Finding Generators of Ideals in Non-Cyclic Number Fields by Using Norm Relations

We present a pre-quantum subfield attack of PIP in a non-cyclic fields with pre-processing by using the norm relation. This algorithm reduce the PIP from the original number field to its low dimensional subfields, hence it plays an effect on lattice reduction. At first we describe a new method to find the norm relation. Then we analyse the time complexity of the algorithm. This algorithm can be put in good use in some
$(l_{1},\ l_{2},\ \ldots l_{s})$
-type number fields.