In recent years, Semantic Communication (SemCom), which aims to achieve efficient and reliable transmission of meaning between agents, has garnered significant attention from both academia and industry. To ensure the security of communication systems, encryption techniques are employed to safeguard confidentiality and integrity. However, traditional cryptography-based encryption algorithms encounter obstacles when applied to SemCom. Motivated by this, this paper explores the feasibility of applying homomorphic encryption to SemCom. Initially, we review the encryption algorithms utilized in mobile communication systems and analyze the challenges associated with their application to SemCom. Subsequently, we employ scale-invariant feature transform to demonstrate that semantic features can be preserved in homomorphic encrypted ciphertext. Based on this finding, we propose a task-oriented SemCom scheme secured through homomorphic encryption. We design the privacy preserved deep joint source-channel coding (JSCC) encoder and decoder, and the frequency of key updates can be adjusted according to service requirements without compromising transmission performance. Simulation results validate that, when compared to plaintext images, the proposed scheme can achieve almost the same classification accuracy performance when dealing with homomorphic ciphertext images. Furthermore, we provide potential future research directions for homomorphic encrypted SemCom.