A Cryptographic Scheme for Construction of Substitution Boxes Using Quantic Fractional Transformation

Abstract

In the new era of cryptography, Substitution Boxes (S-Boxes) are very important to raise confusion in cipher text and the security of encryption directly depends on the algebraic strength of S-box. To avoid a hacker attack, researchers are focusing on creating dynamic S-boxes that are much stronger. The dominating concept for developing S-boxes is linear fractional transformation. In this article, we proposed a novel technique to generate cryptographically strong S-box by using fractional transformation based on finite field. The substitute box is constructed in two phases. Firstly, general form of dynamic fractional transformation designed which work for odd exponents in the range [1-255]. The S-box is then constructed using quantic fractional transformation as an example. Secondly, in order to increase the unpredictability of proposed S-box, we use the symmetric group's S256 permutation. The usefulness of the constructed S-box was also tested using several criteria such as nonlinearity, differential uniformity, strict avalanche criteria, linear approximation probability and bit independence criteria. To assess the reliability of S-box, its performance outcomes are compared to those of previously developed S-boxes. Furthermore, we utilized the suggested S-Box to the image encryption approach. Then, to determine the effectiveness of the encryption scheme, use several tests such as contrast, correlation, homogeneity, entropy, and energy. We have compared our results with different algorithms which ensured that the proposed strategy for ciphered image is excellent.