{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:43:06Z","timestamp":1761061386209},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s00200-021-00503-w","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T02:03:27Z","timestamp":1617847407000},"page":"301-319","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On full differential uniformity of permutations on the ring of integers modulo n"],"prefix":"10.1007","volume":"34","author":[{"given":"P. R.","family":"Mishra","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prachi","family":"Gupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Atul","family":"Gaur","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"issue":"1\u20133","key":"503_CR1","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0012-365X(02)00443-0","volume":"259","author":"MD Atkinson","year":"2002","unstructured":"Atkinson, M.D., Stitt, T.: Restricted permutations and the wreath product. Discrete Math. 259(1\u20133), 19\u201336 (2002)","journal-title":"Discrete Math."},{"issue":"1","key":"503_CR2","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. J. Cryptology 4(1), 3\u201372 (1991)","journal-title":"J. Cryptology"},{"key":"503_CR3","doi-asserted-by":"publisher","unstructured":"Bogdanov, A., Knudsen, L. R., Leander, G., Paar, C., Poschmann, A., Robshaw, M. J. B., Seurin, Y., Vikkelsoe, C.: PRESENT: An Ultra-Lightweight Block Cipher. In: Paillier, P., Verbauwhede, I. (eds) Cryptographic Hardware and Embedded Systems - CHES 2007, LNCS, vol. 4727, pp. 450-466. Springer, Berlin, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-74735-2_31","DOI":"10.1007\/978-3-540-74735-2_31"},{"issue":"3","key":"503_CR4","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1016\/j.ffa.2011.11.006","volume":"18","author":"C Bracken","year":"2012","unstructured":"Bracken, C., Tan, C.H., Tan, Y.: Binomial differentially $$4$$ uniform permutations with high nonlinearity. Finite Fields Appl. 18(3), 537\u2013546 (2012)","journal-title":"Finite Fields Appl."},{"key":"503_CR5","unstructured":"Brignall, R.: Pattern classes of permutations: Constructions, Atomicity and the Finite basis property. http:\/\/users.mct.open.ac.uk\/rb8599\/papers\/MScThesis.pdf (2004)"},{"issue":"2","key":"503_CR6","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/j.disc.2007.12.025","volume":"309","author":"L Budaghyan","year":"2009","unstructured":"Budaghyan, L., Pott, A.: On differential uniformity and nonlinearity of functions. Discrete Math. 309(2), 371\u2013384 (2009)","journal-title":"Discrete Math."},{"key":"503_CR7","doi-asserted-by":"publisher","unstructured":"Carlet, C.: Open Questions on Nonlinearity and on APN Functions. In: Ko\u00e7, \u00c7., Mesnager S., Sava\u015f E. (eds) Arithmetic of Finite Fields. WAIFI 2014, LNCS, vol. 9061, pp. 83 -107. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-16277-5_5","DOI":"10.1007\/978-3-319-16277-5_5"},{"key":"503_CR8","unstructured":"Daemen, J., Rijmen, V.: Rijndael. https:\/\/csrc.nist.gov\/csrc\/media\/projects\/cryptographic-standards-and-guidelines\/documents\/aes-development\/rijndael-ammended.pdf"},{"issue":"15","key":"503_CR9","doi-asserted-by":"publisher","first-page":"3320","DOI":"10.1016\/j.dam.2009.06.029","volume":"157","author":"K Drakakis","year":"2009","unstructured":"Drakakis, K., Gow, R., McGuire, G.: APN permutations on $${{\\mathbb{Z}}}_n$$ and Costas arrays. Discret. Appl. Math. 157(15), 3320\u20133326 (2009)","journal-title":"Discret. Appl. Math."},{"issue":"5","key":"503_CR10","doi-asserted-by":"publisher","first-page":"508","DOI":"10.1016\/j.disc.2006.01.005","volume":"306","author":"A King","year":"2006","unstructured":"King, A.: Generating indecomposable permutations. Discrete Math. 306(5), 508\u2013518 (2006)","journal-title":"Discrete Math."