{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T10:39:34Z","timestamp":1772102374202,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T00:00:00Z","timestamp":1686009600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T00:00:00Z","timestamp":1686009600000},"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":["Multimed Tools Appl"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s11042-023-15965-y","type":"journal-article","created":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T21:03:27Z","timestamp":1686085407000},"page":"7159-7177","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Construction of highly non linear component of block cipher based on mclaurin series and mellin transformation with application in image encryption"],"prefix":"10.1007","volume":"83","author":[{"given":"Abid","family":"Mahboob","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5060-7906","authenticated-orcid":false,"given":"Imran","family":"Siddique","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Asif","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Nadeem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aysha","family":"Saleem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,6]]},"reference":[{"key":"15965_CR1","unstructured":"Abramowitz, Milton, Stegun, Irene A (1970) \u201cHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables\u201d New York: Dover\u2019s Publications, Ninth printing"},{"key":"15965_CR2","doi-asserted-by":"crossref","unstructured":"Ahmad M, Khaja IA, Baz A, Alhakami H, and Alhakami W (2020) Particle swarm optimization based highly nonlinear substitution- boxes generation for security applications. IEEE Access, 8, 116132_116147","DOI":"10.1109\/ACCESS.2020.3004449"},{"key":"15965_CR3","doi-asserted-by":"publisher","first-page":"93795","DOI":"10.1109\/ACCESS.2021.3092512","volume":"9","author":"AS Alanazi","year":"2021","unstructured":"Alanazi AS, Munir N, Khan M, Asif M, Hussain I (2021) Cryptanalysis of Novel Image Encryption Scheme Based on Multiple Chaotic Substitution Boxes. IEEE Access 9:93795\u201393802","journal-title":"IEEE Access"},{"issue":"20","key":"15965_CR4","doi-asserted-by":"publisher","first-page":"7333","DOI":"10.1007\/s11042-020-10048-8","volume":"80","author":"HS Alhadawi","year":"2021","unstructured":"Alhadawi HS, Majid MA, Lambi\u0107 D, Ahmad M (2021) A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm. Multimedia Tools Appl 80(20):7333\u20137350","journal-title":"Multimedia Tools Appl"},{"issue":"129","key":"15965_CR5","first-page":"1","volume":"13","author":"BM Alshammari","year":"2021","unstructured":"Alshammari BM, Guesmi R, Guesmi T, Alsaif H, Alzamil A (2021) Implementing a Symmetric Lightweight Cryptosystem in Highly Constrained IoT Devices by Using a Chaotic S-Box. Symmetry 13(129):1\u201320","journal-title":"Symmetry"},{"issue":"3","key":"15965_CR6","doi-asserted-by":"publisher","first-page":"3925","DOI":"10.3233\/JIFS-190137","volume":"37","author":"M Asif","year":"2019","unstructured":"Asif M, Shah T (2019) BCH Codes with computational approach and its applications in image encryption. Journal of Intelligent & Fuzzy Systems 37(3):3925\u20133939","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"4","key":"15965_CR7","doi-asserted-by":"publisher","first-page":"289","DOI":"10.14257\/ijsia.2015.9.4.27","volume":"9","author":"R Bhanot","year":"2015","unstructured":"Bhanot R, Hans R (2015) A review and comparative analysis of various encryption algorithms. International Journal of Security and Its Applications 9(4):289\u2013306","journal-title":"International Journal of Security and Its Applications"},{"issue":"2","key":"15965_CR8","first-page":"259","volume":"1","author":"S Bhatti","year":"2020","unstructured":"Bhatti S, Safdar R, Shehzad K, Jawad M, Ahmed H (2020) New Cryptographic Scheme with Mellin Transformation. Pakistan Journal of Multidisciplinary Research 1(2):259\u2013272","journal-title":"Pakistan Journal of Multidisciplinary Research"},{"key":"15965_CR9","unstructured":"Daemen, Joan, and Vincent Rijmen (1999) \"Aes proposal: Rijndael, aes algorithm submission, september 3, 1999.