## Section: New Results

### Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries

In [15] we present new results for efficient arithmetic operations in a number field $\mathbb{K}$ represented by successive extensions. These results are based on multi-modular and evaluation–interpolation techniques. We show how to use intrinsic symmetries in order to increase the efficiency of these techniques. Applications to splitting fields of univariate polynomials are presented.