The design approach for fast computation of fourier transform over a finite field

The Fast Fourier Transform can be determined in Complex field and Galois field. The paper suggests the algorithm for finding Fast Fourier Transform over a Galois field. This method uses the advantage of cyclotomic decomposition. Basically decomposition of the original polynomial into a sum of linearized polynomial is done and then evaluated at a set of basis points. The idea of architecture is also proposed. The architecture is composed of two main units principle unit and additional unit. This Fast Fourier Transform methods can be capably used in implementations of discrete Fourier transforms over finite field, which have extensive applications in cryptography and error control codes. The method is becoming popular because of its low computational complexity.