The principal ideal (PIP) is the problem of deciding whether a given number field and, if it is, finding generator. Solving PIP applies to solving major computational tasks in theory. It also connected search approximate short vectors so-called lattices which crucial cryptography. In this paper, we present novel application norm relations utilize information from subfields solve fields degree l...

Many cryptographic schemes have been established based on the hardness of lattice problems. For the asymptotic efficiency, ideal lattices in the ring of cyclotomic integers are suggested to be used in most such schemes. On the other hand in computational algebraic number theory one of the main problem is the principal ideal problem (PIP). Its goal is to find a generator of any principal ideal i...