Inf Coding Theory"},{"key":"2979_CR3","doi-asserted-by":"publisher","first-page":"331","DOI":"10.46586\/tosc.v2020.i1.331-362","volume":"1","author":"H Boukerrou","year":"2020","unstructured":"Boukerrou H, Huynh P, Lallemand V, Mandal B, Minier M (2020) On the Feistel counterpart of the boomerang connectivity table: introduction and analysis of the FBCT. IACR Trans Symmetric Cryptol 1:331\u2013362","journal-title":"IACR Trans Symmetric Cryptol"},{"key":"2979_CR4","doi-asserted-by":"publisher","first-page":"290","DOI":"10.46586\/tosc.v2018.i3.290-310","volume":"3","author":"C Boura","year":"2018","unstructured":"Boura C, Canteaut A (2018) On the boomerang uniformity of cryptographic S-boxes. IACR Trans Symmetric Cryptol 3:290\u2013310","journal-title":"IACR Trans Symmetric Cryptol"},{"key":"2979_CR5","first-page":"683","volume-title":"Advances in cryptology-EUROCRYPT","author":"C Cid","year":"2018","unstructured":"Cid C, Huang T, Peyrin T, Sasaki Y, Song L (2018) Boomerang connectivity table: a new cryptanalysis tool. In: Nielsen J, Rijmen V (eds) Advances in cryptology-EUROCRYPT, vol 10821. Springer, Cham, pp 683\u2013714"},{"issue":"3","key":"2979_CR6","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1017\/S0004972700036200","volume":"69","author":"R Coulter","year":"2004","unstructured":"Coulter R, Henderson M (2004) A note on the roots of trinomials over a finite field. Bull Aust Math Soc 69(3):429\u2013432","journal-title":"Bull Aust Math Soc"},{"key":"2979_CR7","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1007\/s12095-022-00581-8","volume":"14","author":"S Eddahmani","year":"2022","unstructured":"Eddahmani S, Mesnager S (2022) Explicit values of the DDT, the BCT, the FBCT, and the FBDT of the inverse, the gold, and the Bracken-Leander S-boxes. Cryptogr Commun 14:1301\u20131344","journal-title":"Cryptogr Commun"},{"key":"2979_CR8","unstructured":"Garg K, Hasan SU, Riera C, St\u01cenic\u01ce P (2023) The second-order zero differential spectra of some APN and other maps over finite fields. arXiv:2310.13775"},{"key":"2979_CR9","unstructured":"Garg K, Hasan SU, Riera C, St\u01cenic\u01ce P (2023) The second-order zero differential spectra of some functions over finite fields. arXiv:2309.04219"},{"issue":"2","key":"2979_CR10","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 (1999) New families of almost perfect nonlinear power mappings. IEEE Trans Inform Theory 45(2):475\u2013485","journal-title":"IEEE Trans Inform Theory"},{"issue":"2","key":"2979_CR11","first-page":"347","volume":"36","author":"PA Leonard","year":"1972","unstructured":"Leonard PA, Williams KS (1972) Quartics over $${\\mathbb{F} }_{2^n}$$. Proc Am Math Soc 36(2):347\u2013350","journal-title":"Proc Am Math Soc"},{"issue":"6","key":"2979_CR12","doi-asserted-by":"publisher","first-page":"1468","DOI":"10.3934\/amc.2021060","volume":"17","author":"Z Li","year":"2023","unstructured":"Li Z, Yan HD (2023) Differential spectra of a class of power permutations with Niho exponents. Adv Math Commun 17(6):1468\u20131475","journal-title":"Adv Math Commun"},{"issue":"3","key":"2979_CR13","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1007\/s12095-021-00544-5","volume":"14","author":"X Li","year":"2022","unstructured":"Li X, Yue Q, Tang D (2022) The second-order zero differential spectra of almost perfect nonlinear functions and the inverse function in odd characteristic. Cryptogr Commun 14(3):653\u2013662","journal-title":"Cryptogr Commun"},{"key":"2979_CR14","volume-title":"Finite fields","author":"R Lidl","year":"1997","unstructured":"Lidl R, Niederreiter H (1997) Finite fields. Cambridge University Press, Cambridge"},{"key":"2979_CR15","doi-asserted-by":"publisher","unstructured":"Man YY, Li N, Xiang ZJ, Zeng XY (2023) On the second-order zero differential spectra of some power functions over finite fields. Cryptogr Commun. https:\/\/doi.org\/10.1007\/s12095-024-00740-z","DOI":"10.1007\/s12095-024-00740-z"},{"key":"2979_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2022.102100","volume":"84","author":"YY Man","year":"2022","unstructured":"Man YY, Xia YB, Li CL, Helleseth T (2022) On the differential properties of the power mapping $$x^{p^m+2}$$. Finite Fields Appl 84:102100","journal-title":"Finite Fields Appl"},{"issue":"12","key":"2979_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2024.114185","volume":"347","author":"YY Man","year":"2024","unstructured":"Man YY, Mesnager S, Li N, Zeng XY, Tang XH (2024) In-depth analysis of S-boxes over binary finite fields concerning their differential and Feistel boomerang differential uniformities. Discrete Math 347(12):114185","journal-title":"Discrete Math"},{"key":"2979_CR18","first-page":"55","volume-title":"Workshop on the theory and application of cryptographic techniques","author":"K Nyberg","year":"1993","unstructured":"Nyberg K (1993) Differential uniform mappings for cryptography. Workshop on the theory and application of cryptographic techniques. Springer, Lofthus, pp 55\u201364"},{"key":"2979_CR19","first-page":"181","volume-title":"FSE 2007, LNCS","author":"T Shirai","year":"2007","unstructured":"Shirai T, Shibutani K, Akishita T, Moriai S, Iwata T (2007) The 128-bit blockcipher CLEFIA (extended abstract). In: Biryukov A (ed) FSE 2007, LNCS, vol 4593. Springer, Berlin, pp 181\u2013195"},{"key":"2979_CR20","first-page":"156","volume-title":"FSE 1999, LNCS","author":"D Wagner","year":"1999","unstructured":"Wagner D (1999) The boomerang attack. In: Knudsen L (ed) FSE 1999, LNCS, vol 1636. Springer, Berlin, pp 156\u2013170"},{"issue":"8","key":"2979_CR21","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1007\/s10623-017-0416-7","volume":"86","author":"MS Xiong","year":"2018","unstructured":"Xiong MS, Yan HD, Yuan PZ (2018) On a conjecture of differentially 8-uniform power functions. Des Codes Cryptogr 86(8):1601\u20131621","journal-title":"Des Codes Cryptogr"}],"updated-by":[{"DOI":"10.1007\/s40314-024-03009-6","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T00:00:00Z","timestamp":1733356800000}}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02979-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02979-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02979-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T00:14:59Z","timestamp":1741047299000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02979-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["2979"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02979-x","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,1]]},"assertion":[{"value":"16 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 August 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 October 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 December 2024","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s40314-024-03009-6","URL":"https:\/\/doi.org\/10.1007\/s40314-024-03009-6","order":8,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declared that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"13"}}