This paper presents a novel method of calculating the rotated template set operators. Having defined a rotated ring model, the author proposes an efficient way of executing the rotated template set operators, which uses the rotated ring model and a fast cyclic convolution algorithm from the Number Theoretic Transform. The author showns that a class of rotated templates can be modelled as rotated rings and computed efficiently by the fast algorithm with much fewer multiplies than the normal approach in the worse cases.