{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T16:06:31Z","timestamp":1786982791404,"version":"build-2736575974"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T00:00:00Z","timestamp":1677024000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T00:00:00Z","timestamp":1677024000000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s40314-023-02215-y","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T09:03:57Z","timestamp":1677056637000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A novel algebraic construction of strong S-boxes over double GF(27) structures and image protection"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1898-4082","authenticated-orcid":false,"given":"Abdul","family":"Razaq","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4915-9325","authenticated-orcid":false,"given":"Musheer","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5068-2033","authenticated-orcid":false,"given":"Ahmed A. Abd","family":"El-Latif","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,2,22]]},"reference":[{"key":"2215_CR1","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/j.procs.2015.07.394","volume":"57","author":"M Ahmad","year":"2015","unstructured":"Ahmad M, Bhatia D, Hassan Y (2015) A novel ant colony optimization based scheme for substitution box design. Proc Comput Sci 57:572\u2013580","journal-title":"Proc Comput Sci"},{"key":"2215_CR2","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.pisc.2016.06.001","volume":"8","author":"M Ahmad","year":"2016","unstructured":"Ahmad M, Mittal N, Garg P, Khan MM (2016) Efficient cryptographic substitution box design using travelling salesman problem and chaos. Perspect Sci 8:465\u2013468","journal-title":"Perspect Sci"},{"issue":"11","key":"2215_CR3","doi-asserted-by":"crossref","first-page":"7201","DOI":"10.1007\/s00521-018-3557-3","volume":"31","author":"HA Ahmed","year":"2019","unstructured":"Ahmed HA, Zolkipli MF, Ahmad M (2019) A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map. Neural Comput Appl 31(11):7201\u20137210","journal-title":"Neural Comput Appl"},{"issue":"3","key":"2215_CR4","doi-asserted-by":"crossref","DOI":"10.1063\/1.4978264","volume":"7","author":"A Altaleb","year":"2017","unstructured":"Altaleb A, Saeed MS, Hussain I, Aslam M (2017) An algorithm for the construction of substitution box for block ciphers based on projective general linear group. AIP Adv 7(3):035116","journal-title":"AIP Adv"},{"key":"2215_CR5","doi-asserted-by":"crossref","first-page":"55405","DOI":"10.1109\/ACCESS.2018.2871557","volume":"6","author":"AA Alzaidi","year":"2018","unstructured":"Alzaidi AA, Ahmad M, Doja MN, Al Solami E, Beg MS (2018b) A new 1D chaotic map and \u03b2-hill climbing for generating substitution-boxes. IEEE Access 6:55405\u201355418","journal-title":"IEEE Access"},{"key":"2215_CR6","doi-asserted-by":"crossref","unstructured":"Alzaidi, A. A., Ahmad, M., Ahmed, H. S., & Solami, E. A. (2018a). Sine-cosine optimization-based bijective substitution-boxes construction using enhanced dynamics of chaotic map.\u00a0Complexity 2018a","DOI":"10.1155\/2018\/9389065"},{"issue":"4","key":"2215_CR7","first-page":"289","volume":"9","author":"R Bhanot","year":"2015","unstructured":"Bhanot R, Hans R (2015) A review and comparative analysis of various encryption algorithms. Int J Secur Appl 9(4):289\u2013306","journal-title":"Int J Secur Appl"},{"issue":"1","key":"2215_CR8","doi-asserted-by":"crossref","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"},{"key":"2215_CR9","unstructured":"Daemen J, Rijmen V (1999) The Rijndael block cipher: AES proposal. In: First candidate conference (AeS1), pp 343\u2013348"},{"issue":"2","key":"2215_CR10","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1007\/s11071-016-3295-y","volume":"88","author":"T Farah","year":"2017","unstructured":"Farah T, Rhouma R, Belghith S (2017) A novel method for designing S-box based on chaotic map and teaching\u2013learning-based optimization. Nonlinear Dyn 88(2):1059\u20131074","journal-title":"Nonlinear Dyn"},{"issue":"1","key":"2215_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40064-016-3298-7","volume":"5","author":"S Farwa","year":"2016","unstructured":"Farwa S, Shah T, Idrees L (2016) A highly nonlinear S-box based on a fractional linear transformation. Springerplus 5(1):1\u201312","journal-title":"Springerplus"},{"key":"2215_CR12","doi-asserted-by":"crossref","unstructured":"Guesmi