On the conjecture about the nonexistence of rotation symmetric bent functions
This addresses a theoretical problem in cryptography and Boolean function theory, but it is incremental as it builds on prior conjectures and methods.
The paper tackles the problem of proving the nonexistence of homogeneous rotation symmetric bent functions, resulting in new findings that support the conjecture that such functions do not exist for degrees greater than 2, and characterizes degree 2 functions using GCD of polynomials.
In this paper, we describe a different approach to the proof of the nonexistence of homogeneous rotation symmetric bent functions. As a result, we obtain some new results which support the conjecture made in this journal, i.e., there are no homogeneous rotation symmetric bent functions of degree >2. Also we characterize homogeneous degree 2 rotation symmetric bent functions by using GCD of polynomials.