Hybrid multi-criteria decision-making technique for the selection of best cryptographic multivalued Boolean function

Abstract

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–TOPSIS) 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.