},{"issue":"3","key":"503_CR11","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s00200-016-0307-6","volume":"28","author":"Y Kumar","year":"2017","unstructured":"Kumar, Y., Mishra, P.R., Pillai, N.R., Sharma, R.K.: Affine equivalence and non-linearity of permutations over $${{\\mathbb{Z}}}_n$$. Appl. Algebra in Eng. Commun. Comput. 28(3), 257\u2013279 (2017)","journal-title":"nAppl. Algebra in Eng. Commun. Comput."},{"issue":"02","key":"503_CR12","doi-asserted-by":"publisher","first-page":"1850020","DOI":"10.1142\/S1793557118500201","volume":"11","author":"Y Kumar","year":"2018","unstructured":"Kumar, Y., Mishra, P.R., Sharma, R.K.: Nonlinearity of k-cycle permutations on $${{\\mathbb{Z}}}_n$$. Asian-Eur. J. Math. 11(02), 1850020 (2018)","journal-title":"Asian-Eur. J. Math."},{"key":"503_CR13","first-page":"1","volume":"122","author":"K Martin","year":"2003","unstructured":"Klazar, M.: Irreducible and connected permutations. Inst. Teoretick\u00e9 Informatiky 122, 1\u201325 (2003)","journal-title":"Inst. Teoretick\u00e9 Informatiky"},{"key":"503_CR14","unstructured":"Mishra, P. R., Gupta, I., Pillai, N. R.: Non-linearity and affine equivalence of permutations. (2014). https:\/\/eprint.iacr.org\/2014\/974"},{"issue":"1","key":"503_CR15","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1080\/01611194.2017.1325788","volume":"42","author":"PR Mishra","year":"2018","unstructured":"Mishra, P.R., Kumar, Y., Pillai, N.R., Sharma, R.K.: On non-linearity and affine equivalence of permutations over an arbitrary finite commutative ring with unity. Cryptologia 42(1), 81\u201394 (2018)","journal-title":"Cryptologia"},{"key":"503_CR16","unstructured":"National Bureau of Standards. Data Encryption Standard. U.S. Department of Commerce, FIPS pub. 46 (1977). https:\/\/csrc.nist.gov\/CSRC\/media\/Publications\/fips\/46\/archive\/1977-01-15\/documents\/NBS.FIPS.46.pdf"},{"key":"503_CR17","doi-asserted-by":"publisher","unstructured":"Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth T. (eds) Advances in Cryptology \u2014 EUROCRYPT \u201993, LNCS, vol. 765, pp. 55-64. Springer, Berlin, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48285-7_6","DOI":"10.1007\/3-540-48285-7_6"},{"key":"503_CR18","volume-title":"RC4 Stream Cipher and Its Variants","author":"G Paul","year":"2012","unstructured":"Paul, G., Maitra, S.: RC4 Stream Cipher and Its Variants, 1st edn. CRC Press, Boca Raton (2012)","edition":"1"},{"issue":"1\u20132","key":"503_CR19","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/S0166-218X(03)00293-2","volume":"138","author":"A Pott","year":"2004","unstructured":"Pott, A.: Nonlinear functions in abelian groups and relative difference sets. Discret. Appl. Math. 138(1\u20132), 177\u2013193 (2004)","journal-title":"Discret. Appl. Math."},{"key":"503_CR20","doi-asserted-by":"crossref","unstructured":"Zoltak, B.: VMPC One-Way Function and Stream Cipher. Fast Software Encryption 2004, LNCS, 3017, pp. 210-225 (2004)","DOI":"10.1007\/978-3-540-25937-4_14"},{"key":"503_CR21","unstructured":"Zoltak, B.: VMPC-R Cryptographically Secure Pseudo-Random Number Generator Alternative to RC4, https:\/\/eprint.iacr.org\/2013\/768. Last accessed 16 Jan 2019"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-021-00503-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-021-00503-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-021-00503-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T20:58:45Z","timestamp":1677013125000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-021-00503-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,8]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["503"],"URL":"https:\/\/doi.org\/10.1007\/s00200-021-00503-w","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,8]]},"assertion":[{"value":"9 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}