R, Farah MAB, Kachouri A, Samet M (2014) A novel design of Chaos based S-Boxes using genetic algorithm techniques. In: 2014 IEEE\/ACS 11th International Conference on Computer Systems and Applications (AICCSA), IEEE, pp 678\u2013684","DOI":"10.1109\/AICCSA.2014.7073265"},{"issue":"5","key":"2215_CR13","doi-asserted-by":"crossref","first-page":"282","DOI":"10.5560\/zna.2012-0022","volume":"67","author":"I Hussain","year":"2012","unstructured":"Hussain I, Shah T, Gondal MA, Mahmood H (2012) Generalized majority logic criterion to analyze the statistical strength of S-boxes. Zeitschrift F\u00fcr Naturforschung A 67(5):282\u2013288","journal-title":"Zeitschrift F\u00fcr Naturforschung A"},{"issue":"6","key":"2215_CR14","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1007\/s00521-012-0870-0","volume":"22","author":"I Hussain","year":"2013","unstructured":"Hussain I, Shah T, Mahmood H, Gondal MA (2013) A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput Appl 22(6):1085\u20131093","journal-title":"Neural Comput Appl"},{"key":"2215_CR15","doi-asserted-by":"crossref","first-page":"123492","DOI":"10.1109\/ACCESS.2020.3005087","volume":"8","author":"S Hussain","year":"2020","unstructured":"Hussain S, Jamal SS, Shah T, Hussain I (2020) A power associative loop structure for the construction of non-linear components of block cipher. IEEE Access 8:123492\u2013123506","journal-title":"IEEE Access"},{"key":"2215_CR16","doi-asserted-by":"crossref","unstructured":"Hussain S, Shah T, Javeed A (2022) Modified advanced encryption standard (MAES) based on non-associative inverse property loop. Multimed Tools Appl 1\u201320","DOI":"10.1007\/s11042-022-14064-8"},{"issue":"1","key":"2215_CR17","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s11277-017-5054-x","volume":"99","author":"SS Jamal","year":"2018","unstructured":"Jamal SS, Shah T (2018) A novel algebraic technique for the construction of strong substitution box. Wireless Pers Commun 99(1):213\u2013226","journal-title":"Wireless Pers Commun"},{"key":"2215_CR18","doi-asserted-by":"crossref","first-page":"173273","DOI":"10.1109\/ACCESS.2019.2956385","volume":"7","author":"SS Jamal","year":"2019","unstructured":"Jamal SS, Anees A, Ahmad M, Khan MF, Hussain I (2019) Construction of cryptographic S-boxes based on mobius transformation and chaotic tent-sine system. IEEE Access 7:173273\u2013173285","journal-title":"IEEE Access"},{"issue":"9","key":"2215_CR19","doi-asserted-by":"crossref","first-page":"6649","DOI":"10.1007\/s11042-019-08393-4","volume":"79","author":"A Javeed","year":"2020","unstructured":"Javeed A, Shah T (2020) Design of an S-box using Rabinovich\u2013Fabrikant system of differential equations perceiving third order nonlinearity. Multimed Tools Appl 79(9):6649\u20136660","journal-title":"Multimed Tools Appl"},{"issue":"1","key":"2215_CR20","doi-asserted-by":"crossref","first-page":"23","DOI":"10.15388\/Informatica.2009.235","volume":"20","author":"K Kazlauskas","year":"2009","unstructured":"Kazlauskas K, Kazlauskas J (2009) Key-dependent S-box generation in AES block cipher system. Informatica 20(1):23\u201334","journal-title":"Informatica"},{"issue":"3","key":"2215_CR21","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s11071-012-0675-9","volume":"71","author":"M Khan","year":"2013","unstructured":"Khan M, Shah T, Mahmood H, Gondal MA (2013) An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn 71(3):489\u2013492","journal-title":"Nonlinear Dyn"},{"issue":"3","key":"2215_CR22","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s00521-015-1887-y","volume":"27","author":"M Khan","year":"2016","unstructured":"Khan M, Shah T, Batool SI (2016) Construction of S-box based on chaotic Boolean functions and its application in image encryption. Neural Comput Appl 27(3):677\u2013685","journal-title":"Neural Comput Appl"},{"key":"2215_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-17342-4","volume-title":"The block cipher companion","author":"LR Knudsen","year":"2011","unstructured":"Knudsen LR, Robshaw M (2011) The block cipher companion. Springer, Berlin"},{"key":"2215_CR24","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.chaos.2013.11.001","volume":"58","author":"D Lambi\u0107","year":"2014","unstructured":"Lambi\u0107 D (2014) A novel method of S-box design based on chaotic map and composition method. Chaos, Solitons Fractals 58:16\u201321","journal-title":"Chaos, Solitons