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There exist several performance criteria for cryptographically-strong substitution boxes (S-boxes), which are often conflicting with each other. Constructing S-boxes that satisfy multiple criteria with optimal tradeoffs is one of the challenging tasks for cryptographers. In practice, the existing S-box design algorithms are used to optimize performance according to a single performance criterion, mainly the nonlinearity, which usually results in weak scores for other equally-significant criteria. To overcome this problem, a multi-objective optimization-based method is presented in this paper. In this method, <inline-formula> <tex-math notation="LaTeX">$8 \times 8$ </tex-math></inline-formula> S-boxes are constructed satisfying multiple criteria of balancedness, high nonlinearity, low differential uniformity, and low auto-correlation. Multiple objectives are fulfilled by applying the chaos-assisted non-dominated sorting genetic algorithm-II to introduce the S-boxes. The performance assessment of the proposed method and the comparative analysis with available optimization tools and other state-of-the-art algorithms demonstrate its proficiency in generating significantly-better S-box solutions with good Pareto-optimal security features. Eventually, the S-boxes with minimum nonlinearity (NL) of 110, differential uniformity (DU) as low as 8, and auto-correlation function (ACF) as low as 80 are obtained after the optimization. Furthermore, the obtained Pareto-optimal S-box is utilized to put forward a medical image encryption algorithm for secure telemedicine services. The suggested encryption algorithm uses an S-box to perform the required permutation and diffusion of images. The encryption performance assessment and comparison analyses validate its effectiveness for securing medical imagery data in telemedicine networks.

Multi-Objective Evolution of Strong S-Boxes Using Non-Dominated Sorting Genetic Algorithm-II and Chaos for Secure Telemedicine