The paper introduces a novel transciphering technique for Fully Homomorphic Encryption (FHE) that allows for practical secure outsourced computation without relying on a fixed plaintext space. The approach, called "transciphering" or Hybrid Homomorphic Encryption (HHE), involves encrypting data using a block or stream cipher and then homomorphically decrypting it using an FHE scheme. This method reduces the ciphertext expansion, making it more suitable for real-world applications where data size is a significant concern. The main contribution of the paper is a method to compose bits into an integer homomorphically using the FiLIP cipher. The client encrypts each bit of the input data separately using FiLIP, which is designed to have a ciphertext expansion close to one. The server then homomorphically transforms these encrypted bits into FHE ciphertexts and composes them into an integer, depending on the target application's precision requirements. The paper discusses the technical details of the transciphering process, including the setup phase and the online phase. It also provides a detailed algorithm for the transciphering protocol and analyzes the correctness and noise growth of the output ciphertexts. Experimental results using the FINAL FHE scheme demonstrate the efficiency and practicality of the proposed approach, showing significantly lower running times compared to other transciphering methods and achieving better performance in terms of communication cost and ciphertext size. The paper concludes by comparing the proposed transciphering technique with other methods, highlighting its advantages in terms of versatility and efficiency, especially for applications with varying plaintext spaces.The paper introduces a novel transciphering technique for Fully Homomorphic Encryption (FHE) that allows for practical secure outsourced computation without relying on a fixed plaintext space. The approach, called "transciphering" or Hybrid Homomorphic Encryption (HHE), involves encrypting data using a block or stream cipher and then homomorphically decrypting it using an FHE scheme. This method reduces the ciphertext expansion, making it more suitable for real-world applications where data size is a significant concern. The main contribution of the paper is a method to compose bits into an integer homomorphically using the FiLIP cipher. The client encrypts each bit of the input data separately using FiLIP, which is designed to have a ciphertext expansion close to one. The server then homomorphically transforms these encrypted bits into FHE ciphertexts and composes them into an integer, depending on the target application's precision requirements. The paper discusses the technical details of the transciphering process, including the setup phase and the online phase. It also provides a detailed algorithm for the transciphering protocol and analyzes the correctness and noise growth of the output ciphertexts. Experimental results using the FINAL FHE scheme demonstrate the efficiency and practicality of the proposed approach, showing significantly lower running times compared to other transciphering methods and achieving better performance in terms of communication cost and ciphertext size. The paper concludes by comparing the proposed transciphering technique with other methods, highlighting its advantages in terms of versatility and efficiency, especially for applications with varying plaintext spaces.