This paper introduces a practical transciphering approach for fully homomorphic encryption (FHE) that allows the client to encrypt data using a symmetric cipher, and the server to perform homomorphic computations on the encrypted data without requiring the client to specify the plaintext space in advance. The key idea is to homomorphically compose bits into an integer, enabling the server to transform the encrypted bits into an FHE ciphertext encrypting an integer with a message space that fits the application's needs. This approach avoids the need for the client to manage multiple FHE-friendly ciphers for different plaintext spaces, which can be computationally and securely expensive. The authors propose a method to homomorphically evaluate a modified version of the FiLIP cipher's decryption, allowing the server to transform each bit of the encrypted data into an FHE ciphertext encrypting a bit scaled by a corresponding power of 2. This enables the server to homomorphically compose these encrypted bits into an integer, which can then be used for further homomorphic computations. The method is implemented using the FINAL FHE scheme and demonstrates that it is faster and more adaptable to different use cases compared to existing transciphering techniques. The paper also discusses the challenges of using fixed plaintext spaces in FHE-friendly ciphers, which can limit the versatility of the computations. The proposed approach addresses these challenges by allowing the server to dynamically adjust the message space based on the application's requirements, without requiring the client to manage multiple keys or setups. The authors analyze the noise growth in homomorphic operations and show that their method achieves a bounded error growth, making it suitable for practical applications. They also provide a detailed technical overview of the homomorphic operations used in their approach, including the homomorphic XOR gate modulo p and the homomorphic lifting of a bit to the exponent. These operations are essential for transforming the encrypted bits into an integer ciphertext that can be used for further homomorphic computations. The paper concludes with a proof of correctness and a bound on the error growth for the proposed transciphering protocol.This paper introduces a practical transciphering approach for fully homomorphic encryption (FHE) that allows the client to encrypt data using a symmetric cipher, and the server to perform homomorphic computations on the encrypted data without requiring the client to specify the plaintext space in advance. The key idea is to homomorphically compose bits into an integer, enabling the server to transform the encrypted bits into an FHE ciphertext encrypting an integer with a message space that fits the application's needs. This approach avoids the need for the client to manage multiple FHE-friendly ciphers for different plaintext spaces, which can be computationally and securely expensive. The authors propose a method to homomorphically evaluate a modified version of the FiLIP cipher's decryption, allowing the server to transform each bit of the encrypted data into an FHE ciphertext encrypting a bit scaled by a corresponding power of 2. This enables the server to homomorphically compose these encrypted bits into an integer, which can then be used for further homomorphic computations. The method is implemented using the FINAL FHE scheme and demonstrates that it is faster and more adaptable to different use cases compared to existing transciphering techniques. The paper also discusses the challenges of using fixed plaintext spaces in FHE-friendly ciphers, which can limit the versatility of the computations. The proposed approach addresses these challenges by allowing the server to dynamically adjust the message space based on the application's requirements, without requiring the client to manage multiple keys or setups. The authors analyze the noise growth in homomorphic operations and show that their method achieves a bounded error growth, making it suitable for practical applications. They also provide a detailed technical overview of the homomorphic operations used in their approach, including the homomorphic XOR gate modulo p and the homomorphic lifting of a bit to the exponent. These operations are essential for transforming the encrypted bits into an integer ciphertext that can be used for further homomorphic computations. The paper concludes with a proof of correctness and a bound on the error growth for the proposed transciphering protocol.