A Novel Technique to Improve Nonlinearity of Substitution Box Without Disturbing Its Mathematical Properties

Substitution box is a basic nonlinear component in data encryption. It converts the plain text into an enciphered format. The formation of cryptographically secure S-boxes is the most important task for cryptographers to ensure the security of the system. In this paper, we have introduced a novel method to increase the working capability of an S-box without demolishing its basic mathematical structure, that is, Eigen values, characteristic polynomial and determinant of the S-box/16x16 matrix. We considered Skipjack, Xyi, Prime, Jakimoski, Tang and Iqtadar S-boxes and reshuffled their rows/columns in such a way that they become cryptographically stronger. Algebraically, this can be accomplished by using appropriate permutations of the symmetric group S16over rows/columns of the S-boxes. The proposed technique is very constructive in enhancing the performance of S-boxes based on fundamental idea; bijection over the same set. The outcomes of different analyses demonstrated that the improved versions of S-boxes are more reliable than the original ones.