{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:42:13Z","timestamp":1740148933872,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T00:00:00Z","timestamp":1645574400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T00:00:00Z","timestamp":1645574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["309598\/2017-6","409543\/2018- 7"],"award-info":[{"award-number":["309598\/2017-6","409543\/2018- 7"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Funda\u00e7\u00e3o de Amparo \u00e1 Ci\u00eancia e Tecnologia do Estado de Pernambuco","award":["IBPG-0071-3.04\/17"],"award-info":[{"award-number":["IBPG-0071-3.04\/17"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s12095-022-00565-8","type":"journal-article","created":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T14:05:23Z","timestamp":1645625123000},"page":"897-908","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Tangent-chebyshev maps over finite fields: New properties and functional graphs"],"prefix":"10.1007","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1474-1147","authenticated-orcid":false,"given":"Ravi B. D.","family":"Figueiredo","sequence":"first","affiliation":[]},{"given":"Juliano B.","family":"Lima","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,23]]},"reference":[{"key":"565_CR1","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.ffa.2015.02.002","volume":"34","author":"S Bae","year":"2015","unstructured":"Bae, S., Cha, B., Jung, H.: M\u00f6bius function in short intervals for function fields. Finite Fields and Their Applications 34, 235\u2013249 (2015)","journal-title":"Finite Fields and Their Applications"},{"issue":"4","key":"565_CR2","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1016\/j.ffa.2012.01.004","volume":"18","author":"S Bae","year":"2012","unstructured":"Bae, S., Hu, S., Jung, H.: The generalized R\u00e9dei-matrix for function fields. Finite Fields and Their Applications 18(4), 760\u2013780 (2012)","journal-title":"Finite Fields and Their Applications"},{"key":"565_CR3","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.tcs.2019.12.005","volume":"809","author":"M Barbier","year":"2020","unstructured":"Barbier, M., Cheballah, H., Bars, J.M.: On the computation of the M\u00f6bius transform. Theoretical Computer Science 809, 171\u2013188 (2020)","journal-title":"Theoretical Computer Science"},{"key":"565_CR4","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.ffa.2016.01.011","volume":"39","author":"E Bellini","year":"2016","unstructured":"Bellini, E., Murru, N.: An efficient and secure RSA-like cryptosystem exploiting R\u00e9dei rational functions over conics. Finite Fields and Their Applications 39, 179\u2013194 (2016)","journal-title":"Finite Fields and Their Applications"},{"key":"565_CR5","unstructured":"Burton, D.M.: Elementary Number Theory, 7th edn. McGraw-Hill Science\/Engineering\/Math (2010)"},{"issue":"12","key":"565_CR6","doi-asserted-by":"publisher","first-page":"2561","DOI":"10.1007\/s10623-020-00801-3","volume":"88","author":"J Capaverde","year":"2020","unstructured":"Capaverde, J., Masuda, A.M., Rodrigues, V.M.: R\u00e9dei permutations with cycles of the same length. Designs, Codes and Cryptography 88(12), 2561\u20132579 (2020)","journal-title":"Designs, Codes and Cryptography"},{"key":"565_CR7","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1016\/j.cam.2013.07.036","volume":"259","author":"A \u00c7e\u015fmelio\u011flu","year":"2014","unstructured":"\u00c7e\u015fmelio\u011flu, A., Meidl, W., Topuzo\u011flu, A.: Permutations of finite fields with prescribed properties. Journal of Computational and Applied Mathematics 259, 536\u2013545 (2014)","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"4","key":"565_CR8","doi-asserted-by":"publisher","first-page":"2266","DOI":"10.1109\/TIT.2016.2526022","volume":"62","author":"P Charpin","year":"2016","unstructured":"Charpin, P., Mesnager, S., Sarkar, S.: Involutions over the Galois field $$\\mathbb{F}_{2^n}$$. IEEE Trans. Inf. Theory 62(4), 2266\u20132275 (2016)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"565_CR9","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/j.amc.2019.05.047","volume":"361","author":"I Dassios","year":"2019","unstructured":"Dassios, I., Tzounas, G., Milano, F.: The M\u00f6bius transform effect in singular systems of differential equations. Applied Mathematics and Computation 361, 338\u2013353 (2019)","journal-title":"Applied Mathematics and Computation"},{"issue":"6","key":"565_CR10","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1049\/el.2018.6855","volume":"55","author":"RBD Figueiredo","year":"2019","unstructured":"Figueiredo, R.B.D., Lima, J.B.: Fractional angular transform: a number-theoretic approach. Electronics Letters 55(6), 322\u2013325 (2019)","journal-title":"Electronics Letters"},{"issue":"7","key":"565_CR11","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1007\/s10623-018-0548-4","volume":"87","author":"S