A Novel Algebraic Technique for the Construction of Strong Substitution Box

The ability of substitution box (S-box) to create confusion in the cipher attracted different authors to design strong cryptographic S-box. The S-box can further be used in different cryptosystems to create confusion. In this article, a novel scheme is introduced to develop S-box with strong arithmetic background. The construction depends on group action of projective general linear group on units of finite local ring and its features are equated with other promising S-boxes. This S-box is evaluated with the help of bit independent criterion, strict avalanche criterion, non-linearity test, linear approximation probability test and differential approximation probability test. The results of majority logic criterion suggest the strength and implementation of our S-box.