\"&nbsp;URL&nbsp;http:\/\/www.nist.gov\/CryptoToolKit:37\u201338"},{"issue":"1","key":"15965_CR10","first-page":"1","volume":"1","author":"J Daemen","year":"2002","unstructured":"Daemen J, Rijmen V (2002) AES the advanced encryption standard. The design of Rijndael 1(1):1\u2013238","journal-title":"The design of Rijndael"},{"issue":"1","key":"15965_CR11","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1038\/s41598-019-56845-6","volume":"10","author":"AAA El-Latif","year":"2020","unstructured":"El-Latif AAA, Abd-El-Atty B, Amin M, Iliyasu AM (Dec.2020) Quantum inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications. Sci Rep 10(1):116","journal-title":"Sci Rep"},{"key":"15965_CR12","unstructured":"Faheem ZB, Ali A, Khan MA, Ul-Haq ME, and Ahmad W (2020) Highly dispersive substitution box (S-box) design using chaos. ETRI Journal, pp. 1\u201314"},{"issue":"4","key":"15965_CR13","doi-asserted-by":"publisher","first-page":"3041","DOI":"10.1007\/s11071-019-05413-8","volume":"99","author":"MAB Farah","year":"2020","unstructured":"Farah MAB, Farah A, Farah T (2020) An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dyn 99(4):3041\u20133064","journal-title":"Nonlinear Dyn"},{"issue":"6","key":"15965_CR14","doi-asserted-by":"publisher","first-page":"19129","DOI":"10.1007\/s11042-020-08718-8","volume":"79","author":"MAB Farah","year":"2020","unstructured":"Farah MAB, Guesmi R, Kachouri A, Samet M (Mar.2020) A new design of cryptosystem based on S-box and chaotic permutation. Multimedia Tools Appl 79(6):19129\u201319150","journal-title":"Multimedia Tools Appl"},{"key":"15965_CR15","unstructured":"Feng D, Wu W (2000). Design and analysis of block ciphers"},{"issue":"11","key":"15965_CR16","doi-asserted-by":"publisher","first-page":"3871","DOI":"10.1007\/s10773-019-04254-w","volume":"58","author":"F Firdousi","year":"2019","unstructured":"Firdousi F, Batool SI, Amin M (2019) A novel construction scheme for nonlinear component based on quantum map. J Theor Phys 58(11):3871\u20133898","journal-title":"J Theor Phys"},{"key":"15965_CR17","doi-asserted-by":"crossref","unstructured":"Gao W, Idrees B, Zafar S, and Rashid T (2020) Construction of nonlinear component of block cipher by action of modular group PSL(2, Z) on projective line PL(GF(28)).\u00a0 IEEE Access, 8 136736_136749","DOI":"10.1109\/ACCESS.2020.3010615"},{"key":"15965_CR18","doi-asserted-by":"crossref","unstructured":"Hussain S, Jamal SS, Shah T, and Hussain I (2020) A power associative loop structure for the construction of non-linear components of block cipher, IEEE Access, 8 123492_123506","DOI":"10.1109\/ACCESS.2020.3005087"},{"issue":"1","key":"15965_CR19","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00521-012-0914-5","volume":"23","author":"I Hussain","year":"2013","unstructured":"Hussain I, Shah T, Gondal MA, Khan WA, Mahmood H (2013) A group theoretic approach to construct cryptographically strong substitution boxes. Neural Comput Appl 23(1):97\u2013104","journal-title":"Neural Comput Appl"},{"key":"15965_CR20","unstructured":"Hussain T, Shah MA, Gondal and Khan WA (2011) Construction of Cryptographically Strong 8x8 S-boxes. World App. Sc. J., 13, 11, 2389-2395"},{"issue":"1","key":"15965_CR21","doi-asserted-by":"publisher","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"},{"key":"15965_CR22","doi-asserted-by":"crossref","unstructured":"Lambic D (2020) A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design. Nonlinear Dyn\u00a0100","DOI":"10.1007\/s11071-020-05503-y"},{"issue":"1","key":"15965_CR23","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/s11071-020-05503-y","volume":"100","author":"D Lambi\u0107","year":"2020","unstructured":"Lambi\u0107 D (2020) A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design. Nonlinear