Fu","year":"2019","unstructured":"Fu, S., Feng, X., Lin, D., Wang, Q.: A recursive construction of permutation polynomials over $$\\mathbb{F}_{q^2}$$ R\u00e9dei functions. Designs, Codes and Cryptography 87(7), 1481\u20131498 (2019)","journal-title":"Designs, Codes and Cryptography"},{"key":"565_CR12","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.disc.2013.10.014","volume":"315\u2013316","author":"TA Gassert","year":"2014","unstructured":"Gassert, T.A.: Chebyshev action on finite fields. Discrete Mathematics 315\u2013316, 83\u201394 (2014)","journal-title":"Discrete Mathematics"},{"issue":"6","key":"565_CR13","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1007\/s12095-019-00384-4","volume":"11","author":"C Gravel","year":"2019","unstructured":"Gravel, C., Panario, D., Thomson, D.: Unicyclic strong permutations. Cryptography and Communications 11(6), 1211\u20131231 (2019)","journal-title":"Cryptography and Communications"},{"issue":"1","key":"565_CR14","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s11277-017-4869-9","volume":"98","author":"S Hosseinalipour","year":"2018","unstructured":"Hosseinalipour, S., Sakzad, A., Sadeghi, M.R.: Performance of M\u00f6bius interleavers for turbo codes. Wireless Personal Communications 98(1), 271\u2013291 (2018)","journal-title":"Wireless Personal Communications"},{"key":"565_CR15","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.jcta.2019.105121","volume":"169","author":"V Jel\u00ednek","year":"2020","unstructured":"Jel\u00ednek, V., Kantor, I., Kyncl, J., Tancer, M.: On the growth of the M\u00f6bius function of permutations. J. Comb. Theor, Ser. A 169, 105\u2013121 (2020)","journal-title":"J. Comb. Theor, Ser. A"},{"key":"565_CR16","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jctb.2015.07.003","volume":"116","author":"SV Konyagina","year":"2016","unstructured":"Konyagina, S.V., Luca, F., Mans, B., Mathieson, L., Sha, M., Shparlinski, I.E.: Functional graphs of polynomials over finite fields. J. Comb. Theory Ser. B 116, 87\u2013122 (2016)","journal-title":"J. Comb. Theory Ser. B"},{"issue":"6","key":"565_CR17","doi-asserted-by":"publisher","first-page":"2322","DOI":"10.1109\/TCSI.2018.2888688","volume":"66","author":"C Li","year":"2019","unstructured":"Li, C., Feng, B., Li, S., Kurths, J., Chen, G.: Dynamic analysis of digital chaotic maps via state-mapping networks. IEEE Trans. Circuits Syst. I, Reg. Papers 66(6), 2322\u20132335 (2019)","journal-title":"IEEE Trans. Circuits Syst. I, Reg. Papers"},{"issue":"10","key":"565_CR18","doi-asserted-by":"publisher","first-page":"1392","DOI":"10.1109\/TC.2010.148","volume":"59","author":"X Liao","year":"2010","unstructured":"Liao, X., Chen, F., Wong, K.W.: On the security of public-key algorithms based on Chebyshev polynomials over the finite field $$Z_{N}$$. IEEE Trans. Comput. 59(10), 1392\u20131401 (2010)","journal-title":"IEEE Trans. Comput."},{"issue":"2","key":"565_CR19","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.ipl.2010.10.011","volume":"111","author":"JB Lima","year":"2010","unstructured":"Lima, J.B., Panario, D., Campello\u00a0de Souza, R.M.: Public-key encryption based on Chebyshev polynomials over GF(q). Information Processing Letters 111(2), 51\u201356 (2010)","journal-title":"Information Processing Letters"},{"key":"565_CR20","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1017\/CBO9781139696456.016","volume-title":"Applied Algebra and Number Theory","author":"JB Lima","year":"2014","unstructured":"Lima, J.B., Panario, D., de Souza, R.M.C.: A trigonometric approach for Chebyshev polynomials over finite fields. In: Larcher, G., Pillichshammer, F., Winterhof, A., Xing, C. (eds.) Applied Algebra and Number Theory, pp. 255\u2013279. Cambridge University Press, Cambridge (2014)"},{"issue":"8","key":"565_CR21","doi-asserted-by":"publisher","first-page":"3217","DOI":"10.1016\/j.laa.2012.12.021","volume":"438","author":"JB Lima","year":"2013","unstructured":"Lima, J.B., Campello\u00a0de Souza, R.M.: Fractional cosine and sine transforms over finite fields. Linear Algebra and its Applications 438(8), 3217\u20133230 (2013)","journal-title":"Linear Algebra and its Applications"},{"issue":"4","key":"565_CR22","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1109\/TCSII.2019.2923879","volume":"67","author":"JB Lima","year":"2020","unstructured":"Lima, J.B., de\u00a0Souza, R.M.C.: Tangent function and Chebyshev-like rational maps over finite fields. IEEE Trans. Circuits Syst. II, Exp. Briefs 67(4), 775\u2013779 (2020)","journal-title":"IEEE Trans. Circuits Syst. II, Exp. Briefs"},{"key":"565_CR23","unstructured":"LTE: Evolved universal terrestrial radio access (e-utra); multiplexing and channel coding (3gpp ts 36.212 version 8.8.0 release 8) (2010\u201301). Technical Specification, ETSI (2010)"},{"key":"565_CR24","volume-title":"Chebyshev Polynomials","author":"JC