Finding Normal Integral Bases of Cyclic Number Fields of Prime Degree

Abstract

Let L be a cyclic number field of prime degree p. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that an integral basisΓ for L is known. We reduce our problem to the problem of finding the generator of a principal ideal in thep th cyclotomic field. © 2000 Academic Press.