Convolution using a conjugate symmetry property for number theoretic transforms over rings of regular integers

In a recent paper, Dubois and Venetsanopoulos [7] have derived a method for convolving sequences over a ring S, using number theoretic transforms (NTT's) over an extension ring R of S. Until now, their assumptions have only been verified for the special case that R is an extension field of S. This paper examines their assumptions for the very general class of rings of regular integers, a class of rings that was introduced by the authors in [5]. In this paper, we also present an algorithm for the synthesis of rings suitable for number theoretic transforms and with low computational complexity.