Fast polynomial arithmetic in homomorphic encryption with cyclo-multiquadratic fields

This work provides refined polynomial upper bounds for the condition number of the transformation between RLWE/PLWE for cyclotomic number fields with up to 6 primes dividing the conductor. We also provide exact expressions of the condition number for any cyclotomic field, but under what we call the twisted power basis. Finally, from a more practical perspective, we discuss the advantages and limitations of cyclotomic fields to have fast polynomial arithmetic within homomorphic encryption, for which we also study the RLWE/PLWE equivalence of a concrete non-cyclotomic family of number fields. We think this family could be of particular interest due to its arithmetic efficiency properties.