Abstract
For the security of digital data, different cryptosystems have been proposed in recent years. The substitution boxes are used to generate confusion in the cryptosystems for hiding the secret data. In the literature, the techniques for designing substitution boxes have been proposed for the sake of confusion. Among these techniques, the chaotic substitution boxes have more tendency of generating diffusion as compared to confusion. In this article, a novel method is introduced for the construction of substitution permutation boxes to get the advantage of both confusion and diffusion. These substitution permutation boxes are based upon the action of symmetric group on Galois field. This particular group action would also provide mathematical justification of bits permutation. For application purpose, these boxes are applied for a robust steganography scheme. The algebraic and statistical analyses suggest that proposed boxes provide confusion and diffusion of the standard level. The standard analysis of steganography has revealed that proposed boxes are suitable for the techniques of secure communication.