Dyn 100(1):699\u2013711","journal-title":"Nonlinear Dyn"},{"key":"15965_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.amc.2020.125153","volume":"376","author":"H Liu","year":"2020","unstructured":"Liu H, Kadir A, Xu C (2020) Cryptanalysis and constructing S-box based on chaotic map and backtracking. App Math Comp 376:1\u201311","journal-title":"App Math Comp"},{"key":"15965_CR25","doi-asserted-by":"crossref","unstructured":"Lokenath debnath, Dambaru Bhatta, (2016) \u201cIntegral Transforms and their Applications\u201d. CRC press. ISBN 978\u20131\u20134200\u20131091\u20136, 19","DOI":"10.1201\/9781420010916"},{"key":"15965_CR26","doi-asserted-by":"publisher","first-page":"25664","DOI":"10.1109\/ACCESS.2020.2970806","volume":"8","author":"Q Lu","year":"2020","unstructured":"Lu Q, Zhu C, Deng X (2020) An efficient image encryption scheme based on the LSS chaotic map and single S-box. IEEE Access 8:25664\u201325678","journal-title":"IEEE Access"},{"issue":"150\u2013154","key":"15965_CR27","first-page":"25","volume":"48","author":"PP Mar","year":"2008","unstructured":"Mar PP, Latt KM (2008) New analysis methods on strict avalanche criterion of S-boxes. World Academy of Science, Engineering and Technology 48(150\u2013154):25","journal-title":"World Academy of Science, Engineering and Technology"},{"key":"15965_CR28","first-page":"386","volume-title":"\u2018\u2018Linear cryptanalysis method for DES cipher\u2019,\u2019 in Proc","author":"M Matsui","year":"1994","unstructured":"Matsui M (1994) \u2018\u201cLinear cryptanalysis method for DES cipher\u201d,\u2019 in Proc. Adv. Cryptol, Lofthus, Norway, pp 386\u2013397"},{"key":"15965_CR29","doi-asserted-by":"crossref","unstructured":"Muhammad Asif et al (2021) \"A Novel Image Encryption Technique Based on Mobius Transformation. \"&nbsp;Computational Intelligence and Neuroscience&nbsp;2021","DOI":"10.1155\/2021\/1912859"},{"key":"15965_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jisa.2020.102470","volume":"52","author":"KAK Patro","year":"2020","unstructured":"Patro KAK, Soni A, Netam PK, Acharya B (2020) Multiple grayscale image encryption using cross-coupled chaotic maps. Journal of Information Security and Applications 52:102470","journal-title":"Journal of Information Security and Applications"},{"issue":"6","key":"15965_CR31","doi-asserted-by":"publisher","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 Proceedings Part E Computers and Digital Techniques 135(6):325\u2013335","journal-title":"IEE Proceedings Part E Computers and Digital Techniques"},{"key":"15965_CR32","unstructured":"Pub, F. I. P. S. (1999). Data encryption standard (des). FIPS PUB, 46\u20133"},{"issue":"1","key":"15965_CR33","first-page":"12","volume":"5","author":"M Saha","year":"2017","unstructured":"Saha M (2017) Application of Laplace-Mellin transform for cryptography. Rai Journal of Technology Research & Innovation 5(1):12\u201317","journal-title":"Rai Journal of Technology Research & Innovation"},{"key":"15965_CR34","unstructured":"Santana YC (2014) \u201cA Cryptographic Scheme OfMellin Transform,\u201d arXiv preprint arXiv: 1401.1232"},{"issue":"2","key":"15965_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/s13360-020-00187-0","volume":"135","author":"A Shafique","year":"2020","unstructured":"Shafique A (2020) A new algorithm for the construction of substitution box by using chaotic map. Eur Phys J Plus 135(2):1\u201313","journal-title":"Eur Phys J Plus"},{"issue":"4","key":"15965_CR36","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","volume":"28","author":"CE Shannon","year":"1949","unstructured":"Shannon CE (1949) Communication theory of secrecy systems. TBell Syst. Tech. J 28(4):656\u2013715","journal-title":"TBell Syst. Tech. J"},{"key":"15965_CR37","doi-asserted-by":"publisher","first-page":"197630","DOI":"10.1109\/ACCESS.2020.3034832","volume":"8","author":"N Siddiqui","year":"2020","unstructured":"Siddiqui