A novel framework for the construction of cryptographically secure S-boxes

In symmetric cryptography, a cryptographically secure Substitution -Box (S -Box) is a key component of a block cipher. S -Box adds a confusion layer in block ciphers that provide resistance against well-known attacks. The generation of a cryptographically secure S -Box depends upon its generation mechanism. In this paper, we propose a novel framework for the construction of cryptographically secure S -Boxes. This framework uses a combination of linear fractional transformation and permutation functions. S -Boxes security is analyzed against well-known security criteria that include nonlinearity, bijectiveness, strict avalanche and bits independence criteria, linear and differential approximation probability. The S -Boxes can be used in the encryption of any grayscale digital images. The encrypted images are analyzed against well-known image analysis criteria that include pixel changing rates, correlation, entropy, and average change of intensity. The analysis of the encrypted image shows that our image encryption scheme is secure.