Design of cyclotomic Fast Fourier Transform architecture over Galois field for 15 point DFT

The Fast Fourier Transform can be determined in Complex field and Galois field. The paper suggests the architecture 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 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. In this paper the hardware design and implementation of Cyclotomic fast Fourier transform architecture over finite field GF(2⁴) is described.