Abstract: Described are techniques for a method for calculating a fully homomorphically encrypted output value of a function of a transformer-based AI-module, dependent on a fully homomorphically encrypted input value of the function, the function representing a non-linear function to be approximated by the function. The method comprises providing fully homomorphically encrypted precomputed terms which are independent from the input value. The method further comprises calculating the output value of the function, using the transformer-based AI-Module, dependent on the precomputed terms and on polynomials. A respective polynomial depends on a difference between the input value and a center value associated to the respective polynomial. The associated center value indicates a center point at which the respective polynomial is centered and the associated center value differs from polynomial to polynomial.