N, Khalid H, Murtaza F, Ehatisham-Ul-Haq M, Azam MA (2020) A novel algebraic tech- nique for design of computational substitution-boxes using action of matrices on galois field. IEEE Access 8:197630\u2013197643","journal-title":"IEEE Access"},{"issue":"20","key":"15965_CR38","doi-asserted-by":"publisher","first-page":"3015","DOI":"10.1007\/s11277-020-07832-y","volume":"116","author":"N Siddiqui","year":"2021","unstructured":"Siddiqui N, Naseer A, Ehatisham-ul-Haq MA (2021) Novel Scheme of Substitution-Box Design Based on Modified Pascal\u2019s Triangle and Elliptic Curve. Wireless Pers Commun 116(20):3015\u20133030","journal-title":"Wireless Pers Commun"},{"key":"15965_CR39","first-page":"1","volume":"2017","author":"Y Tian","year":"2017","unstructured":"Tian Y, Lu Z (Nov.2017) Chaotic S-box: Intertwining logistic map and bacterial foraging optimization. Math Problems Eng 2017:1\u201311","journal-title":"Math Problems Eng"},{"key":"15965_CR40","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.ins.2019.10.070","volume":"515","author":"N Tsafack","year":"2020","unstructured":"Tsafack N, Kengne J, Abd-El-Atty B, Iliyasu AM, Hirota K, El-Latif A (2020) Design and implementation of a simple dynamical 4-D chaotic circuit with applications in image encryption. Inf Sci 515:191\u2013217","journal-title":"Inf Sci"},{"key":"15965_CR41","doi-asserted-by":"crossref","unstructured":"Webster A, and Tavares S (1986) \u201cOn the design of S-boxes,\u201d in Advances in Cryptology: Proc. of Crypto\u201985 Lecture Notes in Computer Science, 523\u2013534","DOI":"10.1007\/3-540-39799-X_41"},{"key":"15965_CR42","doi-asserted-by":"publisher","first-page":"150326","DOI":"10.1109\/ACCESS.2020.3016401","volume":"8","author":"AH Zahid","year":"2020","unstructured":"Zahid AH, Al-Solami E, Ahmad M (2020) A novel modular approach based substitution-box design for image encryption. IEEE Access 8:150326\u2013150340","journal-title":"IEEE Access"},{"issue":"12","key":"15965_CR43","doi-asserted-by":"publisher","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"},{"issue":"12","key":"15965_CR44","doi-asserted-by":"publisher","first-page":"2087","DOI":"10.3390\/sym12122087","volume":"12","author":"D Zhu","year":"2020","unstructured":"Zhu D, Tong X, Zhang M, Wang Z (2020) A new S-box generation method and advanced design based on combined chaotic system. Symmetry 12(12):2087","journal-title":"Symmetry"},{"key":"15965_CR45","doi-asserted-by":"crossref","unstructured":"Zhang YQ, Hao J-L, and Wang X-Y (2020) \u201cAn efficient image encryption scheme based on S-boxes and fractional-order differential logistic map,\u201d IEEE Access, 8 54175_54188","DOI":"10.1109\/ACCESS.2020.2979827"}],"container-title":["Multimedia Tools and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-023-15965-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11042-023-15965-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-023-15965-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T07:09:27Z","timestamp":1704697767000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11042-023-15965-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,6]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["15965"],"URL":"https:\/\/doi.org\/10.1007\/s11042-023-15965-y","relation":{},"ISSN":["1380-7501","1573-7721"],"issn-type":[{"value":"1380-7501","type":"print"},{"value":"1573-7721","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,6]]},"assertion":[{"value":"25 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 March 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 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":"The writers affirm that they have no established financial or interpersonal conflicts that would have seemed to have an impact on the research presented in this study.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"There is no conflict of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}