Development of new algorithms for performance improvement of chaotic substitution boxes

Substitution boxes have an important place in cryptological protocol design. One of the common methods used to create substitution boxes is random selection based designs. Chaos-based designs come to the fore as the most effective method in the literature for random selection. It has been shown that performance metrics of chaos-based substitution box designs can be improved with new methods developed in this thesis study. Although there are various criteria that can be used for performance analysis in substitution boxes, one of the most obvious features is the nonlinearity criterion. The methods developed in this thesis study aimed to improve the nonlinearity criterion. The importance of the nonlinearity criterion is related to the need for mixing required for cryptological protocols. In a cryptological protocol, in order to fully meet the need for mixing, designs with high nonlinearity are required. It is known that non-linear criteria of chaos-based substitution box designs are worse than algebraic-based designs. It is aimed to overcome this problem with the methods developed throughout the thesis study. As a result of the thesis, four different algorithms have been developed and it has been shown that non-linearity of chaos-based substitution boxes can be improved. These results show that chaos-based substitution boxes can be used successfully in a wide range of applications from block cipher algorithms to key generators, image cipher algorithms to summary functions.