An Examination of Inefficiencies in Key Dependent Variations of the Rijndael S-Box

Substitution boxes, or s-boxes, provide the primary source of non-linearity in symmetric cryptographic primitives. There are a variety methodologies used to design s-boxes. One method, that is widely used, is an s-box that is created at execution time, based on the cipher key. These are usually termed key-dependent s-boxes. Such s-box designs have been demonstrated to be sufficiently secure. However, what has not been adequately studied, is whether the additional overhead required by key-dependent s-boxes actually improves the nonlinearity of the algorithm, or is offset by a decrease in efficiency. Efficiency in algorithms is a growing concern due to devices with limited processing power. Internet of Things (Io‘T), implanted medical devices, and sensors all require security which includes encryption. However, these devices have limited processing power. Additional processing overhead may be counterproductive. This current study examines two questions. The first being how much additional overhead is introduced by key-dependent s-boxes. The focus for this study is on key dependent variations of the Rijndael cipher. The current study shows that while key-dependent variations of Rijndael are sufficiently secure, they do not demonstrate improved non-linearity over the standard Rijndael s-box, and do introduce additional processing overhead. This indicates these key-dependent variations of Rijndael may not have any advantage, and are contra indicated for implementations with limited processing resources.