Efficient calculation of cyclic convolution by means of fast Fourier transform in a finite field

Over a finite field a transformation similar to discrete Fourier transform can be defined that can be efficiently implemented using fast algorithms. One of the main applications of such transformation is calculation of convolutions of long sequences of integers by means of integer arithmetic. In this paper a method of implementation of two vectors convolution using modular arithmetic with Proth-type modulo is considered. A device performing cyclic convolution using modular arithmetic was created. A comparison with binary analogues was carried out.