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Syst."],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Robustness of modern information confidentiality algorithm depends on its individual components. Modern block ciphers highly depend on two  components namely confusion and diffusion. These two main characteristics in any modern cipher are achieved by substitution and permutation boxes. In this article, a decision-making algorithm is utilized for the selection of optimum substitution box (S-box), which plays a significant role in the field of information confidentiality. For this purpose, an interval-based Pythagorean fuzzy technique for order of preference by similarity to the ideal solution (IVPF\u2013TOPSIS) method is introduced to get the desired nonlinear confusion component of block  cipher namely S-box. In this manner, we performed cryptographic analyses of standard S-boxes namely nonlinearity (NL), strict avalanche criterion (SAC), bit-independent criterion (BIC), absolute indicator (ABI), the sum of square and absolute indicator (SSAI), algebraic degree (AD), algebraic immunity (AI), transparency order (TO), composite algebraic immunity (CAI), robustness (RB), signal to noise ratio (SNR), confusion coefficient of variance (CCV). With these cryptographic characteristics, we have used interval-valued based Pythagorean fuzzy TOPSIS multi-criteria decision-making technique to classify standard S-boxes suitable for construction of modern block ciphers.<\/jats:p>","DOI":"10.1007\/s40747-023-01150-z","type":"journal-article","created":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T07:01:37Z","timestamp":1690268497000},"page":"455-468","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Hybrid multi-criteria decision-making technique for the selection of best cryptographic multivalued Boolean function"],"prefix":"10.1007","volume":"10","author":[{"given":"Nabilah","family":"Abughazalah","sequence":"first","affiliation":[]},{"given":"Majid","family":"Khan","sequence":"additional","affiliation":[]},{"given":"Mohsin","family":"Iqbal","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,7,25]]},"reference":[{"issue":"4","key":"1150_CR1","first-page":"B-41","volume":"17","author":"RE Bellman","year":"1970","unstructured":"Bellman RE, Zadeh LA (1970) \u2018Decision-making in a fuzzy environment.\u2019 Manag Sci 17(4):B-41","journal-title":"Manag Sci"},{"key":"1150_CR2","first-page":"1","volume":"20","author":"K Atanassov","year":"2016","unstructured":"Atanassov K (2016) \u2018Intuitionistic fuzzy sets.\u2019 Int J Bioautomat 20:1","journal-title":"Int J Bioautomat"},{"issue":"1","key":"1150_CR3","doi-asserted-by":"crossref","first-page":"851","DOI":"10.2991\/ijcis.2017.10.1.57","volume":"10","author":"S Abdullah","year":"2017","unstructured":"Abdullah S, Ayub S, Hussain I, Bedregal B, Khan MY (2017) \u2018Analyses of S-boxes based on interval valued intuitionistic fuzzy sets and image encryption.\u2019 Int J Computat Intell Syst 10(1):851\u2013865","journal-title":"Int J Computat Intell Syst"},{"key":"1150_CR4","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1016\/j.asoc.2015.10.040","volume":"38","author":"H Garg","year":"2016","unstructured":"Garg H (2016) \u2018A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems.\u2019 Appl Soft Comput 38:988\u2013999","journal-title":"Appl Soft Comput"},{"key":"1150_CR5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.cie.2016.08.017","volume":"101","author":"H Garg","year":"2016","unstructured":"Garg H (2016) \u2018Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making.\u2019 Comput Ind Eng 101:53\u201369","journal-title":"Comput Ind Eng"},{"issue":"4","key":"1150_CR6","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/s13042-016-0589-9","volume":"9","author":"YX Cao","year":"2018","unstructured":"Cao YX, Zhou H, Wang JQ (2018) \u2018An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis.\u2019 Int J Mach Learn Cybern 9(4):629\u2013640","journal-title":"Int J Mach Learn Cybern"},{"issue":"1","key":"1150_CR7","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s12351-015-0199-4","volume":"16","author":"H Zhou","year":"2016","unstructured":"Zhou H, Wang J, Li XE, Wang JQ (2016) \u2018Intuitionistic hesitant linguistic sets and their application in multi-criteria decision-making problems.\u2019 Oper Res Int Journal 16(1):131\u2013160","journal-title":"Oper Res Int Journal"},{"key":"1150_CR8","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.engappai.2017.02.008","volume":"60","author":"H Garg","year":"2017","unstructured":"Garg H (2017) \u2018Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application.\u2019 Eng Appl Artif Intell 60:164\u2013174","journal-title":"Eng Appl Artif Intell"},{"key":"1150_CR9","doi-asserted-by":"crossref","unstructured":"Yager RR (2013) \u2018\u2018Pythagorean fuzzy subsets,\u2019\u2019 In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA\/NAFIPS), IEEE, pp. 57\u201361, 2013.","DOI":"10.1109\/IFSA-NAFIPS.2013.6608375"},{"issue":"4","key":"1150_CR10","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","volume":"22","author":"RR Yager","year":"2013","unstructured":"Yager RR (2013) Pythagorean membership grades in multicriteria decision making. 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