In recent years, the use of cloud computing has become widespread, and homomorphic encryption, which allows data stored in the cloud to be processed with encryption, has attracted much attention. The Ring-LWE problem has attracted attention as a postquantum problem it can be used to construct homomorphic encryption. It is important to analyze the security of Ring-LWE problem because the security of the Ring-LWE problem is directly related to the security of cryptography based on it. The Ring-LWE problem is a problem on the ring of integers of an algebraic number field. A method to reduce the search area of this problem by mapping the ring of integers to a small finite field has been proposed. Furthermore, a method to improve the attack when the relative order of the modulus in the algebraic number field is 2 has been proposed. In this paper, we extend the improved attack for the case of relative order 2 to the case of even relative order greater than or equal to 2. Furthermore, we improve the attack by mapping finite field to prime field and using only appropriate samples for the attack.