Chaos-Based S-Boxes as a Source of Confusion in Cryptographic Primitives

Abstract

In recent years, many chaos-based encryption algorithms have been proposed. Many of these are based on established designs and populate their S-boxes with values derived from chaotic maps, following conventional implementation strategies to enable comparison with their original non-chaotic counterparts. In contrast, this work proposes a novel approach: a Chaos-Based Substitution Box (CB-SBox) implementation, in which conventional ROM-based S-boxes are replaced by a digital circuit that directly executes a selected chaotic map. This method enables the construction of S-boxes with long word lengths through an FPGA-based programmable circuit that allows for variable S-box lengths, facilitating the analysis of S-boxes of varying sizes, and ultimately enhancing security, particularly for larger S-boxes, as demonstrated by increased resistance to linear and differential cryptanalysis. Furthermore, the proposed CB-SBox achieves reductions in both area and power consumption compared to size-comparable ROM-based S-boxes. A 19-bit chaos-based S-box consumes just 0.0238% of the area and 0.0241% of the power required by an equivalent ROM-implemented S-box while providing the same level of security. The inherent unpredictability of non-linear chaotic behavior causes the proposed chaos-based S-boxes to exhibit non-bijective characteristics, making them well suited for application in non-invertible cryptographic primitives, such as hash functions and Feistel networks. The proposed CB-SBox is implemented in a Feistel network as described in the literature, and the results are provided.