The functional bootstrapping scheme plays a significant role in Fully Homomorphic Encryption(FHE). In the original TFHE/FHEW scheme, the functional bootstrapping procedure only works in power-of-two cyclotomic ring. With the development of FHE, it no longer meets the needs of practical application, especially in the field of research for SIMD mode of bootstrapping procedure. It has been a promising field how to extend TFHE/FHEW functional bootstrapping scheme to a general cyclotomic ring. In this paper, we make a comprehensive analysis of the structure of functions with period M. We give the constraint to be satisfied by the function which could be evaluated homomorphically by one BlindRotations procedure in three equivalent forms. The class of such functions is named by M-constraint functions in this paper. besides, we find that each function with period M can be decomposed into the sum of a sequence of d-constraint functions where d|M. We extend TFHE functional bootstrapping scheme to general cyclotomic rings based on the analysis above.