The c-Differential-Linear Connectivity Table of Vectorial Boolean Functions.

Area of Science:

• Coding Theory
• Cryptography
• Information Theory

Background:

• Vectorial Boolean functions are crucial in cryptography and coding theory.
• Existing security analysis tools include DDT, BCT, and DLCT.
• Recent extensions like c-DDT and c-BCT have been proposed.

Purpose of the Study:

• To introduce and analyze extended concepts for vectorial Boolean function security.
• To propose the c-Walsh transform, c-autocorrelation, and c-Differential-Linear Connectivity Table (c-DLCT).
• To investigate the c-DLCT for the inverse vectorial Boolean function.

Main Methods:

• Development of novel cryptographic analysis concepts and tables.
• Theoretical analysis of the properties of these new functions.
• Examination of the c-DLCT for specific important cases, like the inverse function.

Main Results:

• Introduction of the c-Walsh transform, c-autocorrelation, and c-DLCT.
• Characterization of the optimal properties of these novel functions.
• Detailed description of the c-DLCT for the inverse vectorial Boolean function.

Conclusions:

• The proposed extended concepts offer deeper insights into vectorial Boolean function security.
• The findings provide a foundation for designing more secure cryptographic components.
• New avenues for research in linear code design based on these cryptographic insights are opened.