Fractals"},{"issue":"4","key":"2215_CR25","doi-asserted-by":"crossref","first-page":"2407","DOI":"10.1007\/s11071-016-3199-x","volume":"87","author":"D Lambi\u0107","year":"2017","unstructured":"Lambi\u0107 D (2017) A novel method of S-box design based on discrete chaotic map. Nonlinear Dyn 87(4):2407\u20132413","journal-title":"Nonlinear Dyn"},{"issue":"107","key":"2215_CR26","doi-asserted-by":"crossref","first-page":"109","DOI":"10.2298\/PIM1307109L","volume":"93","author":"D Lambi\u0107","year":"2013","unstructured":"Lambi\u0107 D, \u017divkovi\u0107 M (2013) Comparison of random S-box generation methods. Publications De L\u2019institut Mathematique 93(107):109\u2013115","journal-title":"Publications De L'institut Mathematique"},{"key":"2215_CR27","first-page":"109","volume-title":"International workshop on lightweight cryptography for security and privacy","author":"RH Makarim","year":"2014","unstructured":"Makarim RH, Tezcan C (2014) Relating undisturbed bits to other properties of substitution boxes. International workshop on lightweight cryptography for security and privacy. Springer, Cham, pp 109\u2013125"},{"key":"2215_CR28","first-page":"386","volume-title":"Workshop on the theory and application of of cryptographic techniques","author":"M Matsui","year":"1994","unstructured":"Matsui M (1994) Linear cryptanalysis method for DES cipher. Workshop on the theory and application of of cryptographic techniques. Springer, Berlin, pp 386\u2013397"},{"key":"2215_CR29","first-page":"49","volume":"1","author":"F \u00d6zkaynak","year":"2019","unstructured":"\u00d6zkaynak F (2019a) Chaos based substitution boxes as a cryptographic primitives: challenges and opportunities. Chaotic Model Simul 1:49\u201357","journal-title":"Chaotic Model Simul"},{"issue":"8","key":"2215_CR30","doi-asserted-by":"crossref","first-page":"3317","DOI":"10.1007\/s00521-017-3287-y","volume":"31","author":"F \u00d6zkaynak","year":"2019","unstructured":"\u00d6zkaynak F (2019b) Construction of robust substitution boxes based on chaotic systems. Neural Comput Appl 31(8):3317\u20133326","journal-title":"Neural Comput Appl"},{"key":"2215_CR31","volume-title":"Understanding cryptography: a textbook for students and practitioners","author":"C Paar","year":"2009","unstructured":"Paar C, Pelzl J (2009) Understanding cryptography: a textbook for students and practitioners. Springer, Berlin"},{"key":"2215_CR32","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1007\/978-3-319-16501-1_16","volume-title":"European Conference on Genetic Programming","author":"S Picek","year":"2015","unstructured":"Picek S, Jakobovic D, Miller JF, Marchiori E, Batina L (2015) Evolutionary methods for the construction of cryptographic Boolean functions. European Conference on Genetic Programming. Springer, Cham, pp 192\u2013204"},{"issue":"6","key":"2215_CR33","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1049\/ip-e.1988.0044","volume":"135","author":"J Pieprzyk","year":"1988","unstructured":"Pieprzyk J, Finkelstein G (1988) Towards effective nonlinear cryptosystem design. IEE Proc E-Comput Digital Techn 135(6):325\u2013335","journal-title":"IEE Proc E-Comput Digital Techn"},{"issue":"4","key":"2215_CR34","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1007\/s11277-019-06973-z","volume":"111","author":"A Razaq","year":"2020","unstructured":"Razaq A, Ullah A, Waheed A (2020) A novel technique to improve nonlinearity of substitution box without disturbing its mathematical properties. Wireless Pers Commun 111(4):2091\u20132105","journal-title":"Wireless Pers Commun"},{"issue":"1","key":"2215_CR35","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/1366\/1\/012001","volume":"1366","author":"MFB Roslan","year":"2019","unstructured":"Roslan MFB, Seman K, Ab Halim AH, Sayuti MNASM (2019) Substitution box design based from symmetric group composition. J Phys Confer Ser 1366(1):012001","journal-title":"J Phys Confer Ser"},{"key":"2215_CR36","doi-asserted-by":"crossref","unstructured":"Shahzad I, Mushtaq Q, Razaq A (2019) Construction of new S-box using action of quotient of the modular group for multimedia security. Secur Commun Netw 2019","DOI":"10.1155\/2019\/2847801"},{"key":"2215_CR37","doi-asserted-by":"crossref","unstructured":"Shamir A (2004) Stream ciphers: dead or alive?. In: ASIACRYPT","DOI":"10.1007\/978-3-540-30539-2_6"},{"key":"2215_CR38","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.amc.2018.03.019","volume":"332","author":"VM