S-box design based on optimize LFT parameter selection: a practical approach in recommendation system domain Saira Beg 1 & Naveed Ahmad 2 & Adeel Anjum 1 & Mansoor Ahmad 1 & Abid Khan 1 & Faisal Baig 3 & Ahmed Khan 1 Received: 26 February 2019 /Revised: 25 October 2019 /Accepted: 12 November 2019 / Published online: 7 January 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract The strength of cryptography encryption is strongly depended upon the substitution box (S-box), hence highly non-linear S-box is appreciated in cryptography. In this work, we proposed a scheme to select the optimized values for control parameters (a, b, c, d) of linear fractional transform (LFT) to achieve an S-box with non-linearity of 112. For dynamic parameter values, we used location of chaotic sequences. The proposed s-box tested on different criteria such as non-linearity method (NL), probability methods (linear approximation (LP), differential approximation (DP), strictly avalanche criteria (SAC) and bit independence criteria (BIC). Our result shows that proposed s-box achieves better or equal to cryptographic strength as compared with state-of-the-art techniques. More- over, we tested the proposed s-box based encryption method in recommendation system scenario with the idea of text-to-image conversion. The statistical analysis of this image encryption shows the bright prospects of the proposed method. Keywords S-box . Cryptography . Galois field . Projective linear group (PGL) . Chaotic theory . Text-2-image conversion . Recommendation system . NIST standard 1 Introduction In cryptography one of the most essential resources is the substitution box (S-box) that plays an important role. The S-box is used to aid in creating confusion in data and the strength of Multimedia Tools and Applications (2020) 79:11667–11684 https://doi.org/10.1007/s11042-019-08464-6 * Ahmed Khan soft_engr_isb@yahoo.com 1 Department of Computer Science, COMSATS University Islamabad, Islamabad, Pakistan 2 FAST-National University of Computer and Emerging Sciences, Islamabad, Pakistan 3 Federal Urdu University of Arts, Science & Technology, Islamabad, Pakistan