  This paper deals with circulant matrices. It is shown that a circulant matrix
can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity
without making use of an FFT algorithm. With our algorithm we achieve a speedup
of a factor of about 2.25 for the multiplication of two polynomials with
integer coefficients compared to multiplication by an FFT algorithm. Moreover
this paper discusses multiplication of large integers as further application.
