This work uses the RLWE-encryption scheme to construct a novel and efficient two-round post-quantum protocol for a private equality test(PET) between two parties. The basic idea of this protocol is that the private key holder can successfully decrypt a ciphertext only when the associated correct public key pair is used for encryption. In the protocol, only half of the public key pair will be published, while two parties will encode their private message to the other half of the public key pair. Leveraging this approach, we expand the protocol into two separate post-quantum two-round 1-out-of-2 Oblivious Transfer (OT) protocols. While prior OT schemes based on Public Key Encryption have significant communication overhead, our protocols provide novel and efficient frameworks for constructing OT from RLWE encryption. Additionally, our protocols are proven to be secure in a semi-honest adversary model, reflecting their robustness for practical post-quantum security applications. Our PET protocol is significantly more efficient than alternatives based on RLWE homomorphic encryption.