Applied study on cryptographic functions for algorithms used in communications security protocols

Abstract

Communications security is one of the most important fields to take into account when designing a system that manages information, especially when implementing such a system for the military, no matter which branch, Navy, Air Force or Army. One important field when talking about information security in general is cryptology and within cryptology linear and nonlinear Boolean functions and maps are essential, important building blocks. They are used in the design of several block and stream ciphers. The study of cryptographic properties of these functions does not only help cryptanalysis but also plays an important role in the design of cryptographic algorithms that resist well against various cryptographic attacks. Linear and differential cryptanalysis of block ciphers is mainly based on determining and exploiting linear combinations of their components. The most useful mathematical tool for studying linearity of Boolean functions is the Walsh (or Hadamard) transform. This can be regarded as a size-2 discrete Fourier transform. Another method for determining linear combinations of cipher components is that of finding and solving linear systems of equations. This article reflects the authors’ effort to shed some light on this field.