Color image encryption by a non-chain Galois ring extension

The S-box is a vital component for producing nonlinearity in a block cipher. Seldom this component is constructed through finite fields; however, sometimes Galois rings are used for its construction. In this work, we utilize the extended Galois ring to construct a Substitution box (S-box) over the ring GR4,4[x]<x2>. The designed S-box is generated by multiple elements and thus exhibits a high level of confusion compared to typical S-boxes. An encrypted color image is compared to existing encrypted S-box images to investigate their effects. First, we separate the distinct channels from a digital image and create 256-order matrices with 16-bit entries for each channel. We then apply the designed image encryption algorithm to these matrices. For the permutation step, we use the 1-dimensional logistic map to generate the key. Then, we apply the exclusive-or operation to all three layers of the image using the key. Finally, concatenate all these layers to create the encrypted image. The result is the proposal of a new RGB image encryption technique. The proposed encryption technique can replace several image encryption techniques that rely on S-boxes. In general, this technique aims to achieve optimal values.