  Erasure codes are widely used in today's storage systems to cope with
failures. Most of them use the finite field arithmetic. In this paper, we
propose an implementation and a coding speed evaluation of an original method
called PYRIT (PolYnomial RIng Transform) to perform operations between elements
of a finite field into a bigger ring by using fast transforms between these two
structures. Working in such a ring is much easier than working in a finite
field. Firstly, it reduces the coding complexity by design. Secondly, it allows
simple but efficient \texttt{xor}-based implementations by unrolling the
operations thanks to the properties of the ring structure. We evaluate this
proposition for Maximum Distance Separable erasure codes and we show that our
method has better performances than common codes. Compared to the best known
implementations, the coding speeds are increased by a factor varying from $1.5$
to $2$.
