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## 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 $𝕂$ 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.