Finite fields are widely used in numerous fields like computer algebra, cryptography
or error code correcting. It is then important to be able to deal with them efficiently.
The approach we will present here is to use floating-point arithmetic with which computations
can be done efficiently. The main concern is then to deal with rounding errors that can
appear during the computation. To solve this problem, we use error-free
transformations (EFT). Using theses EFT on recent processors (with an FMA), we show
that it is possible to deal with high finite fields. We will present two different
methods for the computation of dot product.
This is a joint work with Jérémy Jean.