Cryptographic functions have important applications in the research of cryptography. This paper describes a more suitable approach to prove the nonexistence of some cryptographic functions, and obtain some new results, which support the conjecture that there are no homogeneous rotation symmetric bent functions of algebraic degree > 2. Also, homogeneous degree 2 rotation symmetric bent functions are characterizedby using GCD of polynomials. The method presented in this paper can also be used to characterize the existence of other forms of bent functions.