A unified framework for substitution box design based on information theory

The design of new block cryptosystems is an important area in cryptography and becomes more so as the confidence in some of the current cryptographic algorithms declines due to technological advances. Substitution boxes (S-boxes) are an important component in the design of many block cryptosystems. This thesis focuses on developing an integrated design framework for the creation of new S-boxes based on information theoretic ideas.;We introduce the concepts of the static and dynamic views of an S-box and use these abstractions to define the information theoretic properties of an Ideal S-box. We then use the properties of an Ideal S-box to create a new comprehensive set of S-box design criteria. Many of the previously proposed design criteria are integrated into the new information theoretic framework. We demonstrate the need for each design criterion in practical cryptosystems and show that a cryptosystem using Ideal S-boxes will be immune to the differential attack. The new criteria are used to analyze the S-boxes of DES and draw some new conclusions about their construction. We demonstrate that the proposed framework is practical by using it to create new S-boxes for DES-like and other types of cryptosystems.