Silva-Garc\u00eda","year":"2018","unstructured":"Silva-Garc\u00eda VM, Flores-Carapia R, Renter\u00eda-M\u00e1rquez C, Luna-Benoso B, Aldape-P\u00e9rez M (2018) Substitution box generation using Chaos: An image encryption application. Appl Math Comput 332:123\u2013135","journal-title":"Appl Math Comput"},{"issue":"7","key":"2215_CR39","doi-asserted-by":"crossref","first-page":"525","DOI":"10.3390\/e20070525","volume":"20","author":"AE Solami","year":"2018","unstructured":"Solami AE, Ahmad M, Volos C, Doja MN, Beg MMS (2018) A new hyperchaotic system-based design for efficient bijective substitution-boxes. Entropy 20(7):525","journal-title":"Entropy"},{"issue":"1","key":"2215_CR40","first-page":"232","volume":"27","author":"Y Tian","year":"2016","unstructured":"Tian Y, Lu Z (2016) S-box: Six-dimensional compound hyperchaotic map and artificial bee colony algorithm. J Syst Eng Electron 27(1):232\u2013241","journal-title":"J Syst Eng Electron"},{"issue":"4","key":"2215_CR41","doi-asserted-by":"crossref","first-page":"2757","DOI":"10.1007\/s11071-017-3409-1","volume":"88","author":"A Ullah","year":"2017","unstructured":"Ullah A, Jamal SS, Shah T (2017) A novel construction of substitution box using a combination of chaotic maps with improved chaotic range. Nonlinear Dyn 88(4):2757\u20132769","journal-title":"Nonlinear Dyn"},{"issue":"12","key":"2215_CR42","doi-asserted-by":"crossref","first-page":"155014771989595","DOI":"10.1177\/1550147719895957","volume":"15","author":"M Usama","year":"2019","unstructured":"Usama M, Rehman O, Memon I, Rizvi S (2019) An efficient construction of key-dependent substitution box based on chaotic sine map. Int J Distrib Sens Netw 15(12):1550147719895957","journal-title":"Int J Distrib Sens Netw"},{"key":"2215_CR43","first-page":"523","volume-title":"Conference on the theory and application of cryptographic techniques","author":"AF Webster","year":"1985","unstructured":"Webster AF, Tavares SE (1985) On the design of S-boxes. Conference on the theory and application of cryptographic techniques. Springer, Berlin, pp 523\u2013534"},{"issue":"3","key":"2215_CR44","doi-asserted-by":"crossref","first-page":"2115","DOI":"10.1007\/s11071-018-4478-5","volume":"94","author":"T Ye","year":"2018","unstructured":"Ye T, Zhimao L (2018) Chaotic S-box: six-dimensional fractional Lorenz\u2013Duffing chaotic system and O-shaped path scrambling. Nonlinear Dyn 94(3):2115\u20132126","journal-title":"Nonlinear Dyn"},{"key":"2215_CR45","doi-asserted-by":"crossref","first-page":"53079","DOI":"10.1109\/ACCESS.2019.2911395","volume":"7","author":"L Yi","year":"2019","unstructured":"Yi L, Tong X, Wang Z, Zhang M, Zhu H, Liu J (2019) A novel block encryption algorithm based on chaotic S-box for wireless sensor network. IEEE Access 7:53079\u201353090","journal-title":"IEEE Access"},{"issue":"4","key":"2215_CR46","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1080\/1023697X.2012.10669006","volume":"19","author":"W Yong","year":"2012","unstructured":"Yong W, Peng L (2012) An improved method to obtaining S-box based on chaos and genetic algorithm. HKIE Trans 19(4):53\u201358","journal-title":"HKIE Trans"},{"issue":"12","key":"2215_CR47","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1109\/TCYB.2018.2846186","volume":"48","author":"T Zhang","year":"2018","unstructured":"Zhang T, Chen CP, Chen L, Xu X, Hu B (2018) Design of highly nonlinear substitution boxes based on I-Ching operators. IEEE Trans Cybern 48(12):3349\u20133358","journal-title":"IEEE Trans Cybern"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02215-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-023-02215-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02215-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T07:32:23Z","timestamp":1701934343000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-023-02215-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,22]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["2215"],"URL":"https:\/\/doi.org\/10.1007\/s40314-023-02215-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,22]]},"assertion":[{"value":"2 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 January 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 February 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No conflict of interest exits in the submission of this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"90"}}