Currently, as one of the candidates for the post-quantum cryptography, there are cryptographies based on the difficulty of solving mathematical problems lattices. Among the lattice problems, the Ring-LWE is a problem of solving a multiple liner system with errors over the ring of integers in an algebraic number
field. Related to the Ring-LWE problem, the algebraic properties of its defining field are expected to reduce the size of ciphertexts and keys. However, in fact, it is difficult to choose an algebraic number field that can construct an efficient encryption based on the Ring-LWE problem freely. The reason is that it is difficult to find the defining polynomial of the defining field over the rational number field. Also, even if we know the representation of bases of the integer ring, it is not always possible to perform multiplication effeciently. Therefore, it is significant to increase the kinds of algebraic number fields that can construct efficient encryption based on the Ring-LWE problem. In this research, we proposed the possibility of using the fixed fields of subgroups of the Galois group of a cyclotomic field. In addition, we performed a comparative experiment using the existing method and the proposed the proposed method, and showed the usefulness of this research.