Mason","year":"2003","unstructured":"Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. Chapman & Hall\/CRC, Boca Raton (2003)"},{"key":"565_CR25","doi-asserted-by":"crossref","unstructured":"Mikhail, M., Abouelseoud, Y., ElKobrosy, G.: Two-phase image encryption scheme based on FFCT and fractals. Security and Communication Networks pp. 1\u201313 (2017)","DOI":"10.1155\/2017\/7367518"},{"issue":"3","key":"565_CR26","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/BF01195335","volume":"6","author":"W More","year":"1995","unstructured":"More, W.: Fast evaluation of R\u00e9dei functions. Applicable Algebra in Engineering, Communication and Computing 6(3), 171\u2013173 (1995)","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"key":"565_CR27","doi-asserted-by":"crossref","unstructured":"Mullen, G.L., Panario, D.: Handbook of Finite Fields. Chapman & Hall\/CRC (2013)","DOI":"10.1201\/b15006"},{"key":"565_CR28","unstructured":"Nour, C.A.: Enhanced turbo codes for NR: Performance evaluation for eMBB and URLLC. Technical report, 3GPP TSG-RAN WG1 Meeting #87 (2016)"},{"issue":"2","key":"565_CR29","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/s10623-018-0547-5","volume":"87","author":"D Panario","year":"2019","unstructured":"Panario, D., Reis, L.: The functional graph of linear maps over finite fields and applications. Designs, Codes and Cryptography 87(2), 437\u2013453 (2019)","journal-title":"Designs, Codes and Cryptography"},{"issue":"3","key":"565_CR30","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1137\/140993338","volume":"29","author":"C Qureshi","year":"2015","unstructured":"Qureshi, C., Panario, D.: R\u00e9dei actions on finite fields and multiplication map in cyclic group. SIAM Journal on Discrete Mathematics 29(3), 1486\u20131503 (2015)","journal-title":"SIAM Journal on Discrete Mathematics"},{"issue":"2","key":"565_CR31","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s10623-018-0545-7","volume":"87","author":"C Qureshi","year":"2019","unstructured":"Qureshi, C., Panario, D.: The graph structure of chebyshev polynomials over finite fields and applications. Designs, Codes and Cryptography 87(2), 393\u2013416 (2019)","journal-title":"Designs, Codes and Cryptography"},{"key":"565_CR32","doi-asserted-by":"crossref","unstructured":"Sakzad, A., Panario, D., Sadeghi, M.R., Eshghi, N.: Self-inverse interleavers based on permutation functions for turbo codes. In: 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) pp. 22\u201328 (2010)","DOI":"10.1109\/ALLERTON.2010.5706883"},{"issue":"14","key":"565_CR33","doi-asserted-by":"publisher","first-page":"8403","DOI":"10.1007\/s11042-015-2755-6","volume":"75","author":"EF da Silva Neto","year":"2016","unstructured":"da Silva Neto, E.F., Lima, J.B.: Audio encryption based on the cosine number transform. Multimedia Tools and Applications 75(14), 8403\u20138418 (2016)","journal-title":"Multimedia Tools and Applications"},{"key":"565_CR34","doi-asserted-by":"crossref","unstructured":"Campello\u00a0de Souza, R.M., de\u00a0Oliveira, H.M., Kauffman, A., Paschoal, A.J.A.: Trigonometry in finite fields and a new Hartley transform. In: Proc. IEEE Int. Symp. Inf. Theory, p. 293. IEEE (1998)","DOI":"10.1109\/ISIT.1998.708898"},{"key":"565_CR35","doi-asserted-by":"crossref","unstructured":"Yoshioka, D.: Periodic properties of Chebyshev polynomial sequences over the residue ring $$\\mathbb{Z}\/2^{k}\\mathbb{Z}$$. IEEE Trans. Circuits Syst. II, Exp. Briefs 63(8), 778\u2013782 (2016)","DOI":"10.1109\/TCSII.2016.2531058"},{"issue":"3","key":"565_CR36","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1109\/TCSII.2017.2739190","volume":"65","author":"D Yoshioka","year":"2018","unstructured":"Yoshioka, D.: Properties of Chebyshev polynomials modulo $$p^{k}$$. IEEE Trans. Circuits Syst. II, Exp. Briefs 65(3), 386\u2013390 (2018)","journal-title":"IEEE Trans. Circuits Syst. II, Exp. Briefs"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-022-00565-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-022-00565-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-022-00565-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T02:49:45Z","timestamp":1726714185000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-022-00565-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,23]]},"references-count":36,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["565"],"URL":"https:\/\/doi.org\/10.1007\/s12095-022-00565-8","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"type":"print","value":"1936-2447"},{"type":"electronic","value":"1936-2455"}],"subject":[],"published":{"date-parts":[[2022,2,23]]},"assertion":[{"value":"8 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 February 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"This work was supported by CNPq under Grants 309598\/2017-6 and 409543\/2018-7, and FACEPE under grant IBPG-0071-3.04\/17.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}}]}}