Weights Of Boolean Kth Monomial Rotation Symmetric Functions

People proved how rotation symmetric Boolean functions can be efficiently used in a cryptographic hash function many years ago. Since then, rotation symmetric functions have proven to be very useful in a few fields of cryptography. Owing to the significance of these functions in cryptography, many scholars began to study their properties in many aspects. But the progress has been quite slow. The most basic properties of Boolean functions are their truth table, weights and nonlinearity. Therefore, in studying these properties, it would be very helpful to reduce the necessary computations as much as possible, both in practice and in theory.This paper studies Boolean kth monomial rotation symmetric functions. Here expanded an algorithm for finding a recursion for the truth table of any kth rotation symmetric Boolean function generated by a monomial, as well as a homogeneous recursion for its weight. When the number of variables increases, this method dramatically reduces the computational complexity of a problem. At the same time, we generalized a method of studying the structure of the functions. The algorithm makes some computations practically accessible that were previously